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An economic analysis of alternative management strategies for the spiny lobster industry

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Title:
An economic analysis of alternative management strategies for the spiny lobster industry
Creator:
Williams, Joel Sylvan, 1947-
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Language:
English
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xiii, 164 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Cost estimates ( jstor )
Fees ( jstor )
Fisheries ( jstor )
Fishers ( jstor )
Fishing ( jstor )
Lobsters ( jstor )
Marginal products ( jstor )
Mathematical variables ( jstor )
Sales rebates ( jstor )
Total costs ( jstor )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Lobster fisheries -- Economic aspects -- Florida ( lcsh )
Spiny lobsters -- Florida ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 159-163.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Joel Sylvan Williams.

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AN ECONUONIC ANALYSIS OF Ai.EPNATIV
MANAGEMENT STRAEGI '4S FOR TIHE SPINY LOBSTER INDOS'TRY











by

JOEL SYLVAN WILLIAMIS











A DISSERT'iION PRESENTED TO TlE CRAD]A (.OUN*CL.
CF THE UN.IVfERSITY OF FLiOREDA
IN PARTIAL FULIL.INENT OF THE .rQUI.rEN[S FOi 'tll
DEGREE OF DOCTOR Or ' 811 OSO'iHY













1976















ACKNOWLEDGMENT S


My debt of gratil:ude for assistance during my graduate career exceeds my ability to provide acknowledgment. I trust that my many unrecognized benefactors will assume my great appreciation and thanks.

The greatest debt should be acknowledged first. fine is to my wife, Susan, for her moral support, understanding, and patience.

Fred Prochaska served as Chairman of my Superqisory Committee,

academic and professional advisor, and friend. Joe Havlicek provided substantial guidance during stages of the final draft. W. W. McPherson provided a wellspring of experience from which I have freely drawn as a student and as author of this dissertation. J.,in Cato provided a comprrehensive critique that greatly improved the overall quality of the final draft. Jim Heaney and Gary Lynne also provided constructive criticism of the study. For these contributions, as well as many left unmentionea, I am grateful and wish to thank the members of my Supervisory Committee.

I wish to thank Leo Polopolus, Chairman of the Food and Resource Economics Departmeat of the UJniversity of filorida, for provide ing, f.nancial assistance during y gradutIe career. in addition, I wish to extend my Ppr ciatiorn to Lloyd Jolhsor: an!d Pt.e Maley of: NfiS and to membPers of t:ie S:t-m.erlanxI K.y Chapter of O.F.2. for their contributions during' the survey of spiny Iobscer captA!ns.

i amra1 .i7c :tindebted to Mis. Sandy Wate Er,: Ms. Carolyn: Almeter [or their: indi.pcs.abie help in the volumii:ous typing tas.k and numero:ts



iI









clerical activities performed during this study. Ms. Jennie Lou Carroll arduously accomplished the transformation of this dissertation from a longhand manuscript into its present form. For this feat she has earned my gratitude and admiration for her considerable ability and perseverance.



















































iii
















TABLE OF CONTENTS


ACKNOWLEDGMENTS . ........ . . . . . . . ................ ii

LIST OF TABLES . .............. . . . ...... . .. viii

LIST OF FIGURES . .......... . ... . . . . . . . . . . xi

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii


CHAPTER

I INTRODUCTION . ............... .. ... 1

Objectives ................ . . . . . . 6

Scope . . . . . . . . . . . . . . . . . . . . . . . 7

II LITERATULiRE REVIEW . . . . . ............. -

Introduction . ............... ... . .. 9

Spiny Lobster Research . ............... 9

General Bioeccomic Management Research ....... . 14 Bioeconomic Lobster Research . ............ 18

Regulatory Management Programs for Florida
Spiny Lobster . .................. . 20

III THEORETICAL MODEL ................ . . . . 2

Biological Theory of a Fishery . ........... 25

Traditional Economic Production Model . ....... 30 Bi.economic Model .. ................ . 32

Sumrnary . . .. . . . . . . . . . . . . . . . ... . 35








iv









TABLE OF CONTENTS (continued)


CHAPTER

IV EMPIRICAL MODEL AND DATA . ............... 36

Definitions . . . . . . . . . . . . . . . . . . . . . 36

Bioeconomic Analysis . .... ........... . . 37

Firm Analysis . ... . .. . .. .. .. .. . .. . 41

Maximum Economic Analysis (MEY) . . . . . . . . . . . 45

Study Area and Data Acquisition . . . . . . . . . . . 47

Sample Selection and Size . . . . . . . . . . . . . 49

Survey Technique . . . . . . . . . . . . . . . . 52

V ANALYSIS OF RESULTS . ............... . . . 54

Bioeconomic Model . . . . . . . . . . . . . . . . . . 54

Maximum Sustainable Yield (MSY) Estimate . . . . . . 59 Value Marginal Product Analysis . . . . . . .... . 62

Analysis of Firm Harxest Function del . . . . . .. 67

Firm Harvest Model . . . . . . . . . . . . . . . . 67

Estimated Parameters . . . . . . . . . . . . . . . 71

Traps per firms (xl) . . . . . . . . . . . . . . 72

Rounds per week (x2) . . . .......... .. .. .73

Weeks fished per season (x3) . . . . . . . . . . 75 Craft size (x ) . . . . . . . . . . . . . . . . 78

Optimum Resource Allocation of the Firm . . . . . . 80

VI THE MANAGEMENT MODEL . . . . . . . . . . . . . . . . . . 87

Maximum Economic Yield for the Industry . . . . . . . 87

Evaluating MEY . . . . . . . . . . . . . . . . . . 89

Policy Implications . . . . . . . . . . . . . . .. . 3



V









TABLE OF CONTENTS (continued)


CHAPTER

VI Discrete Analysis of Alternative Combinations
of Firms and Traps Per Firm . ............ 94

Alternative Number of Firms in the Industry . . . . 94 Alternative Levels of Traps Per Firm . .... . . 97 Evaluation of Estimates . ............ . 97

Isoquant Analysis . ................ . 99

Movement Along An Isoquant . ........... 101

Ridgelines . ...... ........ .... . 105

Summary of Management Tools . ........... 106

Analysis of Traditional Management Programs . .... 106

Licensing Traps . ................. 107

Licensing Firms ...... . ... . . . . . . . . . . 110

Landing Quotas . ................. 113

A Suggested Alternative: Harvest Rebate Program . . . 115

Configuration of the Harvest Rebate Program . . . . 116

Hypothetical Example and Analysis of
Harvest Rebate Program . ............. 120

Assumptions ........ . ... . . . . . . 121

Number of traps per firm at 700 . ....... 122 Number of traps per firm at 618 and 500 . . .. 123 Number of traps per firm ar 429 . ....... 125 Number of traps per firm at 350 and 200 . . .. 125 Overall sumnmary of analysis (Table 17) ..... 125 Breakeven Criterion ......... . . . . . . . 126

VII SALARY ANI) CONCLUSIONS . ........ . . .. . . . . . 131




vi









TABLE OF CONTENTS (continued)


APPENDIX

A Spiny lobster landings and dollar value, Florida and
U.S., 1952-73, economic study of Florida spiny lobster
industry . . . . . . . . . . . . . . . . . . . . . . . ...141

B Spiny lobster capital and labor inputs, Florida west
coast, 1952-72, economic study of Florida spiny lobster
industry . . . . . . . . . . . . . . . . . . . . . . . ...142

C Input/Output relationships, Florida west coast, 1952-72,
economic study of Florida spiny lobster industry ... . .143

D Cross-sectional Data Computations ..... ...... .144

E Spiny lobster landings and dollar values, Florida east
and west coasts, and Monroe County, 1952-73, economic
study of Florida spiny lobster industry ........ .146

F Spiny lobster landings in Florida ports caught in
foreign waters, 1964-73, economic study of Florida
spiny lobster industry .................. .147

G Total product and marginal product equations for firm
harvest function model . . . . . . . . . . . . . . . .148

H Comparison of spiny lobster production practices by
craft length for firms sampled, Florida Keys, 1963-74
season, economic study of Florida spiny lobster
industry . . . . . . . . . . . . . . . . . . . . . . . .. .149

I Table 18 computations ................. . .150

J Spiny Lobster Firm Survey Questionnaire . . . . . . . . .152

K Spiny lobster inputs, outputs, and values, Monroe
County, Florida, 1963-73, economic study of Florida
spiny lobster industry . ................. 157

L Data used to estimate firm harvest function, 1973-74
survey of spiny lobster captains, economic study of
Florida spiny lobster industry ...... . ..... ...158


REFERENCES .... .............. . ... . . . . . . .59

BIOGRAPHI!CAL SKETCH .................. .... . 164





vii















LIST OF TABLES


Table Page

1 Industry harvest function variables in theoretical
model and reduced form, economic study of Florida
spiny lobster industry 39

2 Stratified population of boats and vessels, defined
as firms, economic study of Florida spiny lobster
industry 51

3 Stratified sample of boats and vessels, defined as
firms, economic study of Florida spiny lobster
industry 51

4 Estimated levels of maximum landings (Q) for given
levels of traps per firm (XI), number of firms (X2), and seasonal water temperature (X3), economic study
of Florida spiny lobster industry 60

5 Regression statistics for the cross-sectional firm
harvest function model, economic study of Florida
spiny lobster industry 70

6 Marginal products for various lengths of set periods,
economic study of Florida spiny lobster fishery 74

7 Weekly landings expected for given dates within the
spiny lobster season, economic study of Florida spiny
lobster industry 76

8 Marginal products of craft size (x4) for sample sizes
observed, economic study of Florida spiny lobster
industry 79

9 Optimum levels of trap usage per firm and resulting
levels of profits, total revenue, total cost, and
landings given trap cost, economic study of Florida
spiny lobster industry 83

10 Optimum levels of adjustment factors (x2, x3, and xi) resulting levels of profits, total revenue, total cost, and landings per firm, economic study ef Florida spiny
lobster industry 84




vi.li









LIST OF TABLES (continued)


Table Page

11 Maximum number of firms (X2*), landings, revenues, and costs for industry profit maximization given desired management levels of traps per firm (X1),
economic study of Florida spiny lobster industry 92

12 Analysis of alternative levels for number of firms
(X2) assuming traps per firm (XI) equals 700, mean
seasonal water temperature (X3) equals 77.5910F, and ex-vessel price per pound (P ) equals $1.08,
economic study of Florida spiny lobster industry 96

13 Analysis of alternative levels for number of traps per firm (X1) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals
77.5910F, and ex-vessel price per pound (Py) equals
$1.08, economic study of Florida spiny lobster
industry 98

14 Marginal rate of technical substitutions (MRTSX ) of traps per firm (X1) for number of firms
(X1) holding traps per firm constant at 700,
economic study of Florida spiny lobster industry 103

15 Analysis of alternative levels for number of traps per firm (XI) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals 77.5910F, ex-vessel price per pound (P ) equals
$1.08, and trap license fee equals $1.00 per trap,
economic study of Florida spiny lobster industry 108

16 Analysis of alternative levels for number of firms
(X2) assuming traps per firm (X]) equals 700, mean
seasonal water temperature (X3) equals 77.5910F, exvessel price per pound equals $1.08, and license fee
per firm equals $1,000, economic study of Florida
spiny lobster industry 111

17 Median and mean spiny lobster landings per trap for sample of firms classified according to number of
traps per firm (X1), economic study of Florida
spiny lobster industry 117

18 Median and mean spiny lobster landings per trap for sample of firms classified according to number of
traps per firm (XI), economic study of Florida spiny
lobster industry 128




ix









LIST OF TABLES (continued)


Table

19 Analysis of landings per trap required to breakeven under the harvest rebate program for alternative levels of traps per firm (XI), economic study of
Florida spiny lobster industry 129
















































x















LIST OF FIGURES


Figure Page

1 Growth curve for a fishery stock 26

2 Number of mature progeny as a function of parent
population levels 28

3 Equilibrium harvest as a function of parent population 30

4 Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to landings 34

5 Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to number of firms 41

6 The Florida spiny lobster fishery 48

7 Observed and predicted volume of spiny lobster
landings, 1963-73 for Monroe County, Florida 56

8 Spiny lobster bioeconomic industry harvest function 61

9 Value marginal product of traps per firm (XI) divided
by the maximum number of firms observed (399) in the
industry in 1973 64

10 Value marginal product of firms (X2) 66

11 Firm harvest functions with respect to effort measured as gear (XI), fishing intensity (X2, X3), firm size (XLt),
and adjusted for fishing grounds (X5, X6) 69

12 Marginal product curve for spiny lobster craft size
(t Px) 80

13 Spiny lobster harvest isoquants and ridge lines defining expansion paths where returns equal total costs, (assuming ex-vessel price per pound (P ) equals $1.08, industry
total cost equals $1,876 plus $11.55 per trap per firm
(XI), and mean seasonal water temperature (X3) equals
77.591F) 102
















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Pcquirements for the Degree of Doctor of Philosophy

AN ECONOMIC ANALYSIS OF ALTERNATIVE MANAGEMENT STRATEGIES FO70 THE SPINY LOBSTER INDUSTRY

by

Joel Sylvan Williams

December, 1976


Chairman: Fred J. Prochaska
Major Department: Food and Resource Economics


Florida's spiny lobster fishery has achieved tremendous growth in landings during the past two decades. However, the growth of inputs into the fishery has lately increased at a considerably higher rate, resulting in declining catch rates, over investment and a potential for over exploitation of the spiny lobster stock.

This dissertaticn was designed to evaluate the current level of resource use, determine the maximum sustainable and economic yield levels, and analyze alternative lobster management programs. Bioeco :nAc and firm harvest analytical models were developed and estmated. Maximum sustainable yield was estimated to be approximately seven million pounds while maximum economic yield was estimated to be 5.8 million pounds annually, slightly above current levels. Optimum levels cf input use are 215 lcbate: fir. each fishing 795 traps. Shser leve.,s require a 47 perccn : rcduction in the number of firms in the in0lstr with no reductcon in number of traps fished.









Political and social considerations often make the maximum economic yield not a feasible management alternative. In this case an analysis of input (firm, and trap) substitution was completed and presented for alternative input and output levels. Resulting cost, revenue and profit levels were determined for alternative program levels.

Specific management programs considered in the analysis include licensing, quotas and a harvest rebate program. For each program, maximum yield levels, costs, revenues and profits were determined. For the harvest rebate program alternative levels of administrative costs and related sources of revenue were analyzed.




Chairman
































xiii
















CHAPTER I

INTRODUCTION


The Florida spiny lobster (Panulirus argu) is produced in the

warmer ocea' waters and is easily distinguished from its northern, coldwater cousin, the American lobster (Homarus americanus) by its lack of claws and relatively smaller size. Over the past forty years the Florida spiny lobster has developed from a casual food source of the habitants of the Florida Keys to an important commercial food resource. Second only to shrimp as a seafood, spiny lobster landings in Florida

exceeded 11 million pounds in 1973 with an estimated retail value of over 4C million dollar-. Over 1,100 licensed fishermen landed lobsters in 19 0. Florida represents approximately 98 percent of U.S. spiny lobscer landings (Appendix A). The Florida spiny lobster fishery is expeiecing an ever increasing number of problems that require ilmmediate attEntion by the legislature, regulatory agencies, and researchers.

One of the basic underlying forces creating problems within this fishery is 'conru Er demand given the relatively fixed supply of stock. Spiny lobster is now a preferred item in seafood markets and restaurants. An increasing tendency for U.S. consumers to eat in restaurants has created uowar: shifts in demand. The demand for spiny lobster is highly incoi:mc lacstic but inelastic with respect to its own-price elasticity of dci:andd (llen [1]). U.S. consumption currently accounts for approximately SO p,,rcent of the world spiny lob!stcrr production. Canada and



1




2



Europe account for approximately 10 to 15 percent while the small amount remaining is domestically consumed in the producing countries.

Between 50 to 60 countries produce and export spiny lobster tails to the U.S. The top four spiny lobster producing countries are Australia, Cuba, South Africa, and New Zealand. These countries produce approximately 65 percent of world landings while fifth ranked U.S. produces about 7 percent of the world total (U.S. Department of Commerce [48]).

Retail prices have increased substantially in recent years. In

1960 the retail price of spiny lobster tails was $1.50 per pound and the U.S. consumed 53 percent of the world production. By the 1970s U.S. consumption increased to over 80 percent of the world production of spiny lobsters. The 1970 retail price for spiny lobster tails was $3.43 per pound and reached $5.40 per pond in 1972. Currently, spiny lobster

tails are retailcd for as high as $9.27 per -ound.1 In roughly tn years retail price doubled and has almost tripled in th:e last five years.

Rising retail prices have encouraged increased exploitation of spiny lobster stocks. This has resulted in an increasing number of biological and economic problems in the Florida spiny lobster fishery. Soilv of these problems could also be credited to the nature of this industry or fishery. Unlike most economic en terprises the spiny lobster fishe ry is a common property natural resource which is characterized by unlimited entry. As such, the fishery generates excess use of inputs to iaximri.e catch wi.thout any economic incentive to conserve or replenish thei resource for future use.


January: 24, 1975, average retail ptice for three seafood retailers in Cinesville, Florida.





3



The spiny lobster fishery is currently subject to some limited foim of fishing regulation. Conservation directed regulations presently prohibit stripping eggs from females, specify trap dimensions so small undersized lobsters are released, close areas believed to be nursery areas, and specify a season which protects recruitment.

An investigation of the possible excessive use of resources in the industry gives reason for concern.1 In the last 20 years the number of firms, defined as the sum of vessels and boats, increased from 54 in 1952 to 394 in 1972 (Council of Economic Advisors [18], Bell [3]). Number of vessels began increasing at an increasing rate around 1965. Simultaneously capital and labor inputs began to increase. From 1965 to 1972 firm members increased over 80 percent. Use of other inputs since 1965 also increased substantially: Number of traps by 242 percent; number of traps per firm by 60 percent; and number of fishermen by 101 percent (Appendix B, U.S. Department of Commerce [49], [501).

Landings increased from 956,000 pounds in 1952 to over 5 million pounds in 1972. However, since 1965 landings have increased only 4.4 million pounds or 16 percent. Pounds landed per trap averaged 213 pounds in 1952, 49 pounds in 1965, and 20 pounds in 1972. From 1965 to 1972 dollars generated per trap decreased from $28 to $21; annual landings per firm decreased from 20,301 pounds to 13,069 pounds; and




1Until 1975 approximately 50 percent of spiny lobster landings in Florida were harvested from the Florida domestic fishery. The remaining 50 percent were harvested in foreign water fisheries, primarily the Bahamian fishery. Approximately 10D percent of these landings were reported as Florida "'east coast" statistics.
In 1975 the Bahamian government closed its fishery to U.S. fishermen. Due to this U.S. landings were down approximately 25 percent in 1975 compared to 1974 landings.









annual total revenue per firm increased 23 ptcent from $11,423 to $14,003 (Appendix C).

During the 1952-72 period when total revenue increased at a decreased rate, costs of inputs used in the fishery steadily increased due to upward shifts in the demand for inputs. But, in recent years, input costs skyrocketed primarily due to rapidly increasing inflation which has been shown by changes in the consumer price index (CPI) for major inputs used in this fishery (Barnhart [2)). The CPI (1967 base) for petroleum products was 108.9 in 1972 and increased 109.5 points between 1973 and 1974. For wood products, the CPI was 144.3 in 1972 and increased 11.8 points between 1973 and 1974. CPI representing engines used in the fishery was 117.9 in 1972 and increased 31.0 points from 1972 to 1974.

Infornatioci oil costs of inputs and returns for the 1973-74. spiny lobster season was acquired in a survey of captains of spiny lobster boats and vessels.1 In 1959 the average spiny lobster craft ranged from fourteen-foot wooden skiffs that were either rowed or powered by an outboard motor, to larger wooden-hulled craft ranging in length from 26 to 36 feet and powered by 125 to 150 horsepower gasoline and diesel engines. Average cost of the skiff began at $150 while average cost of the engine and hull of larger craft ranged from $3,000 to $10,000. From the 1974 survey, average cost of only the engine was $8,257. This was based on a range from $500 for a 40 h.p. outboard motor to an excess of $60,000 for




The survey of 25 captains was completed in October, 1974. The random sample was stratified according to length of boat and area of fishery with confidence levels of 90 percent. Individual strata were weighted a,:corlding to landings frcm these areas and size of boats in these areas.





5



diesel engines approaching 500 h.p. Average cost of the hull for this sample was $8,748. The range was from $400 for a sixteen-foor fiberglass skiff to over $20,000 for wooden and fiberglass vessels with a maximum length of 55 feet.

In 1959 a wooden lath trap complete with buoy and line cost an

average of $6.00 each. In 1974 average cost of materials alone for a wooden lath trap was $11.00. The cost was a few dollars more if the trap was used for deep-water fishing. Average cost of fishbeads used for bait was 5 cents per pound in 1959 compared with 11 cents per pound in 1973. The prime interest rate increased from approximately 6 percent in 1959 to 9.5 percent in 1973 signaling a substantial increase in the cost of capital.

Spiny lobster captains surveyed in 1974 claimed the costs of petroleum based products, such as polyethlene rope, styrofoam buoys and fuel, were triple 1973 prices. Engine costs were increasing at the rate of 15 to 25 percent per year. Fiberglass boats were increasing in cost at similar rates. Because of the shortage of cypress lumber the cost of cypress lath for trap construction was also increasing. In addition, the introduction of sonar and other fish locating devices, hydraulic pullers, and other harvesting improvements, has substantially increased the capital investment which the commercial lobster fisherman must make to remain competitive. The increase in number of traps used per fisherman represents a substantial increase in investment.

One problem that appears to exist in the fishery is a resource allocation problem . . . "over-investment" in capital (gear and craft) and labor (fishermen). Too many inputs are employed to produce a relatively fixed supply of spiny lobsters. This is reflected in the substantial









increases in inputs (traps, vessels, and gross tonnage) compared with the increase in landings. The broad over-investment problem of the fishery begins with the fishermen. Capital and labor investments increase at the fishermen's level due to (1) a struggle to overcome a severe price-cost squeeze; and (2) interdependencies in the production function creating negative externalities to the fishing firm or producer.

As a consequence of this increaseing level of effort, a second

problem of the fishery that may be occurring is one of "over-exploitation" of the fishery stock. Decreasing stock levels can cause serious long-term damage to the fishery and welfare of fishermen.


Objectives

The overall problem is defined as one of resource allocation, The general objective is focused upon the determination of an optimal allocation of resources for selected price, cost, and fishery management alternatives. Optimal allocation may entail protecting the stock from reaching a level beyond recovery as well as regulating economic factors of the fishery.

The specific objectives are

(1) To identify the major factors affecting the quantity of

spiny lobster harvested, and to estimate the harvest

function of the Florida spiny lobster fishery;

(2) To evaluate the potential substitution between specific

resources used to harvest spiny lobster in Florida;

(3) To determine an optimal combination of inputs for the

Florida spiny lobster fishery; and





7



(4) To evaluate the impact of selected management programs

on resource allocation in the fishery and on the optimum

combination of inputs used by firms. Specific programs

considered are limiting licensing of firms and traps,

establishing landings quotas, and a harvest rebate program.

The results of this study will provide a basis for establishing guidelines for managing the Florida spiny lobster fishery. The focus is on the analysis of management strategies which might help reduce the cost and difficulties of regulating effort. In addition, study results can be conceivably viewed as a case study applicable, at least in approach, to other marine resource allocation problems. Finally, individual fishermen may use the results of the production analysis as a basis for both long and short-run decision making.


Scope

Spiny lobsters landed in Florida are harvested from the domestic

Florida spiny lobster fishery and foreign water spiny lobster fisheries. More than 95 percent of spiny lobster landings harvested from the domestic fishery are landed in Monroe County. These landings comprise approximately 50 percent or more in past years of all spiny lobster landed in Florida. Without the Bahamian fishery, landings from Monroe County make up over 90 percent of U.S. spiny lobster landings. Consequently, although the scope of this study is defined as the Florida spiny lobster fishery, the data for the empirical analysis are delineated as that of the Florida Keys or Monroe County, Florida.



The majority approximatelyy 90%) of foreign water landings were lost as a result of the 1975 closing of the Bahamian fishery.









A literature review of theoretical and/or applied bioeconomic research is presented in the next chapter. The theoretical model is presented in Chapter III while the data and empirical model are presented in Chapter IV. Results of the analyses and their practical interpretation are given in Chapter V. Four management alternatives and resulting policy implications are reviewed in Chapter VI. Chapter VII, the final chapter, includes a summary, conclusions, and suggestions for further research.















CHAPTER II

LITERATURE REVIEW


Introduction

Previous empirical spiny lobster (Panulirus argus) research is

summarized and some major theoretical and empirical bioeconomic management studies are capsuled in this chapter. This information is the minimum necessary to understand biological and psychological relationships considered in the design of management programs. Furthermore, existing laws must be understood before alternative programs can be considered and thus they are reviewed in this chapter. None of the empirical bioeconomic studies consider the spiny lobster fishery, but they do include analyses of management strategies which may be applicable to the spiny lobster fishery. Several recent bioeconomic studies such as Bromley [8], Fullenbaum [26],and Van Meir [53] contain extensive arnd thorough reviews of past theoretical and empirical studies. This chapter contains a review of selected theoretical concepts and empirical studies directly applicable to this study. The reader is referred to the more extensive reviews where appropriate.


Spiny Lobster Research

There is a lack of economic analysis concerned with management of the spiny lobster (Panulirus argus). Several empirical studies deal primarily with biological characteristics, environmental conditions and physical production analysis of fishing craft, gear, and techniques.


9





10



Scientific research in the U.S. on spiny lobster began as early as 191.6 (Allen [1], Barnhart [2], and Crawford [191), but it was not until 1944 that an investigation of the Florida spiny lobster fishery was conducted by the Marine Laboratory at the University of Miami (Smith [42, 43]). A review of studies since 1948 provides considerable information that may be useful in explaining the behavior of landings (Smith [42, 43], Cope [17], Butler and Pease [9], Dees [22], Chislett and Yesaki [15], and Ting [46]).

Smith's publication in 1958 [43] provides a most complete discussion of the Florida spiny lobster fishery including taxonomy, biological cultivation, fishing gear and methods, dollar value and importance of the fishery, and state regulations of the fishery. Several other studies published since 1958, including Butler and Pease [9], Chislett and Yesaki [15], Cope [17], and Ting [46], updated some Cof Smith's find s.

Butler and Pease [9], rand Chislett and Yesaki [15] determined the feasibility of developing spiny lobster fisheries off coasts of Panama and Jamaica, respectively. Although they primarily compared types of gear and fishing techniques, some biological and environmental observations were documented. Cope [17] analyzed alternative gear and fishing techniques in the Florida fishery. Finally, a recent study by Ting [46] analyzed the potenucal for spiny lobster cultivation from a physical production standpoint but alluded to economic implications. The information obtained from these studies is briefly summarized.

The Florida spinj lobster (Panulirus argus) is one of 30 species distributed nearly world wide in tropical and sub-tropical waters. They differ from the Northern cold-water lobster (Homardie family) in that they lack claws and have long antennae for sensing food and danger.









They are smaller and have numerous spines covering their back (cape) for protection against many natural enemies. The average legal size landed in Florida weighs approximately one and a quarter pounds and is 10 inches long, although in 1968 maximum lengths of 17 inches and weights in excess of 10 pounds were not infrequent (Dees [22]).

Spiny lobsters generally feed at night on a wide variety of foods, primarily small crustaceans. They also forage. During the day they hide in rocks, coral,and other marine growth but are known to resort to cannibalism when crowded. Growth is primarily dependent upon the environment. As body weight of the spiny lobster increases the hard outer shell is shedded. This shedding of the shell is called molting and occurs several times throughout the life cycle. The body weight increases approximately 5 percent during each molting stage. Although younger icbsters molt more frequently, it takes approximately five years for them to reach legal size.

Female spiny lobsters do not begin reproducing until they reach a length of eight to nine inches. An eight-inch spiny lobster can produce approximately 50,000 eggs compared with 500,000 eggs produced by a 14inch lobster. In Florida, mating occurs February through June in shallow waters. The eggs are hatched in deeper water three weeks later. It takes the young larvae three to six months to conform to the shape of the adult lobster. At this stage the young lobster drops to the ocean floor and is approximately 7/8 inch long. The mortality rate from hatching to this stage is hypothesized to be over 99 percent.

Water temperature, food supply, reproduction and weather Influence the. migration of spinay loo users. Usually migration occurs between deep an shallow wat,r but sometimes emigration is north in the summer and





12



south in the winter. Extremely cold weather, extended periods of unseasonable weather, or still, calm weather can cause lobsters to migrate to deeper water (Smith [43]). This is contrary to the findings of Butler and Pease [9) that spiny lobsters prefer placid waters. Smith [43] also reported that spiny lobsters are believed to have migrated over 1,000 miles but generally do not migrate over five miles.

No evidence is available to indicate whether they migrate over deep straits, but it is believed that long movements lead to a gradual mixing which, over time, results in an equalization of the stock. Consequently, the biological stock of a geographical ~rea, characterized by a deep water perimeter, should be treated as a single unit. As such, changes in any part of the fishery will eventually affect the whole fishery. Conversely, as part of the fishery becomes "fished o,,t" it will reple .ish itseIf if left alone for a period of ti i-e. Soie idencec sugSggt that maxi:num exploitation of most spiny lobster stocks in the Caribbean have been reached, with the possible exception of the southern edge of the Caribbean Sea (Idyll [3]).

The major portion of commercial lobster landings in Florida are

harvested at depths of less than 50 feet using wooden traps. At least 80 percent of annual landings are harvested in the first half of the season which lasts from August 1 through March 31. Generally, one to three fishermen per craft fish 200 to 1,000 traps. Length of the craft range from 16 to 55 feet. They usually travel less than 25 miles and return the same day. Based on the theory that a trap offers protection it can be fished without bait. However, freshly baited traps are preferred. There appears to be no difference in landings between traps baited with cowhide, which lasts longer, and traps baited with fish.





13



New traps catch better after being in the water at least five days. Landings are higher if traps are lifted every two to three days rather than over four days. Traps settling on the bottom collect silt and foreign matter, which past experiences indicate reduce landings if the exterior of the trap is not brushed every few days. Landings are higher for traps set next to reefs or forage areas than for traps set on reefs and in flat clean areas.

Butler and Pease [9] found that bottom temperature and salinity

were correlated with the presence of lobsters. In a range of 680-850F more lobsters were landed than in higher bottom temperatures of the 830-850F range. Also in a total salinity range of 280-340/00 landings were higher than at the 310-320/00 salinity level. Lobsters will not feed when water temperatures are near freezing and will migrate from locations with colder water temperaturps to warmer water locations. A study on surface and subsurface water temperature shows that the majority of the fishing area in the Florida spiny lobster fishe:ry Js isothermal year round (Robinson [39]). This means that in depths of less than 50 feet the difference in the bottom temperature and surface temperature is insignificant.

Aquaculture of spiny lobster is possible but currently not economically feasible because they require very exacting care and specialized

conditions (Ting [46]). Spiny lobsters require clean, oxygenated water with a balanced temperature and the individual lobsters kept separated. To accomplish this requires a large volume of space and labor and thus a large capital investment. The growth period from juvenile to marketable size is appro:i lately t:hrce years in an artifically crated cnvironnent, ccinpare,' with five to seven years in the natural environment.





14



General Biceconomic Management Research

Researchers have been contemplating bioeconomic management of the fisheries at least as far back as the 1920's as evidenced by Rich's [38] work on the Gulf of Maine fishing grounds in 1929 and Russell's [40] work in 1931 titled "Some Theoretical Considerations on the 'Overfishing' Problem." In 1943, Ilerrington [29] considered alternative methods of fishing management and Nesbitt [34] investigated the biological and economic problems in management of fisheries.

Major theoretical contributions emerged in the early 1950's in the writings of Schaefer [41], Gordon [28], Christy and Scott [16], Crutchfield and Zellner [21], and Turvey [47]. These antecedents of the past twenty years are generally credited with developing the fundamental bioeconomic theory. Their differences can be briefly analyzed on the basis of four management objectives. Schaefer's biological approach was concerned with maximizing production from the sea in a strictly physical production framework. The others were oriented toward the maximum economic yield concept but differed to a slight degree. Gordon, and Scott and Christy actually defined a monopoly situation as optimum with an objective of maximum economic yield above costs. Crutchfield and Zellner's approach was the same but excluded returns due to monopolistic practices in order to maintain consistency with federal regulations on monopolies. Turvey also maximized economic yield excluding returns to monopolistic practices but, in addition, attempted to maximize consumer surplus.

More recent research deals with the empirical application of the above concepts and with some refinements to the theory. Lampe [32] used a dynamic model of the Cobweb form to investigate the interrela-









tionships between biological and economic aspects of commercial fisheries. Carlson [11, 12] developed a theoretical yield function by integrating an economic production function with a biological growth model and distinguished between firm and industry or aggregate production functions. Van Mair [53] demonstrated that landings will exceed maximum sustainable yield (MSY) as a result of excess effort generated in a competitive economic system such as the George's bank haddock fishery. To curtail effort at MSY he suggested free entry with landings quotas, monopolistic exploitation implying the maximization of net revenue above labor and capital cost, or quotas placed on fishing effort. A problem inherent in all of these alternatives is defining a unit of effort. Smith [44] developed a dynamic competitive model of the interaction between the number of firms (investment) in a fishery and the population 3f an exploited fish species, which included crowding externalities.

Bell's [3, 4, 5, 6] empirical research dealt primarily with

firm analysis and illustrates the use of econometric techniques in marine research. He attempted to determine what factors influence the rate of return and what impact their variability has on the industry. A major criticism of his findings is that the estimates will not withstand rigorous statistical tests primarily because of model misspecification and lack of a randomly selected sample.

After an extensive review of literature the major revelation can best be explained by a quote from the concluding statement of the abstract of a dissertation written in 1969 (Bromley [8, p. 36]) -- "The presence of considerable uncertainty in a fishery, and the lack of perfect knowledge on the part of biologists and economists, renders in sweeping conclusions of traditional writers in fishery, and their subsequent





16



policy recommendations, particular vulnerable to incrudelity." Since the time of this statement considerable documentation of theoretical and empirical marine research has accumulated, yet one has to agree that the quoted statement can still carry conviction today. This is not to imply that the research is not useful, but rather that a need still exists for data, authenticated tools,and methodologies for research applicable to the bioeconomic management of today's marine resources. Many of the works to date develop interesting statistical investigations while others hinge on highly abstract optimization criteria.

The major reason that the success achieved in traditional agricultural research, particularly in estimating production functions, has not been achieved in marine economics research is partly due to basic underlying problems that have yet to be solved in analyzing marine resources. These problems relate to the techniques, assumptions, and empirical limitations (i.e., lack of biological, environmental and economic data) and are characteristic of the common property nature of bioeconomic resources. The very few exceptions to this lack of success have occurred with species existing in what may be termed "closed systems," in which the researcher had considerable control over the individual variables. Very often the problems are related to inadequate specification of the theoretical bioeconomic structure of the fishery, lack of appropriate biological and economic data, lack of multidisciplinary research cooperation in designing models oriented towards a systems approach, misunderstanding the needs of counterparts in a multidisciplinary team, and( often defining objectives dissonant to the researchers or policy makers.





17



This is evidenced in a recent publication edited by Sokoloski [45] in which several researchers addressed the issues and problems encoun-tered when dealing with research directed toward managing marine resources. Sokoloski defined a critical area of marine resources research to be the measurement of the gap between the "optimum" management solution for a given fishery and current management arrangements. To emphasize the relative lack of success with this objective, he listed several critical issues that have been complicating current research efforts. They were characterized as empirical and conceptual in nature and multidisciplinary in scope. One conclusion drawn after reviewing this publication is the fact that substantial uncertainty exists with respect to the reliability of results in marine economics research and accordingly the proposed management programs. Many of these problems need to be solved before sound management programs can be developed for many of the species. Determination of optimal solutions will require considerable time, effort, and financial resources.

Pontecorvo [35] pointed out in his work with Pacific red salmon that the costs of improving information may exceed the benefits. This should be taken into account when deciding the value of increasing the sophistication of models designed for direct applicability in managing a particular fishery. Consequently, when a researcher is given the task of developing management alternatives for a currently existing real problem as in the case of the Florida spiny lobster fishery, he is often not allowed the luxury of exhausting all methodological possibilities in his investigation due to the reasons previously discussed. Because of this he uses what resources are available, such as traditionally acceptable or validated theories in economics and marine biology. For





18



example, such resources include production functions exhibiting diminishing marginal rates of return, downward sloping demand for a commodity, and the bio-mass or population of a fish species which is in part dependent upon its environment and thus exhibiting a semi-sphere-shaped yield curve.

Given lack of data, particularly biological data, and lack of precise models which lend themselves to rigorous statistical testing, it would appear that a reasonable criterion for model building would be "Occum's razor," -- the simpler the better. This may not be too unreasonable since statistical testing may be more efficient, the results are timely, completion of the project remains within the limits of the budget, and it is questionable whether more sophisticated models requiring more resources would improve the results. In light of these observations, the approach for this project presented in the next chapter does not attempt to improve the theory or apply overly-sophisticated empirical models or models requiring inapplicable assumptions or data which are not available.



Bioeconomic Lobster Research

Bioeconomic research related to the Northern American Lobster

fishery, Bell, 1970 [3]; Bell and Fullenbaum, 1972 [7]; Dow, Bell and Harriman, 1973 [24]; Huq, 1973 [30]; and DeWolf, 1974 [23] were considered in the development of the present models. The latter two publications by Bell are extensions of his early work on the American lobster industry. All three of Bell's publications analyze impacts of different types of management programs through changes in a general equilibrium model. In Bell's first publication [31. a liearly





19



additive structural production function is specified as an average product function. From the estimation a simple parabolic yield function was derived. Number of traps was the measure of a unit of effort. Bell and Fullenbaum [7] developed a production function which was derived from an integration of a logistic growth function, an industry production function and an industry revenue relationship. The model includes a biomass variable over time, environmental constraints, total industry cost, a technology variable and other parameters to be estimated, such as catching power of a unit of effort. Variables for which data are lacking are either assumed away or are assumed to be represented by some proxy and ultimately the whole model collapses into a simple second degree polynomial equation presented in Bell's earlier publications. The model appears to be considering all the necessary components of a total bioeconomic systemri when, in fact, Bell does not have direct measures of all independent variables in his first model. Dow, Bell, and Harriman [24] utilized this model and incorporated undated data for the bioeconomic model and som biological information on the Northern American lobster such as history, Tmigration, disease, etc.

Huq [30j analyzed labor mobility and social transfer costs of three representative lobster fishing coi unities in Maine. Hug, concluded that substantial immobility and limited employment opportunities exist in the fishery and thus the human element must be seriously considered in designing any management program.

Fiall':, D'Wolf [23] investigated Canada's lobster fishery. Biological and economic bases of fi3hery regulations were examined. Also examined :ere the economic effects of regulations on the fishery, such as total idtstry value, total landings, and net return per fisherman.





20



No quantitative statistical model was used and efficiency (net returns) was the criterion for evaluation. The conclusions were that previous regulations of limiting effort have led to economic inefficiencies but that economic conditions outside the fishery have had an even greater impact on its present structure.


Regulatory Management Programs
For Florida Spiny Lobster'

Florida laws are designed to regulate the spiny lobster fishing

industry for the purposes of insuring and maintaining the highest possible production of lobster, or in other words, the maximum sustainable yield. These laws have basically represented biological goals and attitudes, but in recent years the need for economic considerations in management schemes has been recognized by all concerned. During the nearly 4C years prior to 1965, Florida management was mainly concerned with the conservation of the spiny lobster population through controls on minimum size and fishing seasons. These regulations are still of importance in the total management program. Although most of the earlier regulations have been revised and new regulations added since 1965, gear regulations were first emphasized in the 1965 legislation. Perhaps more important in the 1965 legislation was the emphasis on the need for effective policing policies through the use of marketing by permit number, and gear and boat identification for surveillance.




1The regulations discussed here are as of March 31, 1976. A more detailed discussion of the present laws and historical pattern of Florida spiny lobster regulations can be found in a review by Prochaska and Baarda [36].





21



A $50 permit is required for all persons intending to catch more than 24 lobsters per day. The permit must be carried on the person at all times and can be suspended or permanently revoked upon the arrest and conviction of a permit holder for violation of any of the lobster fishing laws.

Florida's management program includes two regulations pertaining to the gear and craft. The first is that all gear (traps and buoys) and the craft must be permanently identified by the permit number and/or color code assigned to the fisherman upon receipt of his permit. The figures on the craft must be at least three inches high to permit easy identification from the air. The second regulation pertains to the specific gear requirements. Wooden traps, ice cans, drums, and other similar devices may be used provided that they are not equipped with grains, spears, grabs, hooks, or similar devices. The traps must be designed out of wooden slats not to exceed 3 x 2 x 2 feet or the cubic equivalent. Only the sides of the traps may be reinforced with 16 gauge, one inch poultry wire.

Any gear used to capture lobsters must be marked by a buoy. Up to twenty traps can be attached to a trot-line, and the line is marked at each end by the attachment of a flag buoy. Buoys used must be of sufficient stCength and buoyancy to remain continuously afloat. Any device not conformilne to the specifications listed, or not carrying a valid permit number, way be seized and destroyed by enforcement officials. It is unlawful to interfere with anyone's traps or markers without the owner's permission.

ln 1953 the closed season was set between April 15 and August. 15, and in 1955 it was placed at its present interval of March 31 to





22



August 1. The 1965 act provided that traps may be placed in the water and baited ten days prior to the open season and must be removed within five days after the closing of the season, though no lobsters can be taken during the closed season.

Three types of restrictions on the condition of lobster caught in Florida exist at present. These deal with minimum size, separation of head and tail, and egg-bearing females. The minimum size allowed is a three-inch carapace of a 5 1/2 inch tail, though the tail measurement is inapplicable if the tail is separated from the body. If head and tail are separated under required legal permit, the tail must have a minimum length of six inches. The 1965 act prohibited the catching of eggbearing female lobsters, and those found in traps are to be returned alive to the ocean. Stripping eggs from them is also prohibited. That same act required a special permit if the separation of head and tail was to be done before landing the lobster. A permit for such separation may be granted if the operation is so far from land that it is not practical to keep the lobsters alive until landing them.

Historically, in 1929 the first size restriction was enacted, the minimum being one pound avoirdupois. In 1953 the minimum was redefined to be a lobster with a tail measuring six inches. The 1953 act redefined the minimum size by tail and carapace measurement, with a minimum carapace measurementt of three inches and tail measurement of 5 1/2 inches. Methods of measurement were also given. Finally, a 1969 act allowed a six-inch minimum on tails separated under special permit.

Presently, no legislation has provided for limited traps per firm,

limited licenses, landings quotas or taxes on landings to restrict the over employment of labor and capital in tle fishery. Groups with common





23



interests in and recent concern for the welfare of the fishery have expressed a need for information describing the benefits and consequences of such regulation.
















CHAPTER III

THEORETICAL MODEL


This study dealt with the management of a living marine resource and the consequences of management strategies on the resources and its uses. The production of living marine resources differs from traditional production processes in that it requires the capture of a wild animal without the more traditional production, cultivation and/or manufacturing of the products involved. Biological behavior of the animal, changes in its environment and economic factors of production (labor, capital, management, and land) influence the success of capture or amount of product entering the market.l This relationship between the product, defined as landings, and the above factors or variables that influence landings, was defined as a harvest function. The analyses presented in this study were based on the estimated harvest function for the Florida spiny lobster resource. The theoretical framework of a fishery harvest function is presented in this chapter. A biological growth model of a fishery was combined with the influence of ma. in the- form of fishing effort and termed a bioeconomic model. Finally the procedure in which the bioeconomic model. was used to satisfy the remaining objectives of the study is presented.




Assuming all that is captured enters the market.





24





25



Biological Thcry of a Fishery

The harvest function, or yield function, (Equation 1) form a biological point of view represents the level of biomass (or stock of fish) that can be harvested. The equilibrium level of biomass is that which can be harvested without changing or damaging the parent stock. The yield function may be expressed as

YB = f(Stock) (1) where,

YB = the amount of biomass available for harvest, and

Stock = the total biomass of fish.

This system is exclusive of the influence of man. Biological theory states that the change in the stock of a fishery will follow an S-shaped curve as shown in Figure 1. This theory has been supported by findings from population studies of deer and Inscets. Additional support is presented in a recent study by Cates and Norton [27] who estimated an Sshaped curve for the yellowtail flounder fishery of New England. An

S-shaped curve suggests that the population increases (a) slowly at lower levels, limited by the reproductive capabilities of smaller numbers and the smaller number of fish that are actually growing: (b) rapidly in the intermediate range, as larger numbers of fish produce more eggs than can survive and food supplies are adequate; and finally,

(C) slowly at higher levels where pressure from limited food supplies impedes the population growth in an equilibrium manner and deaths just offset births. Therefore, stock is a function of the biological


Tle material in this section was primarily developed from the
followLing references: Uromley [8], Carlson [10], Christy and Scott [16], Cheung [141., and Prochasha and B ,ada [36].





26







Biological Maxfimum






o Yield Function
4O







0 Time


Figure 1. Growth curve for a fishery stock



relationship between the parent population, the mature progeny, and the influence of the environment on this biological process. The following implicit relationship is suggested:

S = g(S1, S2, S3) (2) where

S = stock

S1 = popaation of mature progeny,

iS2 = parent population, and

S-. = environmental attributes affecting the biological

behavior of the stock.

T!he popa]i i~on cf mature progeny (SI) is a function of the parent population (So) and the ,nviionpent (S-). Alo determining the level of iraturrec pronrCny is ti:e number of young or recruitment; the rate of growth






27



of the progeny; and the natural mortality rate due to di:ases or due to changes in the biological process. Parent population is a function , of the environment, growth rates, and mortality rates. The response of

the parent population to the variables may differ for variot ; levels of parent stock.

Numerous environmental factors significantly affect the biological process. Significant factors are the food supply, predators other than man and hydrographic characteristics including water temperat:-urc, salinity, bottom conditions, currents and atmosphere conditions.

The relation between the number of mature offspring and the parent population may be derived from these basic biological relationships The recruitment of matu-e progeny is of particular interest since that is an important policy variable used in developing management: schemes that .wil aintc. some e;uiiib rium level of catch. The rela tnsh.p bctw#,7een i.ature progeny and parent population is a function of the same variable affecting growth. At very low parent population levels recruitment is low because the number of spawners is small. As the parent population increases, the level of recruitment increases. After some population level is reached, recruitment levels decline for reasons due to thc. environilanti and biology of the species, such as unhealthy fish stocks, an inadequ:ate ecological niche, declining growth rates, increasing tIortality races, severe competition for food, and adverse hydrographic conditicrs. Thus, at some intermediate population level, the

ability of spawners to recruit progeny into the standing population is a raximU . AL low population levels, growth rates are relatively low, but beyond some population le el, the growth rates decline and ai:.ural mortality rates are relatively high.





2 S



RelationsLpEr between the size of the parent population in one time period and the aumnber of mature progeny in the following time period may be summarized as in Figulre 2 (Prochaska 136]). The 45' line, OA, reFresents the level cf a::tue progc.~y Decessary tc maintain the parent population at its present lT'el. That io, OA traces out the number of mature progeny, measured on ,he vertical axis, nece,:sar. to replace the paren:: pc.pulation meaFured on the horizo-ntal axis. The curve, OM, repreS:ents the actual number of mature progeny thac will. be produced by each parent population l.evel. For example, a mature proge-iy of M1, will maintain a parePt population of Pj, but parent population P1 will produce M2 and the total fish stock will increase. This process will continue in nature until the actual production of mature progeny






M2
o M II






, ' o i - - I I



O0 P P1 2 P3
Parent population

Figure 2. Number of mature progeny as a function of parent population
levels





29



just equals that necessary to maintain a stable parent population, at P3 where the lines intersect. At population P2, total production of mature progeny is a maximum, and at P1, the excess of mature progely over that necessary to maintain the parent population is greatest.

The introduction of successful fishing effort while the parent stock is P3, will reduce the parent population since there is no net recruitment with parent stock P3. The reduction of parent stock in the initial time period results in an increase in the production of mature progeny in the following time periods. Increased fishing effort may continue to reduce the parent stock until parent stock, Pi, is reached. Parent stock, PI, will produce the largest marketable surplus defined as equilibrium harvest and represented as M2 - MI in Figure 2. Maximum marketable surplus is not at the parent population level which produces

the maximum mature pr-ognriy (13). If in a-ly time period mere thar: the equilibrium harvest is taken, the parent population will move PO and again the equilibrium in following periods will be reduced. If the level of fishing is that which exactly takes the excess over the needed replacement each season, parent population, P1 will be maintained. This is defined as maximum sustainable yield (MSY).

The equilibrium harvest shown as the area between the mature progeny curve, 0:1, and the replacement line, OA, in Figure 2, may be expressed in Figure 3. Points P0, P1, P2 and P3 correspond with population levels in Figure 2. The maximum sustained yield, YB1' is produced from population P1 which corresponds to P1 in Figure 2. Except at the maximum sustained yield the same equilibrium harvest may be taken at different levels of parent population. For example, equilibrium





30







Maximum Sustainable Yield



P



SY







0 P0 P1 P2 P3
Parent Population

Figure 3. Equilibrium harvest as a
function of parent population




harvest, YB2' may be taken with either parent population PO or P2. MSY occurs at that point of equilibrium harvest curve where its slope is zero.


Traditional Economic Production Model

A production function normally used in economic analysis is defined as the relationship between physical inputs and a resulting level of physical ourput, similar to the biological yield process. The difference occurs in the type of relationship between the inputs and the resulting output. Similarly, theory exists that explains the economic stages of a production process in an economic system.

'rc-dction inputs or factors of production can be defined as units of effort and consist of lend, labor, capital., and management. The





31



production process can be defined as

YE = f(E) (3) E = g(E1, E2, E3, Eq) (4) such that,

YE = f(E1, E2, E3, EL) (5) where,

YE = output as a result of effort,

E = effort = combined unit of inputs, El . . . Eq,

Ei = land,

E2 = labor,

E3 = capital, and

Eq = management.

The assumed objective for firms in the industry is profit maximization. All firms are assumed to operate in a rational economic manner with production occurring under conditions of decreasing returns. The industry is assumed to have an atomistic structure with constant factor prices and independent production processes.

The biological yield function (Equation 1) is actually a physical relationship between the various exogenous biological and environmental attributes and the available fish stock for harvesting. The production function (Equation 3) is a physical relationship between output and exogenous variables representing effort. Biological models of fishery populations without economic considerations are of little value as a tool for developing useful policy for fisheries management. Likewise, an economic model devoid of biological considerations is also of little


The reader is referred to Ferguson [25] or Carlson [13] for a complete presentation of production economics.





32



value. Thus, the integration of biological and economic considerations is needed to accurately estimate the relationship between that levei of product which reaches the market (i.e., pounds landed) and those variables that determine that level of product. This process is necessary to insure that the equilibrium harvest level is both biologically and economically sufficient.


Bioeconomic Model

Variables of the yield function (Equation 1) and the production function (Equation 3) were integrated to form the bioeconomic model or the harvest function:

YE " h(S, E). (6) Substitucing equations (2) and (4) into (6) gives

Y B h(Sl . . . S3, El . . . E4), (7) where,

Y BE is defined as the bioeconomic equilibrium yield.

The biological yield model and the production model provide the basic foundation from which proper management policies are designed. Management policies consider equilibrium harvest (Y ) that does not endanger the parent population (S2) while allowing maximization of harvest (.E ) for a givcn level of inputs. This approach to managing a fishery is known as maintaining maximum sustainable yield (MSY). MSY was previously defined as the greatest equilibrium yield possible without damaging the parent stock and varies in the long-run as a result of effort, biological changes in the stock, and environmental inducements. MSY is an important variable in designing accurate management policies.





33



MSY expresses a physical relationship and has provided the basis for conservation programs of U.S. fisheries with little concern about the economic consequences on the fishermen or society (Sokoloski 145]). In recent years this philosophy of management practices has changed and economics has entered the arena of fishery resource management. Such things as factor prices, product prices, costs, and other pecuniary attributes of the "biceconomic system" must be considered for proper management of a fishery. To many policy makers maximum economic yield (MEY) is now considered the objective of "proper" management as is assumed throughout this dissertation. MEY occurs at a level of landings which are less than those suggested by the MSY criterion and thus requires less fishing pressure.

MEY is defined as that yield where net revenue (NR) is maximized

for the fishery. NtC revecnu for the industry is at a maximum where the greatest positive difference occurs between total revenue (TR) and total cost (TC), as illustrated in Figure 4. MEY occurs where the slopes of the TR curve and TC curve are equal and can be expressed as follows:

8TR 'TC
MEY = - - 2 = 0, (8)
SBE ~BE
where

DTR
-3- represents additional or marginal revenue to the industry
BE
for additional landings, and

BTC
y represents additional or marginal cost to the industry for

additional landings.

Industry total revenue (TR) is derived by multiplying the harvest function (YBE) by ex-vessel price per pound (P). As ex-vessel price





34




TC TR





P











YBE
Landings
Figure 4. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to landings



increases the TR curve shifts up and conversely TR shifts down as exvessel price decreases. Industry total cost (TC) is defined to be a function of the exogeneous variables of the harvest function (YBE) and their related prices. TR and TC may be expressed as

TR = YBE x P (9) TC = h(S,E) (1.0)

One fisherman's harvest function is theoretically interdependent

with all other fishermen's harvest functions. Landings for one fisherman are affected by what other fishermen catch from a given stock. Consequently, as the number of firms in the industry increase, each firm's production function constantly shifts downward while the associated cost functions shift upward. Per unit costs increase for the same amount of effort expended because of fewer landings per unit of





35



effort. Costs per unit of output eventually rise to a level where entry into the industry ceases.

Crutchfield [20, p. 12] identified the consequence of such a situation when he said, ". . . such a market, unregulated, will destroy itself either economically or biologically." Or in Carlson's [11, p. 7] words, "In common property resource, the 'invisible hand' guarantees that the market will arrive at a solution that is suboptimal."


Summary

Biological and economic theory suggests the following bioeconomic harvest model:

YBE = f(Si, S2, S3 El, E2, E3, E4). (11) Major focus of this analysis entailed determining the appropriate input level and subsequent landings where the greatest net revenue is generated to the fishery. Net revenues for various levels of effort such as number of firms in the industry and number of traps were compared. The feasibility of alternatives for limiting effort were assessed by considering the impacts these have on net revenues per firm, number of displaced firms, total revenues to the state from user fees, cost and time of implementation and enforcement of regulations, and expected public acceptability.

Development of the theoretical model for this study has resulted in an examination of the biological theory of a fishery resource and a brief discussion of production theory. Models of these two theoretical frameworks were integrated into a bioeconomic model used to explain the theoretical constructs of management goals, namely MSY and MEY. The empirical model and data analysis are presented in the next chapter.
















CHAPTER IV

EMPIRICAL MODEL AND DATA


The empirical model and estimation procedure are presented in this chapter in three parts. Types of data used are included in the presentation of each structural equation. Delineation of the study area and the method of data acquisition is presented in the final section.

Estimation and theoretical analysis of the industry harvest function are presented in the first part of the chapter. The second part of the analysis is concerned with estimation of a firm harvest function and associated optimum resource allocations for the firm at estimated fishery stock levels. Implicit industry factor prices and costs were derived in the firm analysis. The final part of the analysis involved integrating the results from the industry and firm analyses to estimate maximum economic yield (MEY) for the industry.


Definitions

A few definitions at this point may help clarify relationships within the model. The industry harvest function was estimated using secondary time-series data for 20 years from 1952-71. The firm harvest function was estimated using primary cross-sectional data obtained from a survey conducted in 1974 of 25 full-time spiny lobster fishermen. Capital letters are used to represent variables relating to the industry harvest function, while lower case letters are used to represent variables related to the firm harvest function. The only exception to this 36





37



is P y, which is always used as the ex-vessel product price per pound for the industry and for the firm. Industry landings are represented by Q and firm landings are represented by q. Variables representing inputs into the industry harvest function are X1, X2, and X3. Firm harvest function input variables are xl, x2, x3, x4, x5, and x6. In only one case does a variable from the industry harvest function and the firm harvest function represent a similar measure of inputs, number of traps. X], from time-series data, represents average number of traps per firm in the industry for a given year, while xj, from cross-sectional data, represents the number of traps fished by a given firm. An asterick (*) superimposed on a variable, for example xl*, denotes the variable as an optimum solution and facilitates its identification when substituted in different equations.


Bioeconomic Analysis

Time--series analysis is necessary to determine the direct and indirect effects of increased effort on catch. Resulting effects of the traditional economic production relationships are defined as direct. Indirect effects are the influences on landings from variations in the fish stock due to variations in effort. Time-series analysis is necessary because an analysis for only one point in time will only consider the effect of effort on landings for the given fishery stock in existence at that time. Evaluating effort over time also allows for the consideration of expanding effort on the extensive margin--more firms in the industry.

The Lioeconomic model set forth earlier can be restated as

YBE = h(E1, E2, E3, E4, Si, S2, S3) (12)





38



In the lobster fishery El (land) is not a factor, therefore, El drops out of the theoretical equation. E2 (labor) and E4 (management) are transformed into output in the production process through the fishing traps (the primary type of gear used in Florida). Therefore, X1, traps per firm, is substituted for E2 and E4. The remaining production factor E3 (capital) is represented by both number of traps per firm and number of firms (measured by number of boats and vessels) X2. Thus X2 is substituted for E3. The biological factors population of mature progeny

(S1) and parent population (S2) are not available from secondary data. However both have been shown to be a function of environmental factors,

(S3), in the previous chapter. Water temperature is one of the many variables which can be used to represent the environment. Water temperature however has been shown as a significant factor affecting lobster landings (Bell [3]) and thus was used in this study as a pro:y for S3 and is denoted as X3. Thus with these assumptions and substitutions Equation 12 can be rewritten as

Q = f(X1, X2, X3) (13) Variables in the reduced form equation for the industry harvest function (Equation 13) are compared to variables in the theoretical harvest function (Equation 7) in Table 1.

The reciprocal form of the yield function was selected because it is consistent with current conditions and regulations in the industry. Management regulations such as minimum size limits, gear restrictions, prohibition of egg stripping and a fishing season set after spawning, insures some maximum level of stock. The reciprocal function allows landings to reach a maximum level but does not allow total production





39



Table 1. Industry harvest function variables in theoretical model
and reduced form, economic study of Florida spiny lobster
industry


Variable Variable
In Theoretical Model In Reduced Form

Notation Definition Notation Definition
YBE bioeconomic yield Q total industry landings
El land (area of fishing) -E2 labor X1 traps per firm E3 capital X2 number of firms Eq management X1 traps per firm

S1 population of mature -progeny

S2 parent population -S3 environmental attributes X3 surface water
temperature



to decline with additional fishing effort. In addition, the reciprocal function exhibits diminishing marginal returns which is consistent with the stage of production in which firms are expected to operate. The industry harvest yield function can be expressed in reciprocal form as


Q = a + -1 + -- + 3X3 (14) The industry harvest function is used to determine an estimate of maximum sustainable yield (MSY) to serve as a guideline in developing management programs. Since the reciprocal function only approaches a

maximum, the MSY analysis considers "approximate" or "practical" maxima. These maxima are estimated using various combinations of explanatory





40



variables at reasonable maximum levels within the range of the data to determine a range for MSY.

Maximum economic yield (MEY) for the industry was also determined from the industry harvest function (Equation 14). Total revenue (TR) was computed by multiplying the estimated harvest function (Equation 14) by product price (P y). Py is assumed constant and representative of current prices. P was computed as the current average ex-vessel price per pound.1 Time-series cost data were unavailable. To determine MEY it was necessary to develop an industry cost function from primary data. A cross-sectional survey of spiny lobster firms was used to obtain the necessary data and is presented in a later section. From these data an industry total cost function was developed. Total industry cost (TC) was derived by computing the average total cost per firm (ATC) for the firms in the sample and iithe multiplying ATC per firm by the total nu:ber of firms (N) in the industry. Together, these functions were used

to detcri ine MEY as shown in Figure 5.

Derivation of MEY begins with the determination of the level of

firms2 at which the slopes of the TR and TC curves (Figure 5) are equal. This is determined by equating industry marginal revenue (partial derivative of TR with respect to X2) with industry marginal cost (derivative of TC with respect to X2) and then solving for the number of



IPX uas computed by dividing annual total industry value of landings by' annual total industry landings.


Any input that serves as a policy variable for management purposes is applicable in place of firms. Number of firms is preferred for r-asons to be later discussed in this section.





41


TC

TR
MEY



O *
$4 Y






rI
I

X2
Firms (X2) Figure 5. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to number of firms



firms in the industry which is necessary for industry profit maximization, X2* The optimum number of firms, X2 , is substituted into the industry harvest function to determine Q , defined as EY.


Firm Analysis

The primary purposes of the cross-sectional survey and subsequent firm analyses were to (a) provide cost estimates required to determine MY, (b) determine an optimum allocation of specified inputs for profit


LNotationally the derivation of X2 is a solution of the following equalities:
(a) industry marginal revenue = industry marginal cost,
3TR 3TC
(b) R C and
X2 ax2
SY
(c) Py * X P is price of X2.
y BX2 X2





42



maximization for the firm, and (c) incorporate the analysis of optimum firm input levels into the MEY analysis and related analysis of management alternatives.

The firm harvest function is defined as the physical relationship between landings and various units of effort. Effort may be generally categorized as related to labor, capital, management, and fishing area or location (geographical locations). From Equation 11, the general theoretical harvest function, the typical firm harvest function can be defined as

q = f(el, e2, e3, eq, Sl, S2, s3) (15) where,

q = quantity harvested by the typical firm,

el = attributes of the fishing process related to fishing

area (somewhat similar to land factor input),

e2 = labor,

e3 = capital,

e4= management,

sI = mature progeny,

s2 = parent population, and

s3 = environmental attributes.

Environmental and biological influences within a given area were assumed constant for this analysis, since the data represent the lobster harvesting process at a given period in time. Thus, sl, s2,and s3 were deleted


IStrictly speaking returns to land are to ownershipi" of the resource and has little relevance to geographical location in most instances. Returns to area in fishing is similar to saying a type of soil is better than anther in reference to agricultural production, which has no relationsiJI with "ownership" of tne various soil types.





43



from Equation 15, except that environmental and biological differences among fishing areas were represented by the coefficient for el. The objective of this analysis was to determine differences in el . . . e among firms that influence individual firm landings and thus, production responses to different levels of input use. A detailed summary of definitions and derivations of variables that significantly influence the typical firm harvesting process are presented in Appendix D.

A trap is defined as before to represent the unit of effort through which the traditional factors of production are employed in the production process. Thus traps, xl, was substituted for e2, e3, and eL, in Equation 15. In addition, the intensity at which the trap is fished was included in the model through the inclusion of x2 (number of times

a fisherman pulls his total number of traps in one week) and x3 (the number of weeks fished). These intensity variables adjusted trap use between firms in a cross-sectional survey and in addition represented additional use of traditional production variables such as labor and capital. Variation in firm size and capital investment were included by a proxy variable, x4, defined to be the square footage of the boat or vessel.

Quality of fishing grounds with respect to stock and other environmental attributes is expected to raise or lower firm harvest and therefore, were entered into the model using dummy variables. Fishing grounds were broadly segregated into three different areas defined by the sample stratification. The upper Keys region (x5) was defined as the 44-miles from Key Largo to Lower Matecumbe Key. The lower Keys region (x) was defined as that 31-miles from Big Pine Key to Key West. The middle keys region, the base region, was defined as the 37-mile






44



stretch between the above two areas. If a one is entered for x5 and a

zero for x6 the firm was fishing in the upper Keys region and viceversa for a firm fishing in the lower Keys region. If both x5 and x6 are zeros, the firm was fishing in the middle Keys region. These dummy variables allow the intercept or position of the harvest function to vary for different fishing areas.

Underlying bioeconomic theory for the firm does not specify curvilinearity in the firm harvest function since the stock of lobsters, or sustainable yield, is assumed constant for a given period in time. Thus the Cobb-Douglas functional form was selected which allows for either increasing, constant, or decreasing returns.l An additional reason for the selection of the Cobb-Douglas form was that it requires fewer degrees of freedom to derive the interactive effect among the independent variables. The summnary of these considerations and the final model for estimation is represented by Equation 16.


s - 1 82 83 4 (5 P6
q = ax1 x2 x3 xfy x5 x6 (16) where,

q = estimated landings (harvest) for the typical firm,

x: =- number of traps,

x2 = average number of times a fisherman pulls his total

number of traps in one week,

x3 = number of weeks fished, x4 = measure of craft size,



A detailed discussion of the Cobb-Douglas function is presented in Carlson [13].





45



x5 = dummy variable representing upper Keys region (one

represents upper Keys and zero represents middle Keys),

xg = dummy variable representing lower Keys region (one

represents lower Keys and zero represents middle Keys),

and

a, B1, * * * 6 are parameters to be estimated.

Optimum levels of inputs were determine at the point of profit maximization for the typical firm. The same computational procedure used in the time-series analysis was used to derive TR and TC for the firm and optimal level of input use.


Maximum Economic Analysis (MEY)

The final part of the estimation procedure involved integrating information obtained in the cross-sectional analysis into the timeseries model which estimated the industry harvest function. This was then used to estimate maximum economic yield (MEY).

A recognized short-coming of the industry harvest function model is that the assumption of homogeneity among fishing firms or "fishing effort" does not prevail in the real world. Firms differ in fishing power due to such factors as size of craft, fishing intensity, and amount of gear. However, note that Equation 16 representing the firm harvest function and based on cross-sectional data adjusted for these differences. Size of craft was accounted for by x4, fishing intensity by x2 and x3, and amount of gear by x1. With these adjustments it was

assumed that the firms were homogeneous. The dummy variables, x5 and x6, further influenced this conclusion.





46



Estimation of the effect of traps on landings for the typical firm using the firm harvest function took into consideration influences of craft size, (x4), fishing intensity (x2 and x3) and differences in fishing grounds (x5 and x6). With this estimate an analysis of optimum number of traps (xI ) was made. Then holding trap levels at this economic optimum an estimate of the optimum number of firms was possible. Thus, xl from the cross-sectional firm analysis was substituted for X1 in the time-series industry harvest function model to estimate industry landings assuming firms are employing the optimum number of traps. Equivalent notational form for the industry harvest function now became

^ ^ 1 B2 ^
Q = a + + + 83X3 (17)
X X2
xl

where,

Q = estimated industry landings,

xl = optimal number of traps per firm estimated from firm

analysis,

X2 = number of firms in the industry,

X3 = mean seasonal surface water temperature,

a, 01, 82, 83 are parameters to be estimated.

MEY with respect to number of firms occurs at that point less than MSY where the difference between total industry revenue and total industry cost are maximized. After deriving industry total revenue and total cost curves, their slopes were equated and the solution for the optimal number of firms (X2 ) was determined. X2 occurred when industry marginal revenue equals industry marginal cost of an additional firm. X2 was then substituted into the industry harvest function (Equation 17)





47


and the solution of Q was equal to MEY with respect to X2 for a given level of X1, X2, and X3, expressed as follows:

- ^ 01 62
MEY = Q = a + - + -- +33 (18) xl X2*

Thus, traps per firm, estimated from the firm analysis was used as the constant exogenous variable to characterize firms in the industry harvest function model. Ordinarily least squares regression techniques were used to estimate the parameters.


Study Area and Data Acquisition

The Florida spiny lobster fishery primarily consists of the area known as the Florida Keys region. This region is made up of two counties (Dade and Monroe) and is located in the southernmost portion of the state. Spiny lobsters are landed in small amounts in other counties, mostly Pinellas, but these are usually caught in foreign waters.

Monroe County was selected for the study area for several reasons. A trend analysis of the Florida spiny lobster fishery was conducted using secondary data for 1952-71 (Williams and Prochaska [54]). From this analysis the Florida landings were estimated to be approximately 95 percent of total U.S. landings in recent years. Approximately 50-60 percent in the last five years of Florida landings were caught in foreign waters (Appendix E). The majority (over 90 percent of these foreign lobsters) were landed in Dade County. Of the remaining 40-50 percent of total Florida landings (which came from domestic waters) approximately 80-90 percent were landed in Monroe County (Appendix F). Monroe County is geographically located in the middle of the domestic spiny lobster

fishery (Figure 6). A final consideration is that the impact of confining





48












DADE
COUNTY









MONRO










Figure 6. The Florida spiny lobster fishery




all domestic spiny lobster fishermen to the Keys region can be addressed. For these reasons the study area was delineated to include only Monroe County. In addition, it is realistic to include only that area of the fishery over which the state of Florida has jurisdiction since one of the ultimate objectives is to consider management alternatives.

1
1At the time of this final writing the Bahamian government was
proposing to limit its fishing grounds to only its citizens. This will
mean that future Florida landings will be made up almost exclusively of domestic stock.





49



Department of Commerce secondary data on landings, total value of landings, and effort for 1963-73 were used for the time-series analysis [18],[49]. Measures of effort for the industry during this period were total number of traps; total number of vessels; total number of boats; total number of fishermen classified as, on vessels or casual; and total gross tonnage of vessels in the industry. Gross tonnage was measured only for vessels greater than 5 gross tons and was loosely defined as a measure relating to the net capacity of the craft. Water surface temperature data was acquired from Ocean Survey Branch of NOAA [52]. It was assumed that surface water temperature and bottom water temperature vary in proportion in this study. This assumption was based on findings from a study by Robinson [39] that concluded no thermoclines exist, or the water is isothermal in the delineated study area. Temperature data for the study period waus i the form of mean, minimun, a:d maximum monthly temperatures for three stations located at South Miami, Marathon, and Key West.


Sa__mrple Selection arnd Size

A sample of the population was drawn since surveying the total

population was impractical from a cost and time standpoint. Sample size was determined using the following formula:1

NS
n = 2 (19)
(N - 1) D + Swhere,

n = ample siz ,



1is formula was obtained from Mendenhall [33
Thjis formula was obtained from Mendenhall 1331.





50



N = population size,

S2 = estimate of the population variance,

D = B2/4, and

B = bound on the error of estimation (i.e., 10 percent on

e.ch side).

Data from a sample of 15 observations on 1973-74 landings by individual boats (9) and vessels (6) for sizes ranging from 26 feet to 40 feet in length were obtained for estimating the population variance (S2) [51]. The sample was classified into six vessels and nine boats. S , a pooled variance (within craft class) was estimated from the actual survey data to be 30,129,877.77. B was selected at 10 percent on each side of the population mean to be estimated. N was equal to 226 and was calculated from a list of commercial craft registrations provided by the Florida State Department of Natural Resources. Criteria used to include a firm in the population was (a) that the address of the craft owner be Monroe County; and (b) that lobster fishing was listed as the primary (dollar value) species harvested. A major limitation of this sampling technique was that fishermen may live out of the county and fish in the study area and vice-versa. Sample size, N, was calculated to be 21.

Stratification of the sample was based on length of craft and location of home port. Proportions in each sample strata were equal to proportions of the population in each strata. 'oat length strata were less than 21 feet, 21-30 feet, 31-40 feet, and greater than 40 feet. In the stratification of the study area upper Keys was defined as that area from Key Largo to Lower Matecumbe Key. Middle Keys was defined as that area from Craig Key to Bahia Honda Key and lower Keys was the. area from Big Pine Key to Key West. Based on the population as stratified





51



in Table 2, the following stratified sample illustrated in Table 3 was drawn. Total number of samples drawn was 25 rather than the required 21 in order to round the desired number of samples to whole numbers after stratification.


Table 2. Stratified population of boats and vessels, defined as
firms, economic study of Florida spiny lobster industry Length (feet)
Area
<21 21-30 31-40 >40 Total Upper Keys 8 28 6 2 44 Middle Keys 33 33 14 10 90 Lower Keys 37 25 18 9 89 TOTAL 78 86 38 21 223 (35%) (39%) (17%) (9%) (100%)



Table 3. Stratified sample of boats and vessels, defined as firms,
economic study of Florida spiny lobster industry Length (feet)
Area <21 21-30 31-40 >40 Total Upper Keys 2 2 2 0 6 Middle Keys 3 3 2 1 9 Lower Keys 3 3 3 1 10

TOTAL 8 8 7 2 25




The following formula was used to determine the number of observations to be sampled in each strata:

C C
N i *n (20)
Nij N N





52



where,

Nij = sample size of strata ij,

Ci = number of craft of length class i,

Cij = number of craft of length class i in area j,

n = total sample size to be drawn, and

N = total population of craft.


Survey Technique

Observational units within each strata were not drawn randomly in the usual sense. The data were collected in a very precarious environment, at a very difficult time. Florida spiny lobster fishermen, like most fishermen, are very independent and generally do not divulge information. So, there was first a problem of locating a fisherman that would cooperate. A second problem frequently encountered was that many cooperative fishermen lacked adequate records, particularly costs, so much of the information was "best estimates." To complicate the matter, at the time of the survey the Internal Revenue Service was investigating Florida fishermen because a recent court ruling had changed the tax regulation, retroactively, and thus information was highly guarded. Also it was felt by many that a substantial amount of undersized lobster were "blacknmarketed" from this area. In addition, any list of fishermen was usually out of date because of the highly mobile nature of fishermen. Given these circumstances, it was impossible to collect data on a strictly random basis. Thus, the samples represent fishermen who would cooperate. Personal interviews were conducted until the required number of observations within each strata was accomplished.





53



Initial fishermen contacts were acquired through the Southeastern Fisheries Center in Miami and a local chapter of Organized Fishermen of Florida (O.F.F.).1 In July 1974 the research project was presented and a questionnaire pretested at a local O.F.F. Chapter meeting in the area. Possible benefits to the fishermen were explained as well as soliciting their cooperation for interviews to be conducted in the fall. Also, names of fishhouse managers that would cooperate in encouraging their local lobster fishermen to be interviewed were obtained.

In October 1974 the interviewing began using a thirteen page questionnaireith those fishermen that agreed to cooperate the past July. Once this source of interviews was exhausted, various cooperating fishhouses were then contacted. Managers were asked to recommend fishermen that they felt would cooperate and that were needed to complete the various strata as specified by the sample design. Interviewing continued for three weeks until all observations required in the sample as stratified were collected. Twenty-eight questionnaires were completed and after editing for inconsistencies and incompleteness, twenty-five were used in the analysis. Additional observations were collected for those strata that were weighted heavier to assure completeness. Data comparisons of study projections with industry output characteristics suggest the sample was representative.




1The author is indebted to Mr. Lloyd Johnson and Mr. Pete Maley, agents of the Southeastern Fisheries Center, NOAA, NMFS; and the officers of the Lower Keys Chapter of O.F.F. located in the Summerland Key area.

2Appendix J includes the survey questionnaire.
















CHAPTER V

ANjALYSIS OF RESULTS


Estimated coefficients and their interpretation for the industry

and firms' harvest functions are presented in this chapter. Information from the industry harvest model was used to derive estimates of MSY and MEY. Optimum input levels and related costs at current stock levels for the "typical" firm were derived from the firm harvest model. Information obtained from both analyses was then integrated to analyze alternative fishing practices.


Bioeconomic Model

As previously mentioned, the reciprocal function was selected for the time-series estimation because of its theoretical characteristics and its simplicity. Recall that current management programs such as size limits and protection of berried females suggested the model to be realistic. The management program protects the young until they reach minimum size. Thus, assuming continuous fishing pressure it is possible that (a) there is a Ivel of pounds landed which is a function of the weight of minimum m-sized lobsters and (b) increased effort alone will not cause total leading to decrease because of present size and sex regulations.

The reciprocal function allows landings to reach a maximum limit but does not allow total landings, to decrease with increased effort.




54





55



It also allows decreasing marginal returns to fishing effort.1

The following spiny lobster harvest function is the statistical model estimated using time-series data:

S1 1
Q = a + 1 + B2 2 + 3X3 + e. (21) The estimated coefficients and standard errors are presented in Equation (22):

1 1
Q = 28,379,136 - 1,439,976,169 - 465,173,997 (365,878,684) (216,457,337)
- 239,791 X3.
(170,321) (22)


Overall the model was statistically significant at the .01 level (F3,7 = 9.16). The coefficient of determination, R2 and j2 (which was R2 corrected for degrees of freedom) indicated that the model explained 80 and 75 percent of the variation in annual landings, respectively. A Durbin-Watson value of 2.38 indicated the model hinges on the border between no autocorrelation and inconclusiveness range of the test. The coefficients for traps per firm, B1, and number of firms traps in the industry, 62, were found to be statistically different from zero at the .01 sad .07 levels of significance, respectively.



As a check on thc logic of using the reciprocal form of the function other functions were considered, but none of these yielded
"better" results. For the second degree polynomial function, negative signs were estimated for the parameters but the coefficients estimated were not significantly different from zero.

2Durbin-Watson statistic is not calculated for less than 15
observations. Therefore DW was not used to test in this case. However, there was no apparent pattern of the residuals.





56



Observed and predicted values of landings for 1963-73 are shown in Figure 7. Since 1969, landings have varied between 4 and 5 million pounds, with a slight exception in 1970. Maximum landings observed within the data range occurred in 1970 at 5.24 million pounds. In 1973 landings decreased to 4.99 million pounds. Assuming current management regulations are adequate and new technology does not occur, there is little reason to expect landings to increase substantially above five or six million pounds annually. This assumes that biological and environmental factors will remain substantially unchanged.







6

Predicted
5 Observed

O \ /

3 3



2 Q = 28,379,136 - 1,439,976,169 XR-1

-465,173,997 X2-1 - 239,791 X3





63 64 65 66 67 68 69 70 71 72 73 Year

Figure 7. Observed and predicted volume of spiny lobster landings,
1963-73 for Monroe County, Florida





57



The marginal effect of changes in effort on landings was determined vby the partial derivatives of the bioeconomic industry harvest function (Equation 22) with respect to the specific explanatory variable measuring effort. The following marginal products (P x.) of the harvest func1
tion are partial derivatives with respect to a given explanatory variable, x.:
1

MP Q - 1,439,976,169 (23)
xI X X12 X1



S=2 465,173,997 (24) x2 aX2 X22 2
1 2 X2



MP = ~- = B3 = -239,791 (25)
X3 3X3

The additional pounds of lobsters landed in the industry when each firm. intensifies production by adding one trap is shown by MPX1. As each firm adds a trap total landings increase at a decreasing rate. The MP
additional catch per firm can be calculated by for each MP X2 X1
Additional catch per firm is simply the MPX2 divided by X2. MPX2 is also a declining function of the number of firms in the industry and

is interpreted to be the additional industry landings resulting from adding one additional firm to the industry with the same characteristics as all other firms in the industry.

In the empirical analysis of specific marginal products numerical values of other variables were held constant at their mean levels. Traps per firm (XI) and n;mbcr of firms (X2) were held constant at 429 traps per firm and 399 firms, respectively. Mean seasonal surface'water





58



temperature was 77.5910F. Evaluating MPX1 (Equation 23) at 1973 input

levels gives


MP = 439,976,169 = 7,824 pounds. (26)
(429)2

As each firm in the industry increases the number of traps it fishes by one, total landings for the industry increases by 7,824 pounds. A one trap increase per firm is equivalent to a 399 total trap increase for the industry and an increase of 19.59 pounds per trap.

Evaluating the effect of changing the number of firms in the industry (Equation 24) gives


465,173,997
465, - 73,997 2,922 pounds. (27)
2 (399)

Holding traps par firm and water temperature constant and increasing the number of firms by one increases total industry landings by 2,922 pounds. Increasing the number of firms by one unit and holding traps per firm constant, brings 429 new traps into the industry. The fishing power of an additional trap to the industry may be greater if it is the first trap for a new firm compared to an additional trap for a firm already fishing. However, the marginal analysis as set forth will not allow for this difference.

Evaluating the effect of changes ir, water temperature (Equation 25) gives

MPX3 = 13 = -239,791 pounds. (28) For every one degree increase in the mean surface water temperature for the season, total industry landings will decrease by 239,791 pounds or abGut 5 percent of total landings in 1973. A general concensus among fishermen is that landings increase shortly after meteorological





59



changes such as storms and weather fronts. These weather changes often create lower temperatures and partially explain the inverse relationship of this parameter.


Maximum Sustainable Yield (MSY) Estimate

One of the initial objectives in this study was to address the question of "the status of the spiny lobster fishery with respect to maximum sustainable yield (MSY)." The industry bioeconomic harvest model indicated that industry landings are approaching a maximum sustainable yield. The bioeconomic empirical model based on a theoretical curvilinear harvest function fitted the data very well (R2 = .75). Explanatory variables were individually highly significant and the total "accounted for" variation was significant. At current levels of effort the percentage increase in landings was much less than the percentage increases in inputs.

These conclusions were reached observing the range in landings as inputs were increased to an infinitely large number as shown in Table 4. Inputs were held constant at 1973 mean values while the remaining variables were varied. Landings were also analyzed with seasonal water temperature (Xq) which was held constant at its mean, minimum, and maximum observed values.

The range of maximum landings was from 5.9 million to 8.9 million pounds. Illustrated in Figure 8 is the harvest function as it reaches a maximum of 7.89 million pounds with 2,000 traps per firm (X1), holding total number of firms (X2) at the 1973 level of 399 and seasonal water temperature (X3) at its mean of 77.59. Although some fishermen are fishing 2,000 traps, this number was chosen to illustrate the approximate





60


Table 4. Estimated levels of maximum landings (Q) for given levels of
traps per firm (XI), number of firms (X2), and seasonal water
temperature (X3), economic study of florida spiny lobster
industry


Maximum Variable Level of Variables Held Constant landings (Q) approaching
0 X1 X2 X3 (infinity)

8,152,905 X1 -- 287 77.59 (MEAN) (MEAN)
8,607,871 X1 -- 399 77.59 (MAX, 1973) (MEAN)
8,121,094 X1-- 399 79.62 (MAX, 1973) (MAX, 1972)
8,450,247 X1 -- 287 76.35 (MEAN) (MIN, 1969)
8,905,212 X1 -- 399 76.35 (MAX, 1973) (MIN, 1969)
7,666129 X1 -- 287 79.62 (MEAN) (MAX, 1972)
5,860,742 X2 368 -- 77.59 (MEAN) (MEAN) 6,416,893 X2 429 -- 77.59 (1973) (MEAN) 6,786,218 X2 482 -- 77.59 (MAX, 1971) (MEAN) 6,299,442 X2 482 -- 79.62 (MAX, 1971) (MAX, 1972) 7,083,559 X2 482 -- 76.35 (MAX, 1971) (MIN, 1969)

Note: Mean, minimum, and maximum refer to values for Monroe County
time-series data, 1962-73 (Appendix K). Numbers in parentheses
represent year.


point where the bioeconomic harvest function becomes flat for all practical purposes. This represents a 366 percent increase in traps per

firm and a 58 percent increase in landings. Note that the levels of

inputs required to achieve the maximum output levels in Table 4 were

totally unrealistic at levels of infinity. A 18 to 78 percent increase

















7 Q 28,379,136 - 1,439,976,169(X1)- - 465,173,997(X2)-1

- 239,791(X3) where, R 2 399

5.62 R3 77.591


5.25 .6
,4








'. 03.43 DATA
3 RAN.GE O

2 I










278 482
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 Traps per firm (X1)



Figure 8. Spiny lobster bioeconomic industry harvest function





62



in landings would require an infinite percentage increase in inputs. The same point is illustrated in Figure 8 but traps per firm is presented in a more realistic range. Predicted landings increase by 40 percent, from 5.62 to 7.89 million pounds, as a result of a 115 percent increase in the number of traps per firm (from the maximum observed in the data of 482 to 2,000).

Estimates of MSY chosen for analysis in this study ranged between six million and eight million pounds with a realistic estimate probably in the range of six to seven million pounds. This is not to imply that landings cannot increase above these figures, but rather that these figures are the levels estimated at which landings could be maintained from year to year--maximum sustainable harvest (yield), ceteris paribus. Actually, the limiting factor probably is that the typical firm does not have the capacity to reach the required trap level.

In summary, maximum harvest levels considered here are quite liberal for several reasons. Some illustrations used extremely unrealistic levels of inputs to achieve the maximum levels of harvest and more importantly, some input levels were beyond the range of data. Estimated landings may be beyond maximum economic yield, discussed in the next section. In addition, substantial input increases of this nature may cause irreversible effects on the population, not directly observable in the existing data on which the analysis was based. Therefore, the realistic MSY level was concluded to be in the range of six to seven million pounds annually.


Value Marginal Pr3iuct Analysis

A more comprehensive analysis of maxlmunm economic yield (MEY) is presented in the section Integrating results from the cross-sectionaal





63



and time-series analyses, but come knowledge of levels of expenditures and profit maximization can be gained using results of the time-series industry analysis thus far.

Value marginal products for given inputs were derived by multiplying constant product price times the respective marginal physical product. The value marginal product equation for traps per firm (X1) is1


Pl = Py MP = P (- --) (29)
X y X1 X

where,

P = annual average dockside price per pound of lobster,
y
assumed constant;

- 2= marginal product of Q with respect to input X1 (Equation
X1
23).

VMPx] is the addition to industry total revenue as a result of a marginal increase in traps fished per firm. VMPX1 was divided by the number of firms in the industry in 1973 (399) to demonstrate the effect of price changes on an individual firm (Figure 9).

Product prices per pound used in the analysis were $1.08,2 $1.25, $1.50,and $2.00. In this price range the value marginal product ranged from approximately $4.81 to $140.00 as traps per firm vary from approximately 900 to 168, respectively. At a product price of $1.08 and traps per firm at the mean level for 1952-71 (368) the VMPX1 was $28.77. If the cost for an additional trap were $28.77, this would be the profit


IVMP is with respect to the subscript (x.) denoted in Equation 29.

2Mean ex-vessel price of $1.08 per pound was obtained from a survey of 25 lobster boat captains taken in 1973.







140


130


120


110


100




MXl - 12 80


70 60 6o



39.97 39.22
40 D--A RAG
13.31

S28.77 . 519







4.81

278 368 .29 412 100 180 260 340 420 500 580 660 740 820 900 Traps per firm (X1) Figure 9. Value marginal product of traps per firm (X1) divided by the maximum number of firms
observed (399) in the industry in 1973





65



maximization level of output. Thus as long as the cost of fishing a trap was less than $28.77 it would pay to expand.1 At dockside prices of $1.25, $1.50,and $2.00, marginal cost per trap could increase to $33.31, $39.97,and $53.30, respectively, before the input level for profit maximization would be reached. With traps per firm (X1) at the 1973 level of 429, VMPX1 ranged from $21.16 (assuming a product price of $1.08 per pound) to $39.22 (assuming a product price of $2.00 per pound). Maximum level of traps per firm observed was 482 in 1971. At this level VMPX1 ranged from $16.77 to $31.07 for product prices ranging from $1.08 to $2.00 per pound. These values exceed trap costs and encourage intensification of traps fished per fisherman.

Value marginal product for an additional firm was also analyzed

while holding traps per firm (X1) constant. Value marginal product for the firm was expressed as

B2
VMPX2 = P (- X2 ) (30) where,

82
- = marginal product of Q (Equation 24) with respect to firms
X2
(X2), holding X1 constant.

Estimates of VMPX2 for the mean, minimum, maximum, and 1973 levels of firms are presented in Figure 10 at the product prices used earlier. Profit maximization will occur with 399 firms in the industry when the total cost for the typical firm reaches $',i54, $3,652, $4,383,or $5,844, given product prices of $1.08, $1I.25, $1.50,or $2.00. respectively


Cost of an additional trap includes fixed costs for construction and craft, and variable expenses incurred to fish the trap such as fuel, bait, and labor.







28
26, 892 26 24




20,169'

20 " x, 2 " 2


16s807

10




8 71
'M

: 12




.,,
DATA RANGE






4 3 652


2


186 236 39 100 200 300 400 500 Firms (X2) Figure 10. Value marginal product of firms (X2)





67



respectively (Equation 30, Figure 10). The difference between industry total value of landings in 1973 for 399 firms fishing compared with 400 firms fishing was $3,154 at a product price of $1.08. In order to generate a net profit to the industry, the addition to industry total cost from the 400th firm fishing must be less than $3,154.


Analysis of Firm Harvest Function Model

Time-series data on firms included both part-time and full-time

commercial fishermen. Some of these firms fish in more productive fishing grounds than others which can significantly influence the firm harvest rate. Fishing power and intensity of this power varies substantially between firms which influences the firm harvest rate. Aggregate data measuring explanatory variables such as firms and traps have all of these production input differences confounded in thc:r estimated effects, thus making the interpretation of estimated coefficients very difficult and incomplete. Therefore, one objective of the cross-sectional analysis was to obtain partial estimates adjusted for these other influences. A second objective was to develop cost estimates which would be used with the time-series bioeconomic model to determine maximum economic yield for given measures of effort. That analysis is presented in this section along with a brief analysis of optimum resource allocation for

the firm at a given fishery stock level. Firm Harvest Model

The harvesting process for the typical spiny lobster firm was estimated using a Cobb-Douglas functional form. The empirical data must lie in Stage II of production since diminishing marginal returns are indicate by less than unity values estimated for the parameters. The





68



estimated equation is

.7577 .43991 .37211 .30876 .44455 .13063 q = 4.09000 x1 x2 X3 x4 X5 X6 (31)


Equation 31 was estimated in log linear form using ordinary least square methods. This entails minimizing the sum of squares of the logarithms of residuals. The assumptions of BLUE estinaters are still valid.

Landings per firm (q) were measured in pounds. Average traps

fished per firm (xl) was a weighted average of traps fished per firm. This variable considered the initial number of traps fished at the beginning of the season, the number of traps lost during each month of the season, and the number of times a trap was fished before lost. Rounds per week (x2) was a measure of effort intensity and was defined as the season average proportion of traps pulled per week for the season. A round was defined as a single pulling of all traps. Total number of weeks fished (x3) was another measure of effort intensity. In Florida a maximum of 36 weeks is allowed in the season by law. Fishing power of the firm (x4) was taken into consideration by including a size variable. The square area of the hull was used as a proxy for size. Influences on harvest levels due to quality differences in fishing grounds were accounted for by including dummy variables x5 and x6 which broadly characterized the firms into the three areas previously defined.1

The (2 corrected for small sample size showed that the harvest function explained 82 percent of the variation in a typical firm's


1Derivations and detailed definitions of the explanatory variables
are presented in Appendix D. Appendix G contains the estimating equations for landings (q) and marginal products (MP ). Appendix L contains the data used to estimate the firm harvest xi function.








50 q + x5 15





30 9

25
20 15
133



0 85 500 1,000 1,500 2,000 6 12 is 2 50 2,0
Traps per firm (xl) Weeks fished per year (x3) 36 30


3 25

2 q + x6 E q + x6 '2C
0 n q 18 015


12


6 5


16 14 12 0 8 6 4 2 0 500 1,000 1,500 2,000
Days (set period) Square feet f craft (x4)
.44 .50 .58 .70 .88 1.17 1.75 3.5
Rounds per weeks (x2)


Figure 11. Firm harvest functions with respect to effort measured as gear (X1),
fishing intensity (X2, X3), firm size (X ), and adjusted for fishing
grounds (X5, X6)





70



landings (Table 5). The range in error of estimated landings was computed by expressing the antilog of the standard error of the estimate (SEE) as a percentage of the total estimated value. For Equation 31 landings varied from 31.5 percent above to 24.0 percent below the estimated harvest values.


Table 5. Regression statistics for the cross-sectional firm harvest
function model, economic study of Florida spiny lobster
industry


Independent Estimated Standard Significance Variables (xi.) Coefficient (si) Error t-Ratio Level of Probability

Constant (a) 4.09000 1.2500 1.128 -Traps per firm .75770 .1099 6.895 .9999
(xl)
Rounds per week .43991 .2772 1.587 .8700
(x2)
Weeks fished
.37211 .2400 1.550 .8615
(x3)
Craft size
(x ) .30876 .1358 2.274 .9645 Upper Keys area
Upper Keys area .44455 .1493 2.977 .9919
(x5)
Lower Keys area
.13063 .1653 .790 .5603
(xg)

Note: R2 = .8223, R2 = .9310, d.f. = 18, SEE = .2742, F6,18 = 19.514.


The relationship of landings to effort (x1, x2, x3 and,xt,) for the

firm is presented in Figure 11. Adjustments to the firm harvest function for the influence of different fishing grounds is also illustrated.

An analysis of the estimated effort coefficients (Equation 31)

indicated that the function is homogeneous of degree 1.87848 and thus defined an industry exhibiting increasing returns to scale. The theoretical interpretation was that the marginal returns to a simultaneous





71



increase in all inputs was positive and total landings were increasing at an increasing rate. Homogenity of 1.87848 means that if each of the independent variables of the harvest function are multiplied by a constant k, landings will change by a multiple of k187848. For example, if xl . . . x6 are all doubled (k = 2) landings will more than quadruple. To illustrate the significance of this, assume that the State of Florida determined that MSY had been surpassed and landings would have to be reduced by, say, approximately 50 percent to protect the fishery stock from irreversible damage. Given hcmogenity of 1.87848, all inputs would have to be reduced by only 25 percent to obtain a 58 percent reduction in landings per firm, and thus, for the industry, assuming homogeneous firms.1 If the state does not have control over individual effort, individual firms would have to be provided some inducement to voluntarily cut back input usage, similar to the objective of the Federal Soil Bank Program for agriculture in the 1960s. Although this type of analysis may provide some interesting insights into management of the fishery, it may be argued that the interpretation is non-sensical. Realistically speaking, size of craft and number of weeks are definitely limited beyond some point of expansion.


Estimated Parameters

The estimated coefficients ( oi) of the harvest function presented

in Table 5 explained the percentage change in landings due to a given one percent change in the particular input level, assuming all other inputs


'Notationally the derivation is as follows:
(.75)1.878t8 . q = .58 q
where,
q = firm harvest function (Equation 31).





72



constant. These were defined as output elasticities and can also be expressed as ratios of marginal and average productivities.

Partial differentiation of the harvest function (Equation 31) with respect to given explanatory variables, gave the marginal products as follows:


MP = a Blxl 1-1x2X33x4 x55X6 (32)
xl axl

A A A A ^
- = x 2-21 81xB3x x5B5x6 (33)
X2 ax2

A A A A A ^
P = aq = 3x33-1xl1x2 62xUB4 X5x6 6 (34)
x3 Dx3

A A A A ^
a XX2 28 3X5 B 6 (35) MP = = 4x4 1 2 X3 (35)
x4 ax4


Traps per firms (xl)

The estimated parameter (B1) is interpreted as a 76 percent increase in landings due to a one percent increase in number of traps for the firm. B1 is statistically significant at the 99 percent confidence level.1

The marginal increase in landings due to the addition of one trap by the typical firm is:
-.2423
MP = 62.85xI (36)
Xl

The derivative of MPxI was negative implying marginal landings per trap will decrease as additional traps are added by each firm to the total



1Alternatively, the probability of randomly obtaining a B as large as B1, if 81 is equal to zero is less than .01.





73



number fished. The marginal return to an additional trap was positive and also greater than the marginal return for any of the other three forms of effort.


Rounds per week (x2)

As the firm increased its trap pulling rate by one percent (i.e.,

decreases its set period), landings increased by 44 percent (82 = .43991). Rounds per week is an index measuring fishing intensity as defined in Appendix D. B2 was statistically significant at the 87 percent confidence level. The marginal product of x2 was expressed as


MP = 5317 x2-'5601 (37) As x2 increased the rate of increase in landings decreased. For example, assume the firm is pulling all of its traps once per week. The marginal product (Equation 37) of increasing this rate to twice per week would be approximately 4,500 pounds.

Useful information contained in this index is the expected gain in landings due to increasing the number of days a fisherman's traps set between harvest periods.1 Rounds per week (x2) was computed by dividing the average number of days in a set period for the season into seven days of a week. By substituting this definition for rounds per week into the firm harvest function (Equation 31) the marginal product of increasing the set period an additional day was calculated (Table 6).

For example, a fisherman previously harvesting his traps after the third day can increase his total harvest by 2491 pounds by letting his




This is often referred to as "set period" among fishermen.





74


Table 6. Marginal products for various lengths of set periods, economic
study of Florida spiny lobster fishery


Days in Increase in landing Fishing effort set period due to a one day intensity in terms
(z) increase in set period of rounds per week
(MPz) (x2)


3 2491 2.333 7 735 1.000 10 440 .700 14 271 .500



traps set four days between harvests. Likewise total landings can be increased by 735 pounds by increasing the set period from 7 days to 8 days. Increasing from a 10 day set period to an eleven day set period would increase total landings by 440 pounds, while a 271 pound increase could be expected by allowing traps to set 15 days instead of 14 days. Marginal increases in total landings due to increasing the set period by one day can be estimated for any length of set period by the following equation:


MP = 12116 z-1.43991 (38)
z

where,

MP is the marginal product due to increasing the set period

by one day,

z is the number of days in the set period or between rounds, and

z = 7/x2.

Equivalent levels of fishing effort intensity measured as rounds per week (x2) for the examples shown in Table 6 range from 2.333 rounds per week for fishermen that harvest after a three day set period to .500





75



rounds per week for fishermen that pull all their traps every two weeks.

Interpretation of these estimates of MP' must be treted with x2
care. First, the data represent seasonal meaa levels of landings related to rounds per week which vary greatly from week to week throughout the season. During August, the first month of the season, the mean set period for the 25 total firms in the sample was 5.8 days. By Mar-", the last month of the season, the mean was 1.3.3 days. The March mean was for only 20 of the 25 sample firms since some of the larger, multiple specie fishermen usually stop lobster fishing by the end of December.

Although this question was not specifically asked in the interview a considerable amount of information was volunteered that indicated the

maximum level of set period, relative to poaching and vandalism, was correlated with location of fishing ground to populated arcas, distanc from shore,and depth of water. The remarks indicated that approximately four days was tria mai:imum length of time traps could set between harvest periods, particularly at the beginning of the season. This could be extended to six days if either the traps were in sight of land or fir !s banded together in groups to fish an area several miles from shore. Weeks fished per season ('j3)

Landings increased very rapidly the first few weeks of the season, then leveled off. Recall that in Figure 11 it was shown that approximately 54.5 percent of total landings for the 36-week season arc harvested within the first six weeks. This was supported by the estimated output elasticiiy for ;e.ks. 83 shows that landings increase .37 percn1"'ct for a one percent i;c~ae in weeks fished. Expcted weekly landing. ,





76



beginning at various dates within the season can be estimated using the marginal product of weeks, expressed as follows:


MP = 1093.46 x3-'6279 (39)
x3

The second partial derivative of the harvest function for weeks fished showed MP diminishing at an increasing rate.
x3


2 = -686.58 x3-1.6279 (40)
ax3

Estimated marginal products are presented in Table 7 for various periods throughout the harvest season. B3 was statistically significant at the 86 percent confidence level.


Table 7. Weekly landings expected for given dates within the spiny
lobster season, economic study of Florida spiny lobster
industry


Change in landings
Beginning date of Week (x) for each addition Beginning date of Week Weeks fished week fished (MPx3


August 7 1.00 1,093
14 2.00 708 31 4.43 429 September 15 6.57 335
30 8.71 281 October 31 13.14 217 November 30 17.43 182 December 31 21.86 158 February 28 30.29 128 March 31 36.14 115


An additional week of fishing after August 7 would return approximately 1,093 pounds. By the third and fourth week, landings would drop





77




off to 708 pounds and then to 429 pcunds per week, respectively. After the ist of September weekly landings tended to level off dropping to less than 200 pounds per week by December ist. Some of the larger firms with greater capital investments quit lobster fishing by November Ist and go to other species. The expected net returns from netting mackerel or long-living yellowtail snapper are evidently greater for at least these firms. Four out of the 25 firms in the sample did not fish the entire season. At least three of these four were always ranked in the top five in number of traps (xl), fishing intensity (x2), and size of craft (x4). The cost per pound of fishing extra weeks becomes substantial and returns become relatively small. Smaller firms often did not have the alternative of fishing for other species at higher net returns and remained in the lobster fishery the entire season. On the other hand, larger firms have a comparative advantage in other fisheries and began leaving after the 13th week of the season when approximately 68.6 percent of total landings had been harvested.

By changing species early in the harvest season larger firms can reduce costs substantially for several reasons. After two months the trap lines become frayed and traps break off and are lost in hauling.1 Those traps not lost to frayed buoy lines require additional repairs which reduce the efficiency of the harvesting process. Second, by late summer the probability of ocean storms increases substantially and the risk of losing traps to high winds and rough waters becomes high. Consequently, larger firms fishing in excess of 800 traps have the largest total risk and pull out of trap fishing early in tlie season in an effort to reduce costs.


1Hauling is defined as pulling a trap out of the watar.





78



Craft size (x4)

Craft size, defined as the square area of the hull, was the most significant of several measures developed from characteristics of the craft. It is reasonable to assume that the effect of craft size (84) is confounded. There is decreased speed but increased size which allows more traps to be transported and relocated. B4 was statistically significant at the 97 percent confidence level. From B4, it was concluded that landings increased .31 percent for each one percent increase in craft size and the marginal product of craft size increased at a decreasing rate. This was the smallest response of all the measures of effort. The range of craft size in the sample was from 80 to 1,045 square feet, while the mean of the sample was 326.88 square feet. Number of craft and hull lengths in each group of the sample were: seven, 16-20 feet; seven, 21-30 feet; seven, 31-40 feet; and four. 40-55 feet. Appendix H further elaborates various characteristics and practices classified according to length, for the lobster firms surveyed.

Marginal returns for increases in square footage of the hull (x4)

are presented in Table 8 and were estimated using the following equation:


MP = 558.29 x4-'69124 (41)
x4

Marginal product (MPx4) due to a foot increase in the hull size

ranged from 27.00 pounds for craft 80 square feet in size to 4.57 pounds for craft 675 square feet in size. At levels of x4 less than 350 square feet the marginal product decreased at a greater rate per unit of increase in square footage of hull than for craft greater than 350 square feet. This was determined by the slope of the marginal product curve in Figure 12, being less than zero. This indicated a decreasing rate





79



Table 8. Marginal products of craft size (x4) for sample sizes
observed, economic study of Florida spiny lobster industry


Change in landings for
Craft size (x4) Length Width each additional square (length x width) foot increase in craft size (MPx )

80 16 5 27.00 96 16 6 23.80 140 20 7 18.34 154 22 7 17.17 176 22 8 15.66 200 25 8 14.33 208 26 8 13.95 234 26 9 12.86 240 24 10 12.63 252 28 9 12.22 330 33 10 10.14 340 34 10 9.93 341 31 11 9.91 408 34 12 8.76 432 36 12 8.41 468 36 13 7.96 480 40 12 7.82 574 41 14 6.91 675 45 15 6.18
1045 55 19 4.57



of return. After x4 reached 350 square feet (approximately 34 feet long

times 10 feet wide) returns to increasing the size of the craft began to

level off. For example, in Table 8 marginal product of craft size decreased by 48 percent compared with a 156 percent increase in craft

size, as the square footage increased from 408 (34 feet x 12 feet) to

1,045 (55 feet x 19 feet). The implications were that marginal decreases

in landings due to increases in the size of the craft were smaller for

larger firms than for smaller firms at mean levels of various inputs.

In summary, the estimated firm harvest model fitted the data well

and all individual explanatory variables were highly significant statistically. The model indicated that firms were operating in stage II of





80


28 24


20


S16
0

12
MP
8


4

0 100 200 300 400 500 600 700 square feet (x4)
Figure 12. Marginal product curve for spiny lobster craft size (P 4)


the production process, defined by diminishing marginal returns to the inputs. Number of traps (xj) exhibited the largest returns to increased input usage, and had the highest statistical significance level of all explanatory variables. Estimates of rounds per week (x2) revealed that marginal returns to more frequent pulls or longer set periods would be positive. Number of weeks fished (x3) by law is limited to 36, although the analysis of weeks fished indicated that the economic feasibility of fishing beyond the 13th week is questionable. The diminishing marginal rate of returns to a firm was smaller for larger firms than smaller firms.


Optimum Resource Allocation of the Firm

The analysis and results of determining the level of inputs where profit was maximized for the typical firm are presented in this section.





81



This analysis was expanded to determine the optimum allocation of inputs for each size of craft classified by the sample stratification.

Optimum level of input usage is customarily determine by solving a system of equations determine from the first order conditions. In this case xl . . . x can be considered as factors of production and x5 and xg are simply area adjustment factors. Notationally, the equilibrium between value marginal product (VMP x) and marginal factor price for each input (xi) can be represented as


VMP =P (42)
x. x.
1 1

Thus the optimum solution for x1 . . . xq is determined by simultaneously solving Equations 43-46.


67.85 x]-'2423 = P (43) xl

5557.06 x2- 5603 = p (44) x2

1180.39 x3-^6279 P (45)
x3

602.67 x4-.6912 = P (46) x4

The terms on the left of Equations 43-46 represent the value marginal products for the individual factors determined at the means of the other independent: variables and at a product price of $1.08 per pound. Unfortunately the factor prices (Px.) were not unique exogenous prices. They were interdependent and thus presented problems in arriving at a unique solutioL. Factor price estimates of a trap (P ) are possible and were the pri ary concern in this analysis. As ment oned earlier, the traps (x1) variable was the principle factor through which all





82



inputs were translated into fishing effort. Although analyses of variables measuring effort intensity (x2, x3, and xt,) have provided useful production information, the principle reason for specification of these in the model was to allow for partial estimates of the trap effect. This model adjustment was required because the data base represented a cross-section of firms which varied with respect to x2, x3, and x4. Thus an optimum solution in this analysis will be limited to (a) determination of optimal trap use for given (mean) levels of the adjustment variables and (b) discussion of possible or feasible levels of x2, x3, and x4.

The price of an additional trap fished (Pxl) is not simply the

price of the trap but is the price of the trap and the cost of fishing the additional trap. This latter component presented difficulty in determining P . Total cost per firm was regressed on the number of traps fished per firm. OLS regression technique assuming BLUE estimators was used to estimate the total cost function (TC) expressed in Equation 47:


TC = $1,876 + $11.55 x, (47)


The coefficient of determination corrected for small sample size (R2) was .53 and the estimated coefficient ($11.55) for traps per firm was statistically significant at the 99 percent confidence level (t-value equal 5.328). The constant term ($1,876) was interpreted to represent fixed costs which do not vary with level of trap use. The coefficient, $11.55, represented the marginal factor price of an additional trap fished. Total costs were used for estimation rather than variable costs because a large component of trap cost was included in fixed cost





83



through depreciation.1 The estimate of optimum number of traps per firm

(xl) using this factor cost estimate is presented in Table 9 with respective landings, profit levels, total revenue, and total cost.


Table 9. Optimum levels of trap usage per firm and resulting levels of
profits, total revenue, total cost, and landings given trap
cost, economic study of Florida spiny lobster industry


Optimum Trap Total Total Profits Landings (q) level of factor revenue costs (H) (pounds) trap use price (TR) (TC)
(P 1
xl

$11.55 1,491 $22,742 $17,221 $3,863 21,057


The optimum level of traps given a factor price of $11.55 was 1,491. Relatively small variations in the factor price of a trap produce significant changes in the estimated optimum level of traps. The highly variable nature of the optimum solution is significant in that it offered a possible explanation for the rapid increase in trap usage in the industry. Relatively small changes in product price (P ) or factor price of a trap (Pxl) resulted in considerable expansion of fishing effort on trap usage.

This finding justifies further consideration of trap usage in management considerations in the following chapter.

Before closing this chapter consideration of the remaining independent variables is warranted, given the earlier significant estimates of their marginal effects. One crude method for estimating the factor prices for x2, x3, and x4 involves dividing total cost or total variable for each by the mean input levels of each of these factors. Estimates of



1Traps have an average life expectancy of three years.





84



total cost (TC), total revenue (TR), firm profit (H), landings (q), and

optimal levels x2, x3, and x4, given the crude factor estimates of Px2,

P and P are presented in Table 10. The remaining variables used in x3 x4
the estimation procedure are assumed constant at their sample mean.


Table 10. Optimum levels of adjustment factors (x2, x3, and xif) and
resulting levels of profits, total revenue, total cost, and landings per firm, economic study of Florida spiny lobster
industry


Optimum Factor Estimated Total Total Profits Landings level of price factor revenue costs (H) factor deri- price (TR) (TC) use vation (P )
(x i)
(dollars) (dollars) (dollars) (dollars) (pounds)

TVC
.834 P =--- 6,149.88 12,084 5,129 6,955 11,189
X2 X2

10.30 P = TC 273.00 7,559 2,812 4,747 6,999 x3 x3

TVC
179.11 P =- 17.70 9,690 2,991 718 8,972
x4 X4



Optimum number of rounds per week, or total percentage of traps

pulled was .834.1 The imputed factor cost for rounds per week was derived by dividing average total variable cost per firm from the sample

by the mean level of rounds per week for the sample. Coincidentally,

the optimum level of rounds per week (x ) was equal to the mean of

rounds per week from the sample (x2) which resulted in a $6,955 profit

for the typical firm. Imputed factor costs for weeks were derived by



1Length of set period, measured as days, is derived as follows:
7
Days set period =
x0





85



dividing total costs by the mean number of weeks in the sample. Optimum number of weeks was estimated at 10.3 and profit per firm was estimated at $4,747. Optimum size of craft measured as square footage of hull was estimated at 179.11 square feet. Factor costs were derived by dividing total variable costs by mean craft size for the sample. At this level of craft size profit estimated for the typical firm was $718.

This procedure was presented for illustrative purposes and its usefulness depends on accurate estimates of factor prices. In addition, total revenue, total cost, and resulting profits were also dependent on levels of other inputs which in the above analysis were held at mean levels rather than "optimal" levels. However, it is interesting to note that the predicted level for rounds per week and weeks fished in Table 10 were both close to actual observed values in the industry, thus suggesting that if firms are maximizing profits, the above estimates of factor prices for x2 and x3 are reasonable. The factor price estimated for craft size evidently may be a substantial error because the optimal hull size of the typical craft was predicted at 179.11 square feet, considerably different from the current industry average size of 326.88 square feet. Furthermore, the predicted profit per firm of $718 does not appear reasonable given the survey data.

At this point, one additional conclusion was indicated with respect to variations in firm profits due to fishing areas. Fishing in the upper (x5) and lower (x6) Keys regions produced increased profits. However, only Bg was statistically significant at the 99 percent confidence level, compared with a 56 percent confidence level for 8S. Therefore, there exists a good chance profits will be greater if firms fish above Lower Matecumbe Key rather than fish the adjacent area down to Big Pine





86



Key. Fishing in the region belov Big Pine to Key West most probably does not increase a firm's profits compared to fishing the area from Big Pine Key up to Lower Matecumbe Key. The model would have to be respecified to determine if there exist only two significantly different fishing grounds (regions), i.e., above and below Lower Matecumbe Key. Empirical values for the fishing effort and price variables were held at the respective 1973 levels: 618, for xl; .834, for x2; 33.08, for x3; and 326.88, for x4. Product price, Py, was assumed equal to $1.08 per pound.
















CHAPTER VI

THE MANAGEMENT MODEL


The purpose of this chapter is to present a framework with which

decisionmakers can evaluate management policies. The framework is based on results from the estimated time-series bioeconomic industry on firm harvest models in the study. In the first section the analysis of maximum economic yield (MEY) for the industry is presented. Next, analyses of alternative combinations of traps per firm and number of firms are presented. Finally, the alternative management considerations outlined in the study objectives are analyzed.


Maximum Economic Yield for the Industry1

When the quantity of lobster harvested is such that the cost of an additional unit of input (P ) is equal to the value of the marginal product (VM\ i ) for that input, then maximum economic yield with respect to the . en input (Mr)EYX ) is achieved. Maximum economic yield with respect to inputs X1 and X2 can be determined by first simultaneously determining the optical level of both inputs. These input levels are then substituted into the production function (Equation 22) to predict MEY. To determine optimum levels of X1 and X2 for the industry simultaneously, the profit function (Equation 47) is differentiated with


recall that capital notations fur the variables represent industry inputs and lower case type for variable notations represent firm inputs.
P represents ex-vsssel produce price in the firm and industry models.



87




Full Text
TABLE OF CONTENTS
ACKNOWLEDGMENTS H
LIST OF TABLES viii
LIST OF FIGURES xi
ABSTRACT xii
CHAPTER
I INTRODUCTION
Objectives
Scope
II LITERATURE REVIEW
Introduction .
Spiny Lobster Research ....
General Bioeconomic Management Research
Bioeconomic Lobster Research
Regulatory Management Programs for Florida
Spiny Lobster
Ill THEORETICAL MODEL
Biological Theory of a Fishery
Traditional Economic Production Model .
Bioeconomic Model
Summary ......
6
7
9
9
9
14
18
20
24
30
32
35
iv


21
A $50 permit is required for all persons intending to catch more
than 24 lobsters per day. The permit must be carried on the person at
all times and can be suspended or permanently revoked upon the arrest
and conviction of a permit holder for violation of any of the lobster
fishing laws.
Florida's management program includes two regulations pertaining to
the gear and craft. The first is that all gear (traps and buoys) and
the craft must be permanently identified by the permit number and/or
color code assigned to the fisherman upon receipt of his permit. The
figures on the craft must be at least three inches high to permit easy
identification from the air. The second regulation pertains to the
specific gear requirements. Wooden traps, ice cans, drums, and other
similar devices may be used provided that they are not equipped with
grains, spears, grabs, hooks, or similar devices. The traps must be
designed out of wooden slats not to exceed 3x2x2 feet or the cubic
equivalent. Only the sides of the traps may be reinforced with 16
gauge, one inch poultry wire.
Any gear used to capture lobsters must be marked by a buoy. Up to
twenty traps can be attached to a trot-line, and the line is marked at
each end by the attachment of a flag buoy. Buoys used must be of suffi
cient strength and buoyancy to remain continuously afloat. Any device
not conforming to the specifications listed, or not carrying a valid
permit number, may be seized and destroyed by enforcement officials. It
is unlawful to interfere with anyone's traps or markers without the
owner's permission.
In 1S53 the closed season was set between April 15 and August 15,
and in 1955 it was placed at its present interval of March 31 to


Thousand pounds Thousand pounds
Traps per fina (x¡)
Rounds per weeks (x2)
500 1,000 1,500 2,000
Square feet of craft (xi,)
Figure 11. Firm harvest functions with respect to effort measured as gear (Xj),
fishing intensity (X?_, X3), firm size (X^), and adjusted for fishing
grounds (X5, X6)
O'.
o


127
criterion (BEC in Column 17, Tabic 17) was based on the total cost or
total investment of the firm. This information was transformed into
average product per trap required to cover operating costs and license
fee. Thus a given firm may decide to fish a particular season if the
owner feels he is capable of harvesting an amount equal to or greater
than the BEC per trap.
To obtain the values for BEC. total cost per firm (Column 5 plus
Column 11, Table 17) was divided by the number of traps fished per firm
(Xi, Column 1, Table 17) which was multiplied times the ex-vessel price
(P ). Total firm cost includes the new license fees. The result was
y
the average product per trap (Q/X^) required to cover costs.
To evaluate this criterion, landings per trap derived from the
various data used in this study were compared with estimates of BEC for
comparable input levels. Landings per trap (Q/Xq) for the industry from
1963-73 ranged from a low of 29 pounds in 1973 to a high of 49 pounds in
1966. Landings per trap in the cross-sectional sample ranged from a mini
mum of 10.68 pounds to a maximum of 54.86 pounds for firms fishing 665
and 401 traps, respectively. The median for the sample was 21.43 pounds
for firms fishing 560 traps. The data in Table 18 illustrate the median
and mean landings per trap for the given range of number of traps fished
(X¡) in the sample.
The relatively low values of average landings per trap in the time-
series and cross-sectional data may be due to over-capitalization in
traps since no limits exist on traps. Estimated average landings per
trap (Q/Xj) with the harvest rebate program are higher than comparable


LIST OF TABLES (continued)
Table
19
Page
Analysis of landings per trap required to breakeven
under the harvest rebate program for alternative
levels of traps per firm (X^), economic study of
Florida spiny lobster industry 129
x


63
and time-series analyses, but cone knowledge of levels of expenditures
and profit maximization can be gained using results of the time-series
industry analysis thus far.
Value marginal products for given inputs were derived by multiply
ing constant product price times the respective marginal physical pro
duct. The value marginal product equation for traps per firm (Xj) is^
A
Pi
VMP = P MPV = P ( 7) (29)
Xi y Xi y 2
where,
P = annual average dockside price per pound of lobster,
assumed constant;
A
Pi
- -- = marginal product of Q with respect to input X^ (Equation
X1
23).
VMP is the addition to industry total revenue as a result of a roargi-
X1
nal increase in traps fished per firm. VMP,, was divided by the number
X1
of firms in the industry in 1973 (399) to demonstrate the effect of
price changes on an individual firm (Figure 9).
2
Product prices per pound used in the analysis were $1.08, $1.25,
$1.50,and $2.00. In this price range the value marginal product ranged
from approximately $4.81 to $140.00 as traps per firm vary from approxi
mately 900 to 168, respectively. At a product price of $1.08 and traps
per firm at the mean level for 1952-71 (368) the VMP was $23.77. If
X1
the cost for an additional trap were $28.77, this would be the profit
VMP is with respect to the subscript (x^) denoted in Equation 29.
2
Mean ex-vessel price of $1.08 per pound was obtained from a .
survey of 25 Lobster boat captains taken in 1973.


10
Scientific research in the U.S. on spiny lobster began as early as 1916
(Allen [1] Barnhart [2], and Crawford [19]), but it was not until 1944
that an investigation of the Florida spiny lobster fishery was conducted
by the Marine Laboratory at the University of Miami (Smith [42, 43]).
A review of studies since 1948 provides considerable information that
may be useful in explaining the behavior of landings (Smith [42, 43],
Cope [17], 3utler and Pease [9], Dees [22], Cnislett and Yesaki [15],
and Ting [46]).
Smith's publication in 1958 [43] provides a most complete discus
sion of the Florida spiny lobster fishery including taxonomy, biological
cultivation, fishing gear and methods, dollar value and importance of
the fishery, and state regulations of the fishery. Several other stud
ies published since 1958, including Butler and Pease [9], Chislett and
Yesaki [15], Cope [17], and Ting [46], updated some of Smith's findings.
Butler and Pease [9], and Chislett and Yesaki [15] determined the
feasibility of developing spiny lobster fisheries off coasts of Panama
and Jamaica, respectively. Although they primarily compared types of
gear and fishing techniques, some biological and environmental observa
tions were documented. Cope [17] analyzed alternative gear and fishing
techniques in the Florida fishery. Finally, a recent study by Ting [46]
analyzed the potential for spiny lobster cultivation from a physical
production standpoint but alluded to economic implications. The infor
mation obtained from these studies is briefly summarized.
The Florida spiny lobster (Panulirus arqus) is one of 30 species
distributed nearly world wide in tropical and sub-tropical waters.
They differ from the Northern cold-water lobster (Homardie family) in
that they lack claws and have long antennae for sensing food and danger.


33
In the lobster fishery Ej (land) is not a factor, therefore, Ej drops
out of the theoretical equation. (labor) and E4 (management) are
transformed into output in the production process through the fishing
traps (the primary type of gear used in Florida). Therefore, Xj, traps
per firm, is substituted for E and E4. The remaining production factor
E3 (capital) is represented by both number of traps per firm and number
of firms (measured by number of boats and vessels) X2. Thus X2 is sub
stituted for E3. The biological factors population of mature progeny
(Sj) and parent population (S2) are not available from secondary data.
However both have been shown to be a function of environmental factors,
(S3), in the previous chapter. Water temperature is one of the many
variables which can be used to represent the environment. Water tem
perature however has been shown as a significant factor affecting lob
ster landings (Bell [3]) and thus was used in this study as a proxy for
S3 and is denoted as X3. Thus with these assumptions and substitutions
Equation 12 can be rewritten as
Q = f(Xl9 X2, X3) (13)
Variables in the reduced form equation for the industry harvest function
(Equation 13) are compared to variables in the theoretical harvest func
tion (Equation 7) in Table 1.
The reciprocal form of the yield function was selected because it
is consistent with current conditions and regulations in the industry.
Management regulations such as minimum size limits, gear restrictions,
prohibition of egg stripping and a fishing season set after spawning,
insures some maximum level of stock. The reciprocal function allows
landings to reach a maximum level but does not allow total production


121
numbers of harvestors and rebate receivers, profits before and after the
program, percentage changes in these profits, revenues and costs to the
state, production revenues and costs, and landings with and without the
program. The remainder of this section discusses the assumptions of the
example and the results of some of the specified levels of traps per
firm.
Assumptions
License fees were arbitrarily assigned and were assumed politically
acceptable as were administrative costs for implementation and enforce
ment of the program. Lobster fishermen were assumed to be profit maxi
mizers and thus would select the alternative which was most profitable
to their individual firm.
The ratio of harvesters to rebate payment receivers was determined
by the minimum number of firms (400 in total) required to land the de
sired industry harvest level of 5 million pounds for a given level of
traps per firm. Rebate receivers were maintained at their previous pro
fit levels. License fees were assigned with several objectives in mind,
one of which was to allow harvesters to earn a profit at least five per
cent higher than their previous level (Column 12).
Another major objective in assigning the level of the license fee
was to collect the required revenue to maintain a self-supporting pro
gram, assuming administrative costs were not greater than $250,000. In
addition, higher license fees were assessed for firms fishing larger
numbers of traps since profit percentages per firm increase as the num
ber of traps per firm increases. License fees ranged from $1,000 for
firms fishing 429 traps each to $17,000 for firms fishing 1000 traps each.


120
After the three-week deadline licenses and rebate certificates
would be issued. Licenses would be paid in installments of 25 percent
down; 40 percent by September 15th, since August is usually the best
harvesting month; 25 percent by November 1st; and the final 10 percent
by the first of the year. The installment plan would closely parallel
the timing of the majority of landings. The balance of the license fee
would be paid by the first of the year when the majority of the stock
has been landed. Rebate payments would be made at the same time and
rate.
Alternatively, an auction system could be set up to determine the
first round of harvesters and rebate receivers. This has been suggested
in the literature in a theoretical framework that essentially equates
marginal cost and marginal revenue. This approach could also be used if
economic rent is an important consideration of the analysis, a point with
which this study has not been concerned.
Regulation of the harvest rebate program should not be any more
expensive than the cost of current regulatory programs. All craft and
gear must be easily identifiable from the air. More thought should be
given to legislation and regulation of designated fishing areas prohibit
ing trespassing of all non-licensed fishermen.
Hypothetical Example and Analysis of Harvest Rebate Program
The structure and bioeconomic status of the spiny lobster industry
was analyzed under the harvest rebate program assuming various levels of
traps per firm. The levels of traps per firm selected were previously
used throughout this study and ranged from 200 to 1000 traps per firm.
The results of this analysis are presented in Table .17 and include


5
diesel engines approaching 500 h.p. Average cost of the hull for this
sample was $8,748. The range was from $400 for a sixteen-fooc fiber
glass skiff to over $20,000 for wooden and fiberglass vessels with a
maximum length of 55 feet.
In 1959 a wooden lath trap complete with buoy and line cost an
average of $6.00 each. In 1974 average cost of materials alone for a
wooden lath trap was $11.00. The cost was a few dollars more if the
trap was used for deep-water fishing. Average cost of fishheads used
for bait was 5 cents per pound in 1959 compared with 11 cents per pound
in 1973. The prime interest rate increased from approximately 6 percent
in 1959 to 9.5 percent in 1973 signaling a substantial increase in the
cost of capital.
Spiny lobster captains surveyed in 1974 claimed the costs of petro
leum based products, such as polyethlene rope, styrofoam buoys and fuel,
were triple 1973 prices. Engine costs were increasing at the rate of
15 to 25 percent per year. Fiberglass boats were increasing in cost at
similar rates. Because of the shortage of cypress lumber the cost of
cypress lath for trap construction was also increasing. In addition,
the introduction of sonar and other fish locating devices, hydraulic
pullers, and ot.her harvesting improvements, has substantially increased
the capital investment which the commercial lobster fisherman must make
to remain competitive. The increase in number of traps used per fisher
man represents a substantial increase in investment.
One problem that appears to exist in the fishery is a resource al
location problem . "over-investment" in capital (gear and craft) and
labor (fishermen). Too many inputs are employed to produce a relatively
fixed supply of spiny lobsters. This is reflected in the substantial


49
Department of Commerce secondary data on landings, total value of
landings, and effort for 1963-73 were used for the time-series analysis
[18],[49]. Measures of effort for the industry during this period were
total number of traps; total number of vessels; total number of boats;
total number of fishermen classified as, on vessels or casual; and total
gross tonnage of vessels in the industry. Gross tonnage was measured
only for vessels greater than 5 gross tons and was loosely defined as a
measure relating to the net capacity of the craft. Water surface tem
perature data was acquired from Ocean Survey Branch of NOAA [52]. It
was assumed that surface water temperature and bottom water temperature
vary in proportion in this study. This assumption was based on findings
from a study by Robinson [39] that concluded no thermoclines exist, or
the water is isothermal in the delineated study area. Temperature data
for the study period was in the form of mean, minimum, and maximum
monthly temperatures for three stations located at South Miami, Marathon,
and Key West.
Sample Selection and Size
A sample of the population was drawn since surveying the total
population was impractical from a cost and time standpoint. Sample size
was determined using the following formula:"*'
n
2
(N 1) D + S
where,
n = sample size,
(19)
This formula was obtained from Mendenhall [33j.


93
Estimated earnings and costs for the input levels are also presented
in Table 11. These estimates are with respect to 1973-74 season stock
levels and environmental conditions.
Policy Implications
The estimated MSY of six to seven million pounds presented in
Chapter IV currently has not been attained. Landings are within 20 to
40 percent of this estimate of MSY. It appears unlikely, given the
estimated MEY of 5.8 million pounds, that fishing effort will cause
landings to surpass MSY, at least in the near future. This is based on
the fact that 7 million pounds are not reached until 649 firms enter the
industry with 700 traps each. With the 400 firms presently in the in
dustry each would have to fish 1,000 traps to harvest 7.2 million pounds.
These levels of inputs are considerably above typical levels found in
the industry. Therefore, the current major concern facing the regula
tory agency is maintaining a politically acceptable maximum economic
yield (MEY) for the industry.
From the evaluation of MEY it is obvious the policy maker is faced
with numerous choices of combinations of traps per firm and number of
firms. The optimum combination of these resources depends on the states
management objectives. For example, objectives based upon a strict pro
fit maximization motive may lead to regulatory legislation that would
reduce the current number of firms to less than 300 (based on Table 11),
allowing only the most efficient firms to operate. Conversely, objec
tives based on a social welfare optimization motive may very well en
courage maximum entry of less efficient firms. The number of firms
would be limited only by the probability of landings surpassing MSY.


75
rounds per week for fishermen that pull all their traps every two
weeks.
Interpretation of these estimates of Mi must be treated with
x2
care. First, the data represent seasonal mean levels of landings re
lated to rounds per week which vary greatly from week to week throughout
the season. During August, the first month of the season, the mean set
period for the 25 total firms in the sample was 5.3 days. By March,
the last month of the season, the mean was 13.3 days. The March mean
was for only 20 of the 25 sample firms since some of the larger, multi
ple specie fishermen usually stop lobster fishing by the end of December
Although this question was not specifically asked in the interview
a considerable amount of information was volunteered that indicated the
maximum level of set period, relative to poaching and vandalism, was
correlated with location of fishing ground to populated areas, distance
from shore, and depth of water. The remarks indicated that approximately
four days was the maximum length of time traps could set between harvest
periods, particularly at the beginning of the season. This could be
extended tc six days if either the traps were in sight of land or firms
banded together in groups to fish an area several miles from shore.
Weeks fished per season (x3)
Landings increased very rapidly the first few weeks of the season,
then leveled off. Recall that in Figure 11 it was shown that approxi
mately 54.5 percent of total landings for the 36-week season are harvest
ed within the first six weeks. This was supported by the estimated out
put elasticity for weeks. £3 shows that landings increase .37 percent
for a one percent increase in weeks fished. Expected weekly landings


Table 13. Analysis of alternative levels for number of traps per firm (Xj) assuming number of firms (X^) equals 400, mean
seasonal water temperature (X3) equals 77.591F, and ex-vessel price per pound (F ) equals $1.08, economic study
of Florida spiny lobster industry ^
vO
CO
Note: Asterisks highlight minimum and maximum positive profits for firms and/or industry and respective level of traps per firm (Xj)


94
As more biological information concerning MSY becomes available,
the relationship between MSY and KEY will become more useful in develop
ing management guidelines. An analysis of the impacts of a wider range
of various combinations of inputs and management objectives is presented
in the next section.
Discrete Analysis of Alternative
Combinations of Firms and Traps Per Firm
Extreme variation may occur in the impact of the different manage
ment programs, depending on which resource (X^ or X2) is manipulated and
to what degree. Thus it is extremely important to know the impact of
various combinations of these resources in order to design policy goals
and select parameters for management programs. To illustrate this point
Tables 12 and 13 were developed to show the impact of various combina
tions of traps per firm and numbers of firms, measured as landings
(Q, q), total revenue (TR), total cost (TC), and profit (IT) for the
industry and the average firm. Table 12 was developed for various num
bers of firms in the industry holding traps per firm at 700 traps.
Illustrated in Table 13 are various levels of traps per firm holding
number of firms at the 1973-74 season level of 400 firms.
Alternative Number of Firms in the Industry
Seven hundred traps per firm were assumed because this figure was
felt to be a realistic estimate given results of the various analyses.
In the previous chapter, the average number of traps per firm in the
cross-sectional firm analysis was found to be 842 for the size group with
the highest profits. The average number of traps for the group with the
second highest profit level was 561. For these two groups combined


CHAPTER IV
EMPIRICAL MODEL AND DATA
The empirical model and estimation procedure are presented in this
chapter in three parts. Types of data used are included in the presen
tation of each structural equation. Delineation of the study area and
the method of data acquisition is presented in the final section.
Estimation and theoretical analysis of the industry harvest func
tion are presented in the first part of the chapter. The second part
of the analysis is concerned with estimation of a firm harvest function
and associated optimum resource allocations for the firm at estimated
fishery stock levels. Implicit industry factor prices and costs were
derived in the firm analysis. The final part of the analysis involved
integrating the results from the industry and firm analyses to estimate
maximum economic yield (MEY) for the industry.
Definitions
A few definitions at this point may help clarify relationships
within the model. The industry hardest function was estimated using
secondary time-series d3t.a for 20 years from 1952-71. The firm harvest
function was estimated using primary cross-sectional data obtained from
a survey conducted in 1974 of 25 full-rime spiny lobster fishermen.
Capital letters are used to represent variables relating to the industry
harvest function, while lower case letters are used to represent vari
ables related to the firm harvest function. The only exception to this
36


86
Key. Fishing in the region below big Pine to Key West most probably
does not increase a firm's profits compared to fishing the area from
Big Pine Key up to Lower Matecumbe Key. The model would have to be
respecified to determine if there exist only two significantly dif
ferent fishing grounds (regions), i.e., above and below Lower Matecumbe
Key. Empirical values for the fishing effort and price variables viere
held at the respective 1973 levels: 618, for ; .834, for X£; 33.08,
for X3; and 326.88, for X4. Product price, P was assumed equal to
$1.08 per pound.


ACKNOWLEDGMENTS
My debt of gratitude for assistance during my graduate career
exceeds my ability to provide acknowledgment. I trust that my many
unrecognized benefactors will assume my great appreciation and thanks.
The greatest debt should be acknowledged first. Mine is to my
wifas Susan, for her moral support, understanding, and patience.
Fred Prochaska served as Chairman of my Supervisory Committee,
academic and professional advisor, and friend. Joe Havlicek provided
substantial guidance during stages of the final draft. W. W. McPherson
provided a wellspring of experience from which I have freely drawn as a
student and as author of this dissertation. Jim Cato provided compre
hensive critique that greatly improved the overall quality of the final
draft. Jim Heaney and Gary Lynne also provided constructive criticism
of the study. For tnese contributions, as well as many left unmentioned,
I am grateful and wish to thank the members of my Supervisory Committee.
I wish to thank Leo Polopolus, Chairman of the Food and Resource
Economics Department of the University of Florida, for providing finan
cial assistance during my graduate career. In addition, I wish to
extend my appreciation tc Lloyd Johnson and Pete Maley of NMFS and to
members of the Summerland Key Chapter of O.F.F. for their contributions
during the survey of spiny lobster captains.
I am else Indebted to Ms. Sandy Waters end Ms. Carolyn Aloeter for
their indispensablehelp in the voluminous typing task and numerous


32
inputs were translated into fishing effort. Although analyses of vari
ables measuring effort intensity (xo, X3, and X4) have provided useful-
production information, the principle reason for specification of these
in the model was to allow for partial estimates of the trap effect.
This model adjustment was required because the data base represented a
cross-section of firms which varied with respect to X2, X3, and X4.
Thus an optimum solution in this analysis will be limited to (a) deter
mination of optimal trap use for given (mean) levels of the adjustment
variables and (b) discussion of possible or feasible levels of X2, X3,
and X4.
The price of an additional trap fished (P ) is not simply the
X1
price of the trap but is the price of the trap and the cost of fishing
the additional trap. This latter component presented difficulty in
determining Total cost per firm was regressed on the number of
traps fished per firm. OLS regression technique assuming BLUE estima
tors was used to estimate the total cost function (TC) expressed in
Equation 47:
TC = $1,876 + $11.55 X! (47)
The coefficient of determination corrected for small sample size (R?)
was .53 and the estimated coefficient ($11.55) for traps per firm was
statistically significant at the 99 percent confidence level (t-value
equal 5.328). The constant term ($1,876) was interpreted to represent
fixed costs which do not vary with level of trap use. The coefficient,
$11.55, represented the marginal factor price of an additional trap
fished. Total costs were used for estimation rather than variable costs
because a large component of trap cost was included in fixed cost


106
required, as indicated by the zero slope of the lower left-hand ridge
line. The feasible range for traps per firm increased above 250 traps
as revenues remained above costs.
Summary of Management Tools
When combined with reliable input cost information, isoquant analy
sis can be a very effective tool in evaluating the impact of management
strategies. Discrete analysis is useful if one of the input levels has
been pre-determined, which may often be the case due to social and in
stitutional constrains!. An unconstrained maximum economic yield can be
determined by solving the first order conditions of the industry profit
function. If inputs are limited, maximum economic yield can be derived
by substituting the particular input constraint and an estimate of the
optimal profit maximizing level cf the other input into the bioeconomic
industry harvest model.
These tools have been developed as a result of this study to aid in
the design and evaluation of management strategies. With this goal in
mind the remainder of this chapter is devoted to analyzing a few selected
traditional management programs and a suggested management strategy de
signed from the tools presented in this study.
Analysis of Traditional Management Programs
Types of traditional management programs considered in this study
were (a) regulating inputs through licensing and (b) issuing landings
quotas. Specific evaluation criteria included were industry revenues,
harvesting costs, and enforcement costs. Revenues to the state to cover
implementation and enforcement costs were analyzed with respect to
revenues available from license fees and/or taxes on landings.


83
through depreciation.1 The estimate of optimum number of traps per firm
(xj) using this factor cost estimate is presented in Table 9 with respec
tive landings, profit levels, total revenue, and total cost.
Table 9. Optimum levels of trap usage per firm and resulting levels of
profits, total revenue, total cost, and landings given trap
cost, economic study of Florida spiny lobster industry
Optimum
level of
trap use
Trap
factor
price
(P )
X1
Total
revenue
(TR)
Total
costs
(TC)
Profits
(n)
Landings
(pounds)
$11.55
1,491
$22,742
$17,221
$3,863
21,057
The optimum level of traps given a factor price of $11.55 was 1,491.
Relatively small variations in the factor price of a trap produce signif
icant changes in the estimated optimum level of traps. The highly vari
able nature of the optimum solution is significant in that it offered a
possible explanation for the rapid increase in trap usage in the industry.
Relatively small changes in product price (P ) or factor price of a trap
(P ) resulted in considerable expansion of fishing effort on trap usage.
X1
This finding justifies further consideration of trap usage in management
considerations in the following chapter.
Before closing this chapter consideration of the remaining independ
ent variables is warranted, given the earlier significant estimates of
their marginal effects. One crude method for estimating the factor prices
for X2, X3, and X4 involves dividing total cost or total variable for
each by the mean input levels of each of these factors. Estimates of
Traps have an average life expectancy of three years.


8
A literature review of theoretical and/or applied bioeconomic re
search is presented in the next chapter. The theoretical model is
presented in Chapter III while the data and empirical model are presented
in Chapter IV. Results of the analyses and their practical interpreta
tion are given in Chapter V. Four management alternatives and resulting
policy implications are reviewed in Chapter VI. Chapter VII, the final
chapter, includes a summary, conclusions, and suggestions for further
research.


70
landings (Table 5). The range in error of estimated landings was com
puted by expressing the antilog of the standard error of the estimate
(SEE) as a percentage of the total estimated value. For Equation 31
landings varied from 31.5 percent above to 24.0 percent below the
estimated harvest values.
Table 5. Regression statistics for the cross-sectional firm harvest
function model, economic study of Florida spiny lobster
industry
Independent
Variables (x.)
1
Estimated
Coefficient (8^)
Standard
Error
t-Ratio
Significance
Level of
Probability
Constant (u)
4.09000
1.2500
1.128

Traps per firm
(xi)
.75770
.1099
6.895
.9999
Rounds per week
(X2)
.43991
.2772
1.587
.8700
Weeks fished
(X3)
.37211
.2400
1.550
.8615
Craft size
(x4)
.30876
.1358
2.274
.9645
Upper Keys area
(X5)
.44455
.1493
2.977
.9919
Lower Keys area
(X6)
.13063
.1653
.790
.5603
Note: R2 = .8223
, R2 = .9310, d.f.
= 18, SEE =
.2742, F6>
18 = 19.514.
The relationship of landings to effort (xj, X2, X3 and,x4) for the
firm is presented in Figure 11. Adjustments to the firm harvest function
for the influence of different fishing grounds is also illustrated.
An analysis of the estimated effort coefficients (Equation 31)
indicated that the function is homogeneous of degree 1.87848 and thus
defined an industry exhibiting increasing returns to scale. The theoret
ical interpretation was that the marginal returns to a simultaneous


APPENDIX G
TOTAL PRODUCT AND MARGINAL PRODUCT
EQUATIONS FOR FIRM HARVEST FUNCTION MODEL
(x j) TRAPS
In q = A.41843 + .7577 In x3
In MP = 4.07715 .2423 In x,
*1
(x2) PWK
In q = 9.367628 + .4399 In x2
In MP = 8.5787272 .5601 In x2
x2
(x3) WEEKS
In q = 7.985825 + .3721 In x3
In MP = 7.101433 .6279 In x3
x3
(x4) LOWD
In q = 7.4999502 + .3088 In x4
]n MP = 6.526395 .6912 In x4
x4
(z) DAYS IN SET PERIODS
x2 = 7/z
|* 4.23501 x1Plx363x4^z~(62 + 1} = 12116 z"1-43991
In MPz = 9.40232 1.43991 In z
148


160
[11] "An Economic Theory of Common Property Fishery
Resources," NMFS, ERD, File Manuscript No. 66, July, 1970.
[12] "The Biological and Economic Objectives of
Fishery Management," NMFS, ERD, File Manuscript No. 140,
September, 1971.
[13] Carlson, Sune. A Study of Price Theory of Production, New York:
Kelly and Millman, Inc., 1956.
[14] Cheung, Steven N. S. "Contractual Arrangements and Resource
Allocation In Marine Fisheries," Economics of Fisheries
Management: A Symposium. Edited by A. D. Scott, 1960.
[15] Chislett, G. R. and M. Yesaki. "Spiny Lobster Fishery Explora
tions in the Caribbean," UNDP/FAO Caribbean Fishery Develop
ment Project, Bridgetown, Barbados, 1971.
[16] Christy, Francis T., Jr. and Anthony Scott. The Common Wealth in
OceanFisheries, Baltimore: The John Hopkins Press, 1965.
[L7j Cope, C. E. "Spiny Lobster Gear and Fishing Methods," U.S.
Department of Interior, Fish and Wildlife Service, BCF,
FL No. 487, 1959.
[18] Council of Economic Advisors, Economic Report to the President,
Annual Report of the Council of Economic Advisors, Washington,
D.C.: U.S. Government Printing Office, 1975.
[19] Crawford, D. R. and W. J. J. DeSmidt. "The Spiny Lobster,
Panullrus argus, of Southern Florida: Its Natural History
and Utilization," Bulletin of the U.S. Bureau of Fisheries,
Vol. 38, 1923.
[20] Crutchfield, J. A. "Economic Objectives of Fishery Management,"
The Fisheries: Problems in Resource Management, ed. J. A.
Crutchfield, Seactle, Washington: University of Washington
Press, 19o5.
[21j Crutchfield, James and Arnold Zeliner. "Economic Aspects of the
Pacific Halibut Fishery," Fishery Industrial Review, U.S.
Fish and Wildlife Service, Vol. 1, No. 1, April, 1962.
[22] Dees, L. T. "Spiny Lobsters," U.S. Department of Interior, Fish
and Wildlife Service, BCF, FL No. 523, 1968.
[23] DeWolf, A. Gordon, The Lobster Fishery of the Maritime Provinces:
Economic Effects of Regulations, Bulletin of the Fisheries
Research Board of Canada, Bulletin 187, Ottawa, 1974.
124] Dow, Robert L., Frederick WT. Bell and Donald M. Harrimgn. "Bio-
Eccnomic Relationships for the Maine American Lobster Fishery,
with Consideration of Alternative Management Schemes," NMFS,
ERL', File Manuscript No. 149, April, 1973.


APPENDIX H
Table HI. Comparison of spiny lobster production practices by craft
length for firms sampled, Florida Keys, 1973-74 season,
economic study of Florida spiny lobster industry
Craft length
(feet)
Item
Unit
16-22 24-28
31-36
40-55
Traps fished
no.
341
561
842
809
Traps lost:
Number
no.
98
193
318
371
Percent
%
29
34
38
46
Traps fished per day
no.
139
190
202
272
Hours fished per day
hrs.
7
8
8
9
Pulls per season
no.
27
27
25
27
Weeks fished
wks.
35
36
33
25
Trips per season
no.
66
103
89
48
Boat and vessel size:
Length
ft.
20
26
34
46
Width
ft.
7
9
12
15
Volume of Lobsters:
Per trap
lbs.
18
22
22
20
Per week
lbs.
175
339
549
636
Per trip
lbs.
93
118
204
331
Note: Data reflect averages for classes of craft size.
149


84
total cost (TC), total revenue (TR), firm profit (II), landings (q), and
optimal levels x2, x3, and x4, given the crude factor estimates of P^,
P and P are presented in Table 10. The remaining variables used in
x3 x4
the estimation procedure are assumed constant at their sample mean.
Table 10. Optimum levels of adjustment factors (x2, x3, and x4) and
resulting levels of profits, total revenue, total cost, and
landings per firm, economic study of Florida spiny lobster
industry
Optimum
level of
factor
use
<*i>*
Factor
price
deri
vation
Estimated
factor
price
(P )
x.
X
(dollars)
Total
revenue
(TR)
(dollars)
Total
costs
(TC)
(dollars)
Profits
(n)
(dollars)
Landings
(pounds)
.834
TVC
p
x2 x2
6,149.88
12,084
5,129
6,955
11,189
10.30
p _TC
X3 x3
273.00
7,559
2,812
4,747
6,999
179.11
p
x4 x4
17.70
9,690
2,991
718
8,972
Optimum number of rounds per week, or total percentage of traps
pulled was .834."*" The imputed factor cost for rounds per week was de
rived by dividing average total variable cost per firm from the sample
by the mean level of rounds per week for the sample. Coincidentally,
*
the optimum level of rounds per week (x2 ) was equal to the mean of
rounds per week from the sample (x2) which resulted in a $6,955 profit
for the typical firm. Imputed factor costs for weeks were derived by
Length of set period, measured as days, is derived as follows:
Days set period = ,
Xo


122
Total cost per firm was constant regardless of whether a license
fee was assessed because the number of traps was assumed constant among
firms. Underlying criteria used to arbitrarily assign program costs and
revenues were primarily based on the number of fishing firms (harvesters)
to be supervised and relative profit levels of these firms.
Number of traps per firm at 700
The maximum number of firms required to harvest the desired industry
level of 5 million pounds was estimated to be 171 firms fishing 700 traps
each (Table 17). If only this number of firms choose to participate in
a harvest rebate program as harvesters, 229 firms would elect not to fish
for lobsters and would collect a rebate payment of $7,733 each for the
season (Row 3, Columns 6 and 16). These rebates would cost the state
$1.8 million ($7,733 x 229). Revenues for harvesters in the program
would increase approximately 179.2 percent to $21,593 per firm before
license fee charges (Row 3, Columns 7 and 8). At this rate the state
could charge a maximum license fee per firm of $13,860 and the firm would
be at least as well off than before the program at $7,773 profit per firm
(Row 3, Columns 6 and 10). Approximately $2.4 million (Row 3, Column 9)
in revenue to the state for rebate payments and management of the indus
try would be generated.
Assuming the regulatory agency set the license fee at $11,500 to
cover rebate payments and program expenses, total profit per firm (har
vester), estimated to be $10,093, would be 30.5 percent above profits
before the program. Rebate receivers would collect as much as they were
making before the program without expending any costs. In addition,
these firms could invest their time, skills, and capital elsewhere.


17
This is evidenced in a recent publication edited by Sokolosk.i [A5J
in which several researchers addressed the issues and problems encoun
tered when dealing with research directed toward managing marine re
sources. Sokoloski defined a critical area of marine resources research
to be the measurement of the gap between the "optimum" management solu
tion for a given fishery and current management arrangements. To empha
size the relative lack of success with this objective, he listed several
critical issues that have been complicating current research efforts.
They were characterized as empirical and conceptual in nature and multi
disciplinary in scope. One conclusion drawn after reviewing this publi
cation is the fact that substantial uncertainty exists with respect to
the reliability of results in marine economics research and accordingly
the proposed management programs. Many of these problems need to be
solved before sound management programs can be developed for many of the
species. Determination of optimal solutions will require considerable
time, effort, and financial resources.
Pontecorvo [35] pointed out in his work with Pacific red salmon
that the costs of improving information may exceed the benefits. This
should be taken into account when deciding the value of increasing the
sophistication of models designed for direct applicability in managing
a particular fishery. Consequently, when a researcher is given the task
of developing management alternatives for a currently existing real
problem as in the case of the Florida spiny lobster fishery, he is often
not allowed the luxury of exhausting all methodological possibilities in
his investigation due to the reasons previously discussed. Because of
this he uses what resources are available, such as traditionally accept
able or validated theories in economics and marine biology. For



increases in inputs (traps, vessels, and gross tonnage) compared with
the increase in landings. The broad over-investment problem of the
fishery begins with the fishermen. Capital and labor investments in
crease at the fishermen's level due to (1) a struggle to overcome a
severe price-cost squeeze; and (2) interdependencies in the production
function creating negative externalities to the fishing firm or producer.
As a consequence of this increaseing level of effort, a second
problem of the fishery that may be occurring is one of "over-exploita
tion" of the fishery stock. Decreasing stock levels can cause serious
long-term damage to the fishery and welfare of fishermen.
Objectives
The overall problem is defined as one of resource allocation. The
general objective is focused upon the determination of an optimal allo
cation of resources for selected price, cost, and fishery management
alternatives. Optimal allocation may entail protecting the stock from
reaching a level beyond recovery as well as regulating economic factors
of the fishery.
The specific objectives are
(1) To identify the major factors affecting the quantity of
spiny lobster harvested, and to estimate the harvest
function of the Florida spiny lobster fishery;
(2) To evaluate the potential substitution between specific
resources used to harvest spiny lobster in Florida;
(3) To determine an optimal combination of inputs for the
Florida spiny lobster fishery; and


25
Biological Theory of a Fishery
The harvest function, or yield function, (Equation 1) form a biolog
ical point of view represents the level of biomass (or stock of fish)
that can be harvested. The equilibrium level of biomass is that which
can be harvested without changing or damaging the parent stock. The
yield function may be expressed as
Y f(Stock) (1)
D
where,
\' ~ the amount of biomass available for harvest, and
Stock = the t.ocal biomass of fish.
This system is exclusive of the influence of man. Biological theory
states that the change in the stock of a fishery will follow an S-shaped
curve as shown in Figure 1. This theory has been supported by findings
from population studies of deer and insects. Additional support is pre
sented in a recent study by Gates and Norton [27] who estimated an S~
shaped curve for the yellowtail flounder fishery of New England. An
S-sbaped curve suggests that the population increases (a) slowly at
lower levels, limited by the reproductive capabilities of smaller num
bers and the smaller number of fish that are actually growing; (b)
rapidly in the intermediate range, as larger numbers of fish produce
more eggs than can survive and food supplies are adequate; and finally,
(e) slowly at higher levels where pressure from limited food supplies
impedes the population growth in an equilibrium manner and deaths just
offset births. Therefore, stock is a function of the biological
^The material in this section was primarily developed from the
following references: Bromley [8], Carlson [10], Christy and Scott [16],
Cheung [14], and Prochaska and Bsarda [36].


27
of the progeny; and the natural mortality rate due to diseases or due to
changes in the biological process. Parent population is a function of
the environment, growth rates, and mortality rates. The response of
the parent population to the variables may differ for various levels of
parent stock.
Numerous environmental factors significantly affect the biological
process. Significant factors are the food supply, predators other than
man and hydrographic characteristics including water temperature,
salinity, bottom conditions, currents and atmospheric conditions.
The relation between the number of mature offspring and the parent
population may be derived from these basic biological relationships
The recruitment of mature progeny is of particular interest since that
is an important policy variable used in developing management schemes
that will maintain seme equilibrium level of catch. The relationship
between mature progeny and parent population is a function of the same
variable affecting growth. At very low parent population levels re
cruitment is low because the number of spawners is small. As the parent
population increases, the level of recruitment increases. After some
population level is reached, recruitment levels decline for reasons due
to the environment and biology of the species, such as unhealthy fish
stocks, an inadequate ecological niche, declining growth rates, increas
ing mortality rates, severe competition for food, and adverse hydro-
graphic conditions. Thus, at some intermediate population level, the
ability cf spawners to recruit progeny into the standing population is
a maximum. At low population levels, growth rates are relatively low,
but beyond some population level, the growth rates decline and natural
mortality rates are relatively high.


7
(4) To evaluate the impact of selected management programs
on resource allocation in the fishery and on the optimum
combination of inputs used by firms. Specific programs
considered are limiting licensing of firms and traps,
establishing landings quotas, and a harvest rebate program.
The results of this study will provide a basis for establishing
guidelines for managing the Florida spiny lobster fishery. The focus
is on the analysis of management strategies which might help reduce the
cost and difficulties of regulating effort. In addition, study results
can be conceivably viewed as a case study applicable, at least in ap
proach, to other marine resource allocation problems. Finally, individ
ual fishermen may use the results of the production analysis as a basis
for both long and short-run decision making.
Scope
Spiny lobsters landed in Florida are harvested from the domestic
Florida spiny lobster fishery and foreign water spiny lobster fisheries
More than 95 percent of spiny lobster landings harvested from the domes
tic fishery are landed in Monroe County. These landings comprise ap
proximately 50 percent or more in past years of all spiny lobster
landed in Florida. Without the Bahamian fishery, landings from Monroe
County make up over 90 percent of U.S. spiny lobster landings. Conse
quently, although the scope of this study is defined as the Florida
spiny lobster fishery, the data for the empirical analysis are delin
eated as that of the Florida Keys or Monroe County, Florida.
The majority (approximately 90%) of foreign water landings were
lost as a result of the 1975 closing of the Bahamian fishery.


110
license fee. Notice that beyond 400 traps per firm no regulation of
traps is needed to maintain the desired harvest of 5 million pounds if
the number of firms is limited to 400.
As estimates of enforcement and implementation costs increase the
license fee would need to be adjusted accordingly. The estimates pre
sented in this section would change as different management objectives
and values are assumed for ex-vessel price (P ) number of firms (X2) ,
and the trap license fee.
Such a program may be impractical since the number of traps per
firm is not easily regulated. It would be extremely difficult and expen
sive to regulate the number of traps a firm is fishing. However, the
above analysis provides valuable information with respect to the results
expected as number of traps per firm varies. Further analysis of imple
mentation and enforcement costs may be warranted before any attempt to
manage trap numbers can be a feasible management alternative. Otherwise,
this management program may be deferred until more cost-effective means
of regulating traps are discovered.
Licensing Firms
This type of management program is similar to licensing traps in
that it induces an increased cost per firm through a fee. As firm costs
increase only the more efficient fishermen will be able to make a profit
and remain in the industry. A program that restricts the number of firms
could also require restrictions on number of traps and/or landings but
these restrictions were net assumed in this analysis. For illustrative
purposes a license fee of $1000 per firm was assumed feasible (Table 16).1
Refer to Table 12 for some comparable levels of number of firms
(X2) assuming no firm license fee.


maximization for the firm, and (c.) incorporate the analysis of optimum
firm input levels into the MEY analysis and related analysis of manage
ment alternatives.
The firm harvest function is defined as the physical relationship
between landings and various units of effort. Effort may be generally
categorized as related to labor, capital, management, and fishing area
or location (geographical locations). From Equation 11, the general
theoretical harvest function, the typical firm harvest function can be
defined as
q f (ei, e.2, 63* > 1> 2> 3) (^-5)
where,
q = quantity harvested by the typical firm,
e¡ = attributes of the fishing process related to fishing
area (somewhat similar to land factor input),^
02 ~ labor,
63 = capital,
64 = management,
si = mature progeny,
52 parent population, and
53 = environmental attributes.
Enviroraiental and biological influences within a given area were assumed
constant for this analysis, since the data represent the lobster harvest
ing process at a given period in time. Thus, sj, S2>and S3 were deleted
Strictly speaking returns to land are to "ownership" of the
resource and has little relevance to geographical .location in most
instances. Returns to area in fishing is similar to saying a type of
soil is better than another in reference to agricultural production,
which has no relationship with "ownership" of tne various soil types.


AO
variables at reasonable maximum levels within the range of the data to
determine a range for MSY.
Maximum economic yield (MEY) for the industry was also determined
from the industry harvest function (Equation 1A). Total revenue (TR)
was computed by multiplying the estimated harvest function (Equation 1A)
by product price (P^). Py is assumed constant and representative of
current prices. was computed as the current average ex-vessel price
per pound.'*' Time-series cost data were unavailable. To determine MEY
it was necessary1 to develop an industry cost function from primary data.
A cross-sectional survey of spiny lobster firms was used to obtain the
necessary data and is presented in a later section. From these data an
industry total cost function was developed. Total industry cost (TC)
was derived by computing the average total cost per firm (ATC) for the
firms in the sample and then multiplying ATC per firm by the total num
ber of firms (N) in the industry. Together, these functions were used
to determine MEY as shown in Figure 5.
Derivation of MEY begins with the determination of the level of
2
firms at which the slopes of the TR and TC curves (Figure 5) are equal.
This is determined by equating industry marginal revenue (partial
derivative, of TR with respect to X2) with industry marginal cost (deriv
ative of TC with respect to X) and then solving for the number of
P was computed by dividing annual total industry value of land
ings bv'annual total industry landings.
2
Any input that serves as a policy variable for management pur
poses is applicable in place of firms. Number of firms is preferred
for reasons to be later discussed in this section.


65
maximization level of output. Thus as long as the cost of fishing a
trap was less than $28.77 it would pay to expand.'*' At dockside prices
of $1.25, $1.50,and $2.00, marginal cost per trap could increase to
$33.31, $39.97, and $53.30, respectively, before the input level for
profit maximization would be reached. With traps per firm (X¡) at the
1973 level of 429, VHP ranged from $21.16 (assuming a product price
A1
of $1.08 per pound) to $39.22 (assuming a product price of $2.00 per
pound). Maximum level of traps per firm observed was 482 in 1971. At
this level VMP ranged from $16.77 to $31.07 for product prices ranging
X1
from $1.08 to $2.00 per pound. These values exceed trap costs and en
courage intensification of traps fished per fisherman.
Value marginal product for an additional firm was also analyzed
while holding traps per firm (X^) constant. Value marginal product for
the firm was expressed as
$2
VMPy = P ( t) (30)
x2 y X22
where,
B2
- rr = marginal product of Q (Equation 24) with respect to firms
X2
(X2), holding X} constant.
Estimates of VMP for the mean, minimum, maximum, and 1973 levels of
X2
firms are presented in Figure 10 at the product prices used earlier.
Profit maximization will occur with 399 firms in the industry when the
total cost for the typical firm reaches $3,154, $3,652, $4,383>or $5,844,
given product prices of $1.08, $1.25, $1.50,or $2.00, respectively
'cost of an additional trap includes fixed costs for construction
find craft, and variable expenses incurred to fish the trap such as'
fuel, bait, and labor.


11
They are smaller and have numerous spines covering their back (cape) for
protection against many natural enemies. The average legal size landed
in Florida weighs approximately one and a quarter pounds and is 10
inches long, although in 1968 maximum lengths of 17 inches and weights
in excess of 10 pounds were not infrequent (Dees [22]).
Spiny lobsters generally feed at night on a wide variety of foods,
primarily small crustaceans. They also forage. During the day they
hide in rocks, coral, and other marine, growth but are known to resort to
cannibalism when crowded. Growth is primarily dependent upon the en
vironment. As body weight of the spiny lobster increases the hard outer
shell is shedded. This shedding of the shell is called molting and
occurs several times throughout the life cycle. The body weight in
creases approximately 5 percent during each molting stage. Although
younger lobsters molt more frequently, it takes approximately five
years for them to reach legal size.
Female spiny lobsters do not begin reproducing until they reach a
length of eight to nine inches. An eight-inch spiny lobster can produce
approximately 50,000 eggs compared with 500,000 eggs produced by a 14-
inch lobster. In Florida, mating occurs February through June in shal
low waters. The eggs are hatched in deeper W3ter three weeks later. It
takes the young larvae three to six months to conform to the shape of
the adult lobster. At this stage the young lobster drops to the ocean
floor and is approximately 7/8 inch long. The mortality rate from
hatching to this stage is hypothesized to he over 99 percent.
Water temperature, food supply, reproduction and weather influence
the migration of spiny lobsters. Usually migration occurs between deep
and shallow water but sometimes migration is north in the summer and


125
Number of traps per firm at 429
At 429 traps per firm the program could not support itself and would
experience a $201,560 deficit (Column 14). Only $328,000 of the $529,560
(Column 16 x Column 6) rebate payments could be met with a license fee
of $1,000. At this level firm profits would increase 17.3 percent com
pared with profits outside the program. To help make up the deficit in
rebate payments, the license fee would have to be increased to $1,535
which would decrease firm profits to 5.0 percent. Still, a $26,080
deficit in payments would remain with no budget for administrative costs.
Another alternative would be to reduce rebate payments to non-fishermen
to a profit level less than what they were making fishing for lobsters.
Assuming idle capital and labor resources were invested elsewhere, this
may be a feasible alternative.
Number of traps per firm at 350 and 200
If firms were limited to 350 and 200 traps each, all firms would be
needed to harvest the 4.5 and 1.4 million pounds, respectively. Since
more firms would be required to harvest the desired level of 5 million
pounds no management program would be needed since more firms than cur
rently exist are required to harvest MEY (Rows 7 and 8). The average
product per firm with 350 traps was 11,241 pounds and with 200 traps was
3,527 pounds. A total of 445 firms with 350 traps each, or a total of
1,416 firms with 200 traps each, could be allowed in the industry to
harvest an MEY of 5 million pounds.
Overall summary of analysis (Table 17)
For the range of 200 to 1000 traps per firm selected industry land
ings were maintained at 5 million pounds under the program, whereas


132
the fishery also raises concern about the possibility of "over-
exploitation" of the fishery stock.
The primary objectives of this study were to (a) evaluate the
extent of fishing effort in the industry and determine both the maximum
sustainable yield and the maximum economic yield, and (b) analyze alter
native management programs which would allow for a more efficient utili
zation of the fishery stock. To achieve these objectives, two analytical
models were developed for the Florida Keys spiny lobster fishery. A
bioeconoroic model was estimated for a time period in which the biologi
cal stock was allowed to vary. The second model (firm harvest function)
was estimated for a given stock of lobster resources. With these two
models the impacts of selected management programs were analyzed by
simulating the industry with respect to estimated optimum levels of
inputs.
The scope of the study was defined to include only the Florida
spiny lobster fishery. The data for the empirical analysis represented
Monroe County, Florida, since approximately 80 percent of Florida
domestic landings are landed in Monroe County.
Theoretical considerations and industry data availability required
that the bioeconomic model be estimated as a function of traps per firm,
number of firms employed in the industry, and mean seasonal water tem
perature. The mathematical form of the model was a reciprocal equation
which represented behavior consistent with suggested theory and the cur
rent status of the industry with respect to sustainable yield and pre
sent management policies. Annual time-series data from 1963 to 1973
were used for estimation. The overall explanatory power was high.and
each coefficient was statistically significant in the model.


154
III. COSTS OF PRODUCTION
A. Initial Costs (fixed costs):
1. Value of vessel (boat) (Excluding gear, electronic, and
hydraulic equipment)? ($ )
2. Type (make) and value of electronic equipment on board?
Value $ Describe
3. Replacement value of engine? $
4. Value of Hydraulic and other equipment on board? Value $
Describe.
5. Cost of insurance?
a. Protection and indemnity (P & I)? ($ )
b. Hull ($ )
6. Interest on Loan? ($ )
7. Fishing and vessel (boat) licenses and permits? ($ )
8. Trap construction:
a. Number of traps built for 1973-74 season?
b. Cost of line? ($) Type used
c. Cost of wood? ($) Type used
d. Cost of buoy? ($) Type used
e. Cost of labor used in building traps? ($)
f. Other costs (i.e., cement, oil, nails, wire)? (Specify
amount)
9. Please describe and give value of other miscellaneous initial
expenses?
B. Operating Costs (Variable Costs). 1973-74 season. Please leave
blank if the item does not pertain to your operation.
Item .... Amount Used .... Total Cost ($)
1. Fuel (gals.)
2. Oil (gals.)
3. Bait (lbs.)
4. Ice (lbs.)
5. Groceries
6. Other miscellaneous trip expenses
7. Labor costs
a. Captain share (%)
b. Crew share (%)
c. Boat share (%)
d. Wages (hours)
e. Bonuses
f. Labor taxes
g. Other (specify)
8. Maintenance and repair costs
a. Hull
b. Engine
c. Electronic equipment
d. Other machinery
e. Gear (traps)
f. Other (specify)
9. Cost of trap losses No. of traps lest
10.Other expenses (Specify)


99
firm using 618 traps.1 These estimates are not unrealistic when one
considers that the number of firms in the secondary data includes small
part-time and recreational firms with low net revenues as well as large
commercial firms.
Discrete input substitution analysis was limited by the fact that
only a limited number of selected combinations of input levels can be
evaluated. However, it was possible to evaluate all economically fea
sible combinations of number of traps per firm and number of firms in
the industry by analyzing isoquants developed from the bioeconomic
industry harvest model.
Isoquant Analysis
A production isoquant can be defined to show the various combina
tions of traps per firm (Xi) and number of firms (X2) that are capable
of harvesting a given level of landings (Q). The isoquant can then be
used by analyzing the marginal rate of technical substitution between
inputs to illustrate the broad range of alternative combinations of
traps per firm and firms to achieve management objectives and the
2
ultimate limit of the use of a particular resource.
The rate at which traps per firm (X^) and number of firms (X2) are
substituted for each other is important in determining the results of
changes in the combination of inputs. This rate can be defined as the
Total costs do not include opportunity costs such as captain's
salary and returns to investment. Captain's salary was estimated at
$5,130 for the typical firm.
'Notationally Isoquants in Figure 13 can be represented as
- - 8 83
Xi = 81 [Q a -
X2 X3
]


44
stretch between the above two areas. If a one is entered for X5 and a
zero for xg the firm was fishing in the upper Keys region and vice-
versa for a firm fishing in the lower Keys region. If both X5 and X6
are zeros, the firm was fishing in the middle Keys region. These dummy
variables allow the intercept or position of the harvest function to
vary for different fishing areas.
Underlying bioeconomic theory for the firm does not specify curvi-
linearity in the firm harvest function since the stock of lobsters, or
sustainable yield, is assumed constant for a given period in time. Thus
the Cobb-Douglas functional form was selected which allows for either
increasing, constant, or decreasing returns.*' An additional reason for
the selection of the Cobb-Douglas form was that it requires fewer de
grees of freedom to derive the interactive effect among the independent
variables. The summary of these considerations and the final model for
estimation is represented by Equation 16.
A A A A A A
- 3i 62 33 34 35 36
q = axj x2 x3 x(( x5 x6 (16)
where,
A.
q = estimated landings (harvest) for the typical firm,
X-, number of traps,
x2 average number of times a fisherman pulls his total
number of traps in one week,
X3 = number of weeks fished,
= measure of craft size,
i
"A detailed discussion of the Cobb-Douglas function is presented
in Carlson [13].


Political and social considerations often make the maximum economic
yield not a feasible management alternative. In this case an analysis
of input (firm and trap) substitution was completed and presented for
alternative input and output levels. Resulting cost, revenue and pro
fit levels were determined for alternative program levels.
Specific management programs considered in the analysis include
licensing, quotas and a harvest rebate program. For each program,
maximum yield levels, costs, revenues and profits were determined. For
the harvest rebate program alternative levels of administrative costs
and related sources of revenue were analyzed.
xiii


18
example, such resources include production functions exhibiting diminish
ing marginal rates of return, downward sloping demand for a commodity,
and the bio-mass or population of a fish species which is in part depend
ent upon its environment and thus exhibiting a semi-sphere-shaped yield
curve.
Given lack of data, particularly biological data, and lack of pre
cise models which lend themselves to rigorous statistical testing, it
would appear that a reasonable criterion for model building would be
"Occum's razor," the simpler the better. This may not be too unrea
sonable since statistical testing may be more efficient, the results are
timely, completion of the project remains within the limits of the
budget, and it is questionable whether more sophisticated models requir
ing more resources would improve the results. In light of these obser
vations, the approach for this project presented in the next chapter
does not attempt to improve the theory or apply overly-sophisticated
empirical models or models requiring inapplicable assumptions or data
which are not available.
Bloeconomic Lobster Research
Bioeconomic research related to the Northern American Lobster
fishery, Bell, 1970 [3]; Bell and Fullenbaum, 1972 [7]; Dow, Bell
and Harriman, 1973 [24]; Huq, 1973 [30]; and DeWolf, 1974 [23] were
considered in the development of the present models. The latter two
publications by Bell are extensions of his early work on the American
lobster industry. All three of Bell's publications analyze impacts
of different types of management programs through changes in a general
equilibrium model. In Bell's first publication [3], a linearly


31
production process can be defined as
Ye f(E)
E ~ g(Ej, E2, E3, E4)
(3)
(4)
such that,
Ye = f(Ei, E2, E3, E4)
(3)
where,
Y = output as a result of effort,
1j
E = effort = combined unit of inputs, . E4,
Ej = land,
E2 = labor,
E3 = capital, and
E4 = management.
The assumed objective for firms in the industry is profit maximiza
tion. All firms are assumed to operate in a rational economic manner
with production occurring under conditions of decreasing returns. The
industry is assumed to have an atomistic structure with constant factor
prices and independent production processes.'*'
The biological yield function (Equation 1) is actually a physical
relationship between the various exogenous biological and environmental
attributes and the available fish stock for harvesting. The production
function (Equation 3) is a physical relationship between output and
exogenous variables representing effort. Biological models of fishery
populations without economic considerations are of little value as a
tool for developing useful policy for fisheries management. Likewise,
an economic model devoid of biological considerations is also of little
*The reader is referred to Ferguson [25] or Carlson [13] for a
complete presentation of production economics.


62
in landings would require an infinite percentage increase in inputs.
The same point is illustrated in Figure 8 but traps per firm is presented
in a more realistic range. Predicted landings increase by 40 percent,
from 5.62 to 7.89 million pounds, as a result of a 115 percent increase
in the number of traps per firm (from the maximum observed in the data
of 482 to 2,000).
Estimates of MSY chosen for analysis in this study ranged between
six million and eight million pounds with a realistic estimate probably
in the range of six to seven million pounds. This is not to imply that
landings cannot increase above these figures, but rather that these fig
ures are the levels estimated at which landings could be maintained from
year to yearmaximum sustainable harvest (yield) ceteris paribus.
Actually, the limiting factor probably is that the typical firm does not
have the capacity to reach the required trap level.
In summary, maximum harvest levels considered here are quite liberal
for several reasons. Some illustrations used extremely unrealistic
levels of inputs to achieve the maximum levels of harvest and more impor
tantly, some input levels were beyond the range of data. Estimated
landings may be beyond maximum economic yield, discussed in the next
sectJ-on. In addition, substantial input increases of this nature may
cause irreversible effects on the population, not directly observable
in the existing data on which the analysis was based. Therefore, the
realistic MSY level was concluded to be in the range of six to seven
million pounds annually.
Value Marginal Product Amtlysis
A more comprehensive analysis of maximum economic yield (MEY) is
presented in the section integrating results from the cross-sectional


50
N = population size,
2
S = estimate of the population variance,
D = B2/4, and
B = bound on the error of estimation (i.e., 10 percent on
each side)
Data from a sample of 15 observations on 1973-74 landings by individual
boats (S) and vessels (6) for sizes ranging from 26 feet to 40 feet in
2
length were obtained for estimating the population variance (S ) [51].
2
The sample was classified into six vessels and nine boats. S a pooled
variance (within craft class) was estimated from the actual survey data
to be 30,129,877.77. B was selected at 10 percent on each side of the
population mean to be estimated. N was equal to 226 and was calculated
from a list of commercial craft registrations provided by the Florida
State Department of Natural Resources. Criteria used to include a firm
in the population was (a) that the address of the craft owner be Monroe
County; and (b) that lobster fishing was listed as the primary (dollar
value) species harvested. A major limitation of this sampling technique
was that fishermen may live out of the county and fish in the study area
and vice-versa. Sample size, N, was calculated to be 21.
Stratification of the sample was based on length of craft and loca
tion of home port. Proportions in each sample strata were equal to
proportions of the population in each strata. Boat length strata were
less than 21 feet, 21-30 feet, 31-40 feet, and greater than 40 feet.
In the stratification of the study area upper Keys was defined as that
area from Key Largo to Lower Matecumbe Key. Middle. Keys was defined as
that area from Craig Key to Bahia Honda Key and lower Keys was the.area
from Big Pine Key to Key West. Based on the population as stratified


41
TC
Firms (X2)
Figure 5. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to number of firms
firms in the industry which is necessary for industry profit maximiza-
j. 2. k ,
tion, X2 The optimum number of firms, X2 is substituted into the
k
industry harvest function to determine Q defined as MEY.
Firm Analysis
The primary purposes of the cross-sectional survey and subsequent
firm analyses were to (a) provide cost estimates required to determine
MEY, (b) determine an optimum allocation of specified inputs for profit
^Notationally the derivation of X2 is a solution of the following
equalities:
(a) industry marginal revenue - industry marginal cost,
% 3TR 3TC
(b) TxT axj and
(c)
p
y
3Y
3X2
P is price of Xo.
X2


52
where,
N = sample size of strata ij,
Ch = number of craft of length class i,
= number of craft of length class i in area j,
n = total sample size to be drawn, and
N = total populatioii of craft.
Survey Technique
Observational units within each strata were not drawn randomly in
the usual sense. The data were collected in a very precarious environ
ment, at a very difficult time. Florida spiny lobster fishermen, like
most fishermen, are very independent and generally do not divulge infor
mation. So, there was first a problem of locating a fisherman that
would cooperate. A second problem frequently encountered was that many
cooperative fishermen lacked adequate records, particularly costs, so
much of the information was "best estimates." To complicate the matter,
at the time of the survey the Internal Revenue Service was investigating
Florida fishermen because a recent court ruling had changed the tax
regulation, retroactively, and thus information was highly guarded.
Also it was felt by many that a substantial amount of undersized lob
ster were "blackmarketed" from this area. In addition, any list of
fishermen was usually out of date because of the highly mobile nature
of fishermen. Given these circumstances, it was impossible to collect
data on a strictly random basis. Thus, the samples represent fishermen
who would cooperate. Personal interviews were conducted until the re
quired number of observations within each strata was accomplished.


113
be attached to the firm license to insure actual landings equal projected
desired landings.
Landing Quotas
Under this management alternative each firm would be allocated a
percentage of the desired harvest. This percentage could be based on
landing records of individual firms and desired harvest levels. The de
sired harvest level would be announced prior to the opening of the sea
son. For example if each firm of the 400 in the industry were allotted
.25 percent of an estimated 5 million pound harvest level, the landings
quota per firm would be 12,500 pounds. Profits per firm would be a
function of fixed costs plus the number of traps each firm fished since
the number of traps per firm determine total cost. In order that effi
ciency and technological innovation would not be impeded, firms could be
allowed to lease part or all of their quotas at the market price. To
prevent monopolistic practices from developing a maximum number of quotas
per firm could be established.
An alternative to establishing a constant quota per firm would be
to vary the quota per firm based on percentages of previous years' land
ings. For example, percentages could be 60 percent of the first year,
25 percent of the second and 15 percent of the third. This absolute
figure is adjusted up or down by a constant percentage per firm depend
ing on the percentage increase or decrease in the estimated sustained
yield for the coming season. Other activities such as leasing would not
change.
The license fee paid for the quota could be based on estimated pro
fits per firm in conjunction with implementation costs as discussed


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
'tim-SL £
;
mes C. Cato
Assistant Professor of Food and
Resource Economics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
:7a
Gary
Assistant Professor^ of Food ana
Resource Economics
This dissertation was submitted to the Graduate Faculty of the College
of Agriculture and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
December 1976
/( cf"
Dean, College of Apiculture
Dean, Graduate School


162
[37] Prochaska, F. J. and J. S. Williams. "Economic Analysis of Cost
and Returns in the Spiny Lobster Fishery by Boat and Vessel
Size," A Florida Sea Grant Publication No. SUSF-SG-76-004,
University of Florida, Gainesville, July, 1976.
[38] Rich, Jack. "Natural Resources and External Economics: Regula
tion of the Pacific Halibut Fishery," Ocean Fishery Manage
ment : Discussions and Research, U.S. Department of Commerce,
NOAA and NMFS, NOAA Technical Report NMFS CIRC-371, April,
1973.
[39] Robinson, M. K. "Atlas of Monthly Mean Surface and Subsurface
Temperature and Depth of the Top of the Thermocline: Gulf
of Mexico and Caribbean Sea," Scripps Institute of Oceano
graphy, University of California, San Diego, S10 No. 73-8,
March, 1973.
[40] Russell, E. S. "Some Theoretical Considerations on the 'Overfish
ing' Problem," Journal of Conservation and International Ex
ploration, March 6, 1931.
[41] Schaefer, Milner B. "Some Considerations of Population Dynamics
and Economics in Relation to the Management of the Commercial
Marine Fisheries," Journal of Fishery Research Board of
Canada, Vol. 14, No. 5, 1957, pp. 669-681.
[4V.J SmJ'b, F. G. W. "The Spiny Lobster Industry of the Caribbean."
Caribbean Research Council, Fisheries Series, No. 3, 1948.
[43] _ "The Spiny Lobster Industry of Florida," Florida
State Board of Conservation, Educational Series No. 11,
Marine Laboratory, University of Miami, 1958.
[44] Smith, V. L. "On Models of Commercial Fishing," Journal _of
E'olitlcal Economy, Vol. 77, No. 6, March/April, 1969.
[45] Sokoloski, Adam A. "The Status of Fisheries Management Research:
An Overview," Ocean Fishery Management: Discussions and
Research, U.S. Department of Commerce, NOAA and NMFS, NOAA
Technical Report NMFS CIRC-371, April, 1973.
[46] Ting, R. Y. "Cultural Potential of Spiny Lobster (Panulirus argus
Larreille)," Ecosystems Department, Battelle Northwest
Laboratories, Richland, Washington, 1,973.
[47] Turvey, Ralph. "Optimization and Suboptimization in Fishery
Regulation," The American Economic Review. Vol. LIV, No. 2,
Part 1, March, 1964, pp. 64-76.
U.S. Department of Commerce (Formerly Bureau of Commercial Fish
eries), NOAA, NMFS. "Basic Economic Indicators: American and
Spiny Lobsters," U.S. Government Printing Office, Current
Fisheries Statistics No. 627, Washington, D.C.: August, 1974.
[48]


37
is P which is always used as the ex-vessel product price per pound for
y
the industry and for the firm. Industry landings are represented by Q
and firm landings are represented by q. Variables representing inputs
into the industry harvest function are Xi, X?, and X3. Firm harvest
function input variables are xj, X2, X3, X4, X5, and x6. In only one
case does a variable from the industry harvest function and the firm
harvest function represent a similar measure of inputs, number of traps.
Xi, from time-series data, represents average number of traps per firm
in the industry for a given year, while xj, from cross-sectional data,
represents the number of traps fished by a given firm. An asterick (*)
superimposed on a variable, for example xj denotes the variable as an
op*-ir.;um solution and facilitates its identification when substituted in
different equations.
Bloeconomic Analysis
Time-series analysis is necessary to determine the direct and in
direct effects of increased effort on catch. Resulting effects of the
traditional economic production relationships are defined as direct.
Indirect effects are the influences on landings from variations in the
fish stock due to variations in effort. Time-series analysis is neces
sary because an analysis for only one point in time will only consider
the effect of effort on landings for the given fishery stock in exist
ence at that time. Evaluating effort over time also allows for the
consideration of expanding effort on the extensive marginmore firms
in the industry.
The bioeconomic model set forth earlier can be restated as
YBE h(El E2 E3, E4 Sl* S2 S3)
(12)


115
landings are considerably less than MSY thus highly accurate estimates
of MSY are not required for reasons of over-fishing from a strictly bio
logical point of view. Therefore, it is questionable whether the addi
tional research expense to accurately determine MSY is justified in the
short run for management of the spiny lobster industry.
Another possible misconception is that a quota system leads to MEY.
This is not necessarily true, particularly with respect to an industry
such as the spiny lobster industry where a large percentage of landings
are caught in the beginning of the season. With a quota system, effort
can just as easily become excessive (meaning, fishing as many traps as
without the management program) as fishermen attempt to fill their quotas
early before lobsters become scarce. This situation would cause harvest
ing costs to Increase due to the larger number of traps fished.
A Suggested Alternative: Harvest Rebate Program
The harvest rebate program integrates several features of previously
discussed programs. In this program effort measured by the number of
firms would be limited and would include a license fee. The harvest re
bate program offers the flexibility of allowing each firm to maximize
landings. Finally, this program allows the market system to regulate
harvest since higher license fees will discourage inefficient fishermen.
Landings regulated in this manner could be substantially less costly to
regulate due to less government intervention than in the more traditional
management programs discussed.
These advantages are not to imply that the harvest rebate program
is "the approach" for fishery management. Rather, this program was de
signed to specifically consider problems of the spiny lobster industry,


145
DERIVATIONS:
xi
P
F.
i
R
x2
x4
P
R (1)
8
I (T ) (R ) (2)
1=1
Pi
SP.
8
E
i=l
R.
(3)
(4)
R_
x3
(5)
(LO) (WD)
(6)


135
number of firms that could enter the industry based on rational profit
maximizing objectives of the regulatory agency. As a result, total in
dustry landings would range from 3.87 million pounds with 121 firms to
5.65 million pounds with 225 firms.
Considerable substitution between number of traps per firm and num
ber of firms can be made without changing the level of landings thus
providing numerous policy alternatives. Rates of substitution between
numbers of traps per firm and number of firms were determined. Beyond
400 firms substantial increases in number of firms would be required to
maintain landings due to a reduction in traps per firm. An analysis of
the possible range of combinations of traps per firm and number of firms
where profits are positive was presented with the use of isoquant map.
The conclusion was that profits would not be possible if more than 900
firms would enter the industry, nor would it be feasible for a firm to
fish with less than 75 traps.
For purposes of this study "management" was defined to include
maintaining current levels of inputs, as well as increasing or decreas
ing their levels. Traditional programs were analyzed by simulating the
behavior of the spiny lobster fishery under programs which would license
traps, license firms and issue landing quotas. Finally, an alternative
management scheme, entitled "harvest rebate program," was suggested.
This program would incorporate aspects of the traditional system.
Programs were analyzed under the previously stated factor costs
and product price assumptions. The desired value for landings was as
sumed to be 5 million pounds. Seven hundred traps were determined as
optimum for 1973-74 stock levels for profit maximization.


16
policy recommendations, particulary vulnerable to incrudelity." Since
the time of this statement considerable documentation of theoretical and
empirical marine research has accumulated, yet one has to agree that the
quoted statement can still carry conviction today. This is not to imply
that the research is not useful, but rather that a need still exists for
data, authenticated tools, and methodologies for research applicable to
the bioeconomic management of today's marine resources. Many of the
works to date develop interesting statistical investigations while
others hinge on highly abstract optimization criteria.
The major reason that the success achieved in traditional agricul
tural research, particularly in estimating production functions, has not
been achieved in marine economics research is partly due to basic under
lying problems that have yet to be solved in analyzing marine resources.
These problems relate to the techniques, assumptions, and empirical
limitations (i.e., lack of biological, environmental and economic data)
and are characteristic of the common property nature of bioeconomic re
sources. The very few exceptions to this lack of success have occurred
with species existing in what may be termed "closed systems," in which
the researcher had considerable control over the individual variables.
Very often the problems are related to inadequate specification of the
theoretical bioeconomic structure of the fishery, lack of appropriate
biological and economic data, lack of multidisciplinary research
cooperation in designing models oriented towards a systems approach,
misunderstanding the needs of counterparts in a multidisciplinary team,
and often defining objectives dissonant to the researchers or policy
makers.


- 7,000,000
Q 6.000,000
Q 5,848,203
Q 5,000,000
Q 6,000,000
Figure 13. Spiny lobster harvest isoquants and ridge lines
defining expansion paths where returns equal total
costs, (assuming ex-vessel price per pound (Py)
equals $1.08, industry total cost equals $1,876
plus $11.55 per trap per firm (Xi), and mean
seasonal water temperature (X3) equals 77.591F)
102


45
X5 = dummy variable representing upper Keys region (one
represents upper Keys and zero represents middle Keys),
X0 = dummy variable representing lower Keys region (one
represents lower Keys and zero represents middle Keys),
and
A A A
a, 0i, . .36 are parameters to be estimated.
Optimum levels of inputs were determine at the point of profit maximi
zation for the typical firm. The same computational procedure used in
the time-series analysis was used to derive TR and TC for the firm and
optimal level of input use.
Maximum Economic Analysis (MEY)
The final part of the estimation procedure involved integrating
information obtained in the cross-sectional analysis into the time-
series model which estimated the industry harvest function. This was
then used to estimate maximum economic yield (MEY).
A recognized short-coming of the industry harvest function model
is that the assumption of homogeneity among fishing firms or "fishing
effort" does not prevail in the real world. Firms differ in fishing
power due to such factors as size of craft, fishing intensity, and
amount of gear. However, note that Equation 16 representing the firm
harvest function and based on cross-sectional data adjusted for these
differences. Size of craft was accounted for by xu, fishing intensity
by X£ and X3, and amount of gear by xj. With these adjustments it was
assumed that the firms were homogeneous. The dummy variables, X5 and
X0, further influenced this conclusion.


48
Figure 6. The Florida spiny lobster fishery
all domestic spiny lobster fishermen to the Keys region can be ad
dressed,^- For these reasons the study area was delineated to include
only Monroe County. In addition, it is realistic to include only that
area of the fishery over which the state of Florida has jurisdiction
since one of the ultimate objectives is to consider management alterna
tives .
At the time of this final writing the Bahamian government was
proposing to limit its fishing grounds to only its citizens. This will
moan that future Florida landings will be made up almost exclusively
of domestic stock.


29
just equals that necessary to maintain a stable parent population, at
P3 where the lines intersect. At population P?., total production of
mature progeny is a maximum, and at P the excess of mature progeny
over that necessary to maintain the parent population is greatest.
The introduction of successful fishing effort while the parent
stock is P3, vill reduce the parent population since there is no net
recruitment with parent stock P3. The reduction of parent stock in the
initial time period results in an increase in the production of mature
progeny in the following time periods. Increased fishing effort may
continue to reduce the parent stock until parent stock, Pi, is reached.
Parent stock, P¡, will produce the largest marketable surplus defined
as equilibrium harvest and represented as M2 Mj in Figure 2. Maximum
marketable surplus is not at the parent population level which produces
the maximum mature progeny (M3). If in any time period more than the
equilibrium harvest is taken, the parent population will move Pq and
again the equilibrium in following periods will be reduced. If the
level of fishing is that which exactly takes the excess over the needed
replacement each season, parent population, Pj will be maintained. This
is defined as maximum sustainable yield (MSY).
The equilibrium harvest shown as the area between the mature prog
eny curve, OM, and the replacement line, OA, in Figure 2, may be ex
pressed in Figure 3. Points Pq, Pi, and P3 correspond with popula
tion levels in Figure 2. The maximum sustained yield, Y is produced
B1
from population Pj which corresponds to P\ in Figure 2. Except at the
maximum sustained yield the same equilibrium harvest may be taken at
different levels of parent population. For example, equilibrium .


151
14. Administrative Revenue = (Column 13) [(Column 6) x (Column 16)]
15. % A
Tot. Ind. = [(Column 7) x (Column 2)] = [(Column 6) x 400] 1
77
16. X2 400 Column (2)
17. B.E.C. = [(Column 5) + (Column 11)] [(Column 1) x (1.08)]


73
number fished. The marginal return to an additional trap was positive
and also greater than the marginal return for any of the other three
forms of effort.
Rounds per week (x?)
As the firm increased its trap pulling rate by one percent (i.e.,
A
decreases its set period), landings increased by 44 percent (32 = -43991).
Rounds per week is an index measuring fishing intensity as defined in
A
Appendix D. g2 was statistically significant at the 87 percent confi
dence level. The marginal product of x2 was expressed as
MP = 5317 x2-*5601 (37)
x2
As x2 increased the rate of increase in landings decreased. For
example, assume the firm is pulling all of its traps once per week. The
marginal product (Equation 37) of increasing this rate to twice per week
would be approximately 4,500 pounds.
Useful information contained in this index is the expected gain in
landings due to increasing the number of days a fisherman's traps set
between harvest periods."* Rounds per week (x2) was computed by dividing
the average number of days in a set period for the season into seven
days of a week. By substituting this definition for rounds per week
into the firm harvest function (Equation 31) the marginal product of
increasing the set period an additional day was calculated (Table 6).
For example, a fisherman previously harvesting his traps after the
third day can increase his total harvest by 2491 pounds by letting his
This is often referred t.o as "set period" among fishermen.


112
Profits per firm decreased approximately six percent as a result of the
$1*000 firm license fee with a range from $23,599 for 121 firms to $4
for 694 firms. Total industry costs increased with the license fee and
ranged from $1.3 million for 121 firms to $10.6 million for 966 firms.
As a result, the optimum number of firms for maximum industry profit de
creased from 225 firms (Table 12) to 211 firms. Total industry landings
were reduced by 336,447 pounds due to fewer firms fishing but profit per
firm increased by $2,846 because total industry cost was reduced more
than total industry revenue. The optimum level of firms for maximum
firm profits remained the same at 121 firms as a result of the parallel
shift in the industry cost function.
Implications of this analysis are that inputs (traps) used in the
fishery would be reduced through rational economic behavior of firms
when license fees are charged cr. a per firm basis. License fees could
be set to allow the desired level of firms to maximize profits while
harvesting the level of landings desired by management authorities.
Licensing firms would appear to be a more manageable and enforceable
program for regulating entry of effort into the fishery due to the rela
tively fewer number of firms than traps in the industry and current
craft registration requirements.
The number of licenses issued would be based on desired levels of
traps per firm (Xj), landings (Q) and expected prices of inputs and
outputs. If traps are not regulated, limiting firm numbers does not
guarantee that the desired harvest level selected would not be surpassed
if the harvest level desired is less than MEY. Depending on the impor
tance of maintaining a desired level or landings, a landings quota could


BIOGRAPHICAL SKETCH
Joel Sylvan Williams, the son of Joe and Ann Williams, was born
July 29, 1947 in Houston, Texas. The major portion of his life was
spent in a small rural community located in the southern portion of
Louisiana, commonly referred to as "cajn country."
After graduating from Hessmer High School, Hessmer, Louisiana,
in May 1965, be entered Louisiana State University located in Baton
Rouge, Louisiana. There he received a Bachelor of Science degree in
Agricultural Business in August, 1969. He then entered the Graduate
School of Purdue University as a graduate research assistant and re
ceived his Master of Science degree in Agricultural Economics in
January 1972.
In September 1971 he enrolled in the Graduate School of the
University of Florida, Gainesville, Florida. As a graduate research
assistant in the Food and Resource Economics Department he pursued the
degree of Doctor of Philosophy. In March, 1975 he was employed by
Virginia Polytechnic Institute and State University as an assistant
professor in the Department of Agricultural Economics.
Joel Sylvan Williams is married to the former Susan Emily Tate, a
cajn queen from Big Mamou, Louisiana. He is a member of Omicron Delta
Kappa, Gamma Sigma Delta, Omicron Delta Epsilon, and the American and
Southern Agricultural Economics Associations.
164


89
resources. However, management authorities allocating factor resources
could consider factors such as "grandfather clause" and minimum levels
of input uses (such as more firms than the optimum 213 firms solved for
in this study). Consequently, only one input at a time will most likely
be considered for regulation. Alternatively, the management authorities
may not strive to reach the most profitable level of utilization, at
least initially, since social and political institutions must be consid
ered. For these reasons the remainder of this chapter will consider
alternative levels of maximum economic yield with respect to given con
straints. That is one input will be analyzed while other inputs are
held at current levels.
Evaluating MEY
Maximum economic yield was estimated in the previous section using
the bioeconomic industry harvest model. In the previous chapter it was
explained that the traps data used to estimate the parameters for the
industry model were not adjusted for influences that make a trap catch
"better" for one firm than another. The reason for this was that data
such as that used to estimate the parameters for the firm harvest model
were not available over time. Trap data in the analysis of the firm
harvest function included these influences making estimation of the
optimal nuaiber of traps a partial effect and probably more accurate.
Consequently, MEY was reestimated constraining the number of traps per
firm to three levels most likely to be politically acceptable based on
analysis in this study. This evaluation involves comparing landings
(MEY), total revenues (TR), total costs (TC) and profits (TI) for the
industry and the firm, among the three levels of traps per firm (Xi).


92
Table 11. Maximum number of firms (X2*), landings, revenues, and costs
for industry profit maximization given desired management
levels of traps per firm (Xj), economic study of Florida
spiny lobster industry
Optimum
number
firms
(x2*)
Traps
per
firm
(xx)
Landings
(MEY)
Total
revenue
(TR)
Total
cost
(TC)
Profit
(n)
271
429
4,700,384
5,076,414
1,851,201
3,225,213
236
618
5,472,346
5,910,134
2,127,304
3,782,830
225
700
5,648,932
6,100,846
2,241,225
3,859,621
Note: Definitions for Table 11:
X2* = Determined as optimum level of X2 given X^ for profit
maximization (VMP,r = Pv ) .
A2 A2
Xi = Assumed desired management levels for Xj as previously
defined.
MEY = Maximum economic yield given X2x and Xi.
TR = Total revenue from landings, assuming 1974 ex-vessel
price (Py) of $1.08 per pound (TR = P^ MEY).
TC = Total operating costs [TC = X2(1,876 + 11.55 Xj)].
II = Profit; total revenue (TR) minus total cost (TC) .
This would result in total landings of approximately 5.5 million pounds.
As number of traps fished per firm increases to 700, the optimum number
of firms required for profit maximization is 225, resulting in landings
of 5.6 million pounds. Thus for given levels of traps per firm which
have either been observed or estimated as typical in this study, the
optimum number of firms required in the industry to maximize industry
profits ranges from 225 to 271 firms. Maximum economic yield for these
input levels was also within a reasonable estimate ranging from 6 per
cent below 1973 landings of 5 million pounds to 12 percent above.


APPENDIX J
Spaces provided for answers have been omitted from the original
thirteen page questionnaire for inclusion in this text. The questions
and multiple choice answers are the same. A map of the study area used
to identify the actual fishing grounds for each fisherman has also been
excluded.
(CONFIDENTIAL: Please do not give name)
SPINY LOBSTER FIRM SURVEY QUESTIONNAIRE
Please answer all questions based on 1973-74 season. Answer all
questions as accurately as possible. If the exact answer cannot be
recalled, please give your best approximation. If additional space is
needed to answer (or simply comment on) a question use the back of that
page and properly indicate additional comments.
I.DESCRIPTION OF LOBSTER PRODUCTION UNIT
A. Operation Unit: ( ) Vessel, Boat
1. Fabrication (i.e., wood, fiberglass, steel, etc.)
2. Length (feet), Breadth (width) (feet)
3. Depth (feet), Draft feet (loaded) (feet)
4. Gross Tons, Net Tons
5. Engine Make, Horsepower
6. Age of Vessel, Age of Engine
7. Top speed: Empty, Loaded, Average Speed
E. Method and Crew:
1. Type ( ): Trap, Diving, Bull Net, Other
2. If trap: Single, Trot Line
3. Number of men in crew excluding captain
4. Approximate age of regular crew members (4 blanks)
5. Does a single trip involve more than one day away from port?
Yes, No. If yes, what is the average length of time away
from port per trip? (Days)
C. Gear:
1. Traps: a. Average number of traps fished in each month.
b. Maximum number of traps fished at any one time:
2. Electronic equipment on board. Give make and model number.
3. Method used to haul traps. If hydraulic, please give capacity,
size, and make if known.
4. Preservation techniques used? Live, Ice, Freeze, Other
5. Please list other gear used but not listed above.
152


72
constant. These were defined as output elasticities and can also be
expressed as ratios of marginal and average productivities.
Partial differentiation of the harvest function (Equation 31) with
respect to given explanatory variables, gave the marginal products as
follows:
. 3q 2 3il 62 $3 $4 3s $6
MPxi = ^ = 3ixj x2 x3 Jx4 hx5 '5x6
(32)
MP = |3- = a 32x2B2"2x1ei-e3-
X2 9x2
x3 "X4 'x5 -x6
A A
9q 2 63-1 3i 3p 34 3s 8r
MP = = a 83X3 X! xx2 zx4 4x5 dx6
X3 9x3
A A
mo 2 84-1 81 82 83 85 86
MPx4 = 3x^ = a 134X4 Xl X2 X3 X5 X6
(33)
(34)
(35)
Traps per firms (xi)
The estimated parameter (3i) is interpreted as a 76 percent in
crease in landings due to a one percent increase in number of traps for
the firm. 3i is statistically significant at the 99 percent confidence
level. ^
The marginal increase in landings due to the addition of one trap
by the typical firm is:
-.2423
MP = 62.85xi
X1
(36)
The derivative of MP was negative implying marginal landings per trap
X1
will decrease as additional traps are added by each firm to the total
Alternatively, the probability of randomly obtaining a 3 as large
as 81> if 81 is equal to zero is less than .01.


CHAPTER VII
SUMMARY AND CONCLUSIONS
Florida's spiny lobster (Panulirus argus) industry achieved tremen
dous growth during the past two decades and is presently the second most
important fishery in the state in terms of dockside value of landings.
Spiny lobster landings in Florida exceeded 11 million pounds in 1973
with an estimated retail value of over $40 million. Florida landings
represent approximately 98 percent of total U.S. landings.
The tremendous growth in landings is a result of a disproportionate
increase in inputs into the fishery. Number of spiny lobster firms,
number of traps, and size of firms (gross tonnage) have increased
throughout the past two decades. The rate of increase lias been greatest
since 1965. The increase in number of firms and total traps fished was
80 percent and 242 percent, respectively, between 1965 and 1972. During
this same period total industry landings increased only 16 percent,
while landings per firm actually decreased by approximately 60 percent.
An increase in the retail price of lobster tails from $1.50 per pound in
1960 to over $9.00 per pound in 1975 has induced the growth in inputs
employed in the spiny lobster harvesting process. Thus the immediate
problem addressed in this dissertation was that of answering economic
questions relative to industry growth. "Over investment" in capital
(gear and craft) and labor (fishermen) has occurred in an effort to
harvest a relatively fixed supply. The increased fishing effort in
131


30
Figure 12. Marginal product curve for spiny
lobster craft size (MP )
x4
the production process, defined by diminishing marginal returns to the
inputs. Number of traps (x¡) exhibited the largest returns to increased
input usage, and had the highest statistical significance level of all
explanatory variables. Estimates of rounds per week (X2) revealed that
marginal returns to more frequent pulls or longer set periods would be
positive. Number of weeks fished (X3) by law is limited to 36, although
the analysis of weeks fished indicated that the economic feasibility of
fishing beyond the 13th week is questionable. The diminishing marginal
rate of returns to a firm was smaller for larger firms than smaller
firms.
Optimum Resource Allocation of the Firm
The analysis and results of determining the level of inputs where
profit was maximized for the typical firm are presented in this section.


101
MRTS diminishes as more firms are substituted for traps per
xlx2
firm and this is illustrated by the concave isoquants in Figure 13.
Tliis condition is recognized as satisfying the principle of diminishing
marginal rate of technical substitution and is caused by two factors.
First, the marginal product of firms (MP ) diminishes as the number of
x2
firms increases while the number of traps per firm is held constant.
This is defined as a downward movement along the MP curve. Second, as
X2
the number of traps per firm decreases, the marginal product function of
firms decreases (thus shifting the >0? curve downward). As more firms
X2
(X2) are substituted for fewer traps per firm (Xj) the marginal produc
tivity of the additional firm in the industry will be less. The oppo
site occurs as the number of traps per firm (Xq) is substituted for the
number of firms (X2). The same two forces act to increase the marginal
product of number of traps per firm (X^) while the marginal product
function of number of firms (X2) decreases.
Analysis of the marginal rate of technical substitution between
inputs can be of importance in providing a priori information to decision'
makers about the results of suggested changes in the structure of the
harvesting sector of the fishery. This analysis includes (a) observing
the effect of movements along an isoquant and (b) determining the loca
tion of ridge-lines (defined).
Movement Along An Isoquant
For firms fishing 700 traps, MRTS ranges from -.0632 for 100
xlx2
firms to -14.2143 for 1,500 (Table 14). MRTS v for 249 firms (-.3922),
xlx2 .
for example, means that if decisionmakers decided to allow the number of
films in the fishery to increase by one to 250, and yet still maintain


97
Alternative Levels of Traps Per Firm
The effects of varying traps per firm from 2C0 to 1,000, holding
the number of firms at the 1973-74 level of 400, is presented in Table
13. Total industry landings (Q) decreased from a maximum of 7.2 mil
lion pounds using 1,000 traps per firm to 1.4 million pounds using 200
traps per firm. At levels less than 205 traps per firm total costs were
greater than total revenues (Table 13). Maximum profit for the industry
and per firm occurred when the average number of traps per firm was 580.
At this level total industry landings were 6.1 million pounds.
Landings (q) per firm ranged from 3,527 to 17,926 pounds for a
variation in traps from 200 to 1,000 traps per firm. Total costs per
firm ranged from $4,186 to $13,426 at these input levels. Profits per
firm ranged from a maximum $7,970 with 580 traps per firm to $39 with
205 traps per firm. At 618 traps per firm (sample mean) total industry
landings (Q) were 6.3 million pounds. This level of landings was
greater than the 5.3 million pounds estimated using the mean number of
traps per firm in the time-series analysis (429 traps per firm).
Evaluation of Estimares
Model estimations thus far appear to be reasonable in comparison
to actual primary and secondary data. In 1973, 399 firms fishing an
average of 429 traps entered the industry and landed 4.99 million
pounds. According to the analysis, 400 firms each fishing 429 traps
would land approximately 5.3 million pounds. The average full-time
firm earned a profit of $8,719 in 1973 fishing 618 traps (Prochaska and
Williams [37]). This compares with the estimated profit of $7,943 per


105
Ridgelines
The boundary lines shown in Figure 13 indicate the maximum amount
of one input that can be combined with another input without causing
profits to be negative. This boundary is calculated as those points
1
where the firms total revenue equals total cost. The boundary lines
were calculated by setting total revenue minus total operating cost
equal to zero and then solving for each input in terms of the other.
The economically feasible combinations of traps per firm (Xj) and number
of firms (X2) are shown in Figure 13. The area between the ridge lines
defines the region of profits for the firm. Note that any number of
firms beyond approximately 950 will result in negative returns at any
level of trap use. The minimum number of firms required to yield reve
nues equal to costs was 16. The left-hand ridge-line asymptotically
approached this limit of firms (X2), but beyond the realistic range of
traps per firm (Xj) The production function specified that a minimum
of 51 traps per firm was required to land a positive yield, but when
costs of production are considered, at least 207 traps per firm were
^The right-hand ridge-line is expressed as the following relation
ship :
3l 62
P (K ) = P + TC X2
y xj x2 y
The left-hand ridge-line can be expressed as
A A
$2 61
P K P 1,876 X2 = p 11.55 XiX2
y y X2 z y Xi 1
where,
A
k = a 83X3 977380.707,
X3 = 77.591,
TC = total operating costs (previously defined), and
P^ = $1.08 per pound.


55
It also allows decreasing marginal returns to fishing effort.
The following spiny lobster harvest function is the statistical
model estimated using time-series data:
q = ¡ + 3i^-+32^- + 33x3 e. (21)
Al X2
The estimated coefficients and standard errors are presented in
Equation (22):
Q = 28,379,136 1,439,976,169 465,173,997 J-
*1 X2
(365,878,684) (216,457,337)
- 239,791 X3.
(170,321) (22)
Overall the model was statistically significant at the .01 level
(F3j7 = 9.16). The coefficient of determination, R2 and R2 (which was
R2 corrected for degrees of freedom) indicated that the model explained
80 and 75 percent of the variation in annual landings, respectively. A
Durbin-Watson value of 2.38 indicated the model hinges on the border
2
between no autocorrelation and inconclusiveness range of the test.
The coefficients for traps per firm, 6i> and number of firms traps in
the industry, g2, were found to be statistically different from zero
at the .01 and .07 levels of significance, respectively.
As a check on the logic of using the reciprocal form of the
function other functions were considered, but none of these yielded
"better" results. For the second degree polynomial function, negative
signs were estimated for the parameters but the coefficients estimated
were not significantly different from zero.
2
Durbin-Watson statistic is not calculated for less than 15
observations. Therefore DW was not used to test in this case. However,
there was no apparent pattern of the residuals.


134
was estimated to be 5.8 million pounds. The optimum level of firms was
determined to be 213, each fishing 795 traps. Estimates were based on
1973-74 ex-vessel prices ($1.08 per pound) and 1973-74 total costs per
firm and per trap. These optimum levels would require a reduction of
47 percent in number of firms and a slight reduction of 1,836 traps in
the total industry from 1973 levels. Total industry landings would be
increased approximately 16 percent over 1973-74 season harvest. Esti
mates will change depending on relative changes in the cost of produc
tion and product prices. As usual, maximum economic yield was less than
the predicted maximum sustained yield.
Recognizing that maximum economic yield may not be the immediate
goal for management because of the political and social consequences of
extreme adjustments in the short-run, further analyses were completed.
The analyses considered (a) parameters from the firm harvest function
which represented current stock levels and thus would be relevant for
current management programs and (b) alternative levels of one input
while holding the other input at politically realistic levels. These
analyses provide information to regulatory agencies which could be used
in assessing benefits and costs of alternative management programs.
Fewer than the optimum number of firms would be allowed to enter
the industry if the major objective of the regulatory agency was to
maximize average net return per firm. This objective was evaluated
using value marginal product analysis with respect to the industry har
vest function. The results showed only 121 firms could be allowed to
eater the industry assuming 700 traps per firm and 1973-74 factor costs
and product price. Total industry profits would be maximized w'ith 225
firms using value marginal product analysis, thus defining the range of


109
returns to investment from each firm's profit, the residual could be
considered the maximum amount in total fees the firm could afford to
pay. This value divided by the number of traps is the maximum trap fee.
If management objectives would insure the maintenance of a minimum
$5,000 salary for the captain and average profit of $7,325 for the firm,
the maximum trap license fee would be $5.81^ per trap. Any difference
between a lower fee and $5.81 would be considered residual returns to
ownership. To compute the values in Table 15, the trap fee was treated
as an additional variable cost to the firm and added to the estimated
$11.55 cost per trap.
The optimum number of traps per firm which resulted in maximum pro
fits per firm ($7,970) was 580 (Table 13) when no license fee was im
posed. Optimum number of traps decreases to 557 if a $1.00 per trap
2
license fee is charged. This results in maximum profits per firm de
creasing to $7,402 (Table 15). The number of traps per firm required to
maintain industry landings at the assumed desirable management level of
5 million pounds would not change, but profit per firm at this level
would drop 5.7 percent to $6,623 due to the trap license fee. Profit
per firm ranged from near zero to $7,402 with the license fee (Table 15),
compared with near zero to $7,970 without the license fee (Table 13).
The percentage difference in firm profits ranged from 6 to 17 percent
and was greatest at the higher levels of traps per firm (Xi). Beyond
207 traps per firm, the firm does not return a profit if a $1.00 license
must be paid. This source compared with 205 traps per firm without a
^($7,325 $5,000) t 400 traps = $5.81 maximum license fee.
2
Considered In the range of a politically feasible fee.


Traps per firm (Xj)
Figure 9. Value marginal product of traps per firm (X^) divided by the maximum number of firms
observed (399) in the industry in 1973


130
First, the estimation of traps per firm could be reevaluated. As
previously mentioned, considerable effort and funds could be spent to
accurately estimate average traps fished per firm. Second, the license
fee could be too high if too many firms have applied for a rebate. On
the other hand, the license fee could be too low if too many firms have
applied for a license. In the short-run, the rebate could be increased
before the suggested three-week deadline if too many license applica
tions were received. If too many applications were received for re
bates the license fee could be lowered during this period.
Finally, another problem might be that estimates of input and output
prices could be different from various sectors of the industry. The
state should be prepared to absorb the inaccuracies of the program
should the ratio still be out of proportion after short-run remedies
have failed. Program adjustments could be made the following year based
on experiences in the previous year(s).
In summary, the harvest rebate program is offered as a non-tradition-
al alternative. Its features include increased profits to the industry
and firm, depending on estimated levels of traps per firm. Since inputs
would be reduced, current over-capitalization would be reduced, allowing
more efficient harvesting through such activities as economies of scale.
More importantly the rebate program would allow the fishermen to make
the decision of whether or not to fish. It could also lead to improved
stock and fishing grounds since fewer traps and craft would be employed
in the harvesting process of the industry.


LIST OF TABLES (continued)
Table
11
12
13
14
15
16
17
13
Maximum number of firms (X2*), landings, revenues,
and costs for industry profit maximization given
desired management levels of traps per firm (Xj),
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of firms
(X2) assuming traps per firm (X^) equals 700, mean
seasonal water temperature (X3) equals 77.591F,
and ex-vessel price per pound (Py) equals $1.08,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of traps
per firm (Xq) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals
77.591F, and ex-vessel price per pound (Py) equals
$1.08, economic study of Florida spiny lobster
industry
Marginal rate of technical substitutions (MRTS^ ^ )
of traps per firm (X^) for number of firms 1 2
(Xi) holding traps per firm constant at 700,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of traps
per firm (X][) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals
77.591F, ex-vessel price per pound (Py) equals
$1.08, and trap license fee equals $1.00 per trap,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of firms
(X2) assuming traps per firm (X]) equals 700, mean
seasonal water temperature (X3) equals 77.591F, ex
vessel price per pound equals $1.08, and license fee
per firm equals $1,000, economic study of Florida
spiny lobster industry
Page
92
96
98
103
108
111
Median and mean spiny lobster landings per trap for
sample of firms classified according to number of
traps per firm (Xj), economic study of Florida
spiny lobster industry 117
Median and mean spiny lobster landings per trap for
sample of firms classified according to number of
traps per firm (X¡), economic study of Florida spiny
lobster industry 128
ix


14
General Biceconomic Management Research
Researchers have been contemplating bioeconomic management of the
fisheries at least as far back as the 1920's as evidenced by Rich's [38]
work on the Gulf of Maine fishing grounds in 1929 and Russell's [40]
work in 1931 titled "Some Theoretical Considerations on the 'Over
fishing' Problem." In 1943, Herrington [29] considered alternative
methods of fishing management and Nesbitt [34] investigated the biologi
cal and economic problems in management of fisheries.
Major theoretical contributions emerged in the early 1950's in the
writings of Schaefer [41], Gordon [28], Christy and Scott [16], Crutch
field and Zellner [21], and Turvey [47]. These antecedents of the past
twenty years are generally credited with developing the fundamental bio-
economic theory. Their differences can be briefly analyzed on the basis
of four management objectives. Schaefer's biological approach was con
cerned with maximizing production from the sea in a strictly physical
production framework. The others were oriented toward the maximum eco
nomic yield concept but differed to a slight degree. Gordon, and
Scott and Christy actually defined a monopoly situation as optimum with
an objective of maximum economic yield above costs. Crutchfield and
Zellner's approach was the same but excluded returns due to monopolistic
practices in order to maintain consistency with federal regulations on
monopolies. Turvey also maximized economic yield excluding returns to
monopolistic practices but, in addition, attempted to maximize consumer
surplus,
More recent research deals with the empirical application of the
above concepts and with some refinements to the theory. Lampe [32]
used a dynamic model of the Cobweb form to investigate the interrela-


35
effort. Costs per unit of output eventually rise to a level where
entry into the industry ceases.
Crutchfield [20, p. 12] identified the consequence of such a situa
tion when he said, "... such a market, unregulated, will destroy itself
either economically or biologically." Or in Carlson's [11, p. 7] words,
"In common property resource, the 'invisible hand' guarantees that the
market will arrive at a solution that is suboptimal."
Summary
Biological and economic theory suggests the following bioeconomic
harvest model:
Ybe = f(Si, S2, S3, Elf E2, E3, E4). (11)
Major focus of this analysis entailed determining the appropriate input
Level and subsequent landings where the greatest net revenue is gener
ated to the fishery. Net revenues for various levels of effort such as
number of firms in the industry and number of traps were compared. The
feasibility of alternatives for limiting effort were assessed by con
sidering the impacts these have on net revenues per firm, number of
displaced firms, total revenues to the state from user fees, cost and
time of implementation and enforcement of regulations, and expected
public acceptability.
Development of the theoretical model for this study has resulted
in an examination of the biological theory of a fishery resource and a
brief discussion of production theory. Models of these two theoretical
frameworks were integrated into a bioeconomic model used to explain the
theoretical constructs of management goals, namely MSY and MEY. The
empirical model and data analysis are presented in the next chapter.


88
respect: to Xx and X2 and set equal to zero to determine a maximum (or
minimum) level of inputs.
nx = TR TC
A A
81 B2
n, = p (K + + )- X2[1876 + 11.55 Xx] (48)
y xi x2
where,
Hi = industry profit,
1876 + 11.55 Xj = per firm total costs expressed as a function
of traps, and other terms are defined as before.
V
11.55 X2 = 0
an_
ax2
- 1876 11.55 X]
0
(49)
(50)
Solving Equations 48 and 49 simultaneously results in 213 firms in
the industry, each fishing 795 traps. Using Equation 22 maximum economic
yield was estimated at 5,778,274 pounds. This estimate was 16 percent
higher than industry landings in 1973. The number of firms in the in
dustry, at 399 in 1973, was 87 percent higher but each firm fished 429
traps, 87 percent less than the estimated value. Several implications
can be drawn from this analysis. First, industry profits have currently
not been maximized nor has total industry landings reached a peak.
Second, firms could be larger and more efficient, maximizing profits
through economics of size. Finally, total industry costs could be re
duced due to fewer firms, resulting in a larger total industry profit.
Maximum economic yield was less than the estimated maximum sus
tainable yield (MSY) and resulted from an optimum allocation of factor


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103
the previous level of landings (5,848,203 pounds) where industry profits
were maximized, the number of traps per firm would have to be decreased
by 2.55.1 This was illustrated in Figure 13 as moving along the iso
quant where landings (Q) equals 5,848,203 pounds.
Table 14.
Marginal rate of technical substitutions
(mrtsx,x2
) of traps
per firm (Xi) for number of firms (Xi) holding traps per
firm constant at 700, economic study of Florida spiny lobster
industry
Number of
Marginal rate
firms
of technical
(X2)
substitution (MRTSV v )
XiX2
100
- .0632
150
- .1421
200
- .2527
250
- .3922
300
- .5686
350
- .7739
400
- 1.0108
425
- 1.1411
450
- 1.2793
500
- 1.5794
1000
- 6.3175
1500
-14.2143
Carrying this example one step further and assuming a $1.08 product
price and previously estimated total costs per firm, the net effect on
industry and firm profits can be easily approximated. Since each firm
is fishing approximately three (2.55 rounded) fewer traps with the addi
tional firm in the fishery, total costs per firm decreased by $11.55
Notationally this can be expressed as
1
MRTS
XjX2
-AXj.
For Xi = 700 and X2 = 250, the change in Xi was
1
.3922
= -2.55.


133
The firm harvest function was estimated from a cross-sectional
sample of lobster firms. Spiny lobster fishermen selected by a statis
tically designed sample were interviewed in 1974 concerning specific
aspects of the spiny lobster harvesting process. This data was used to
analyze the lobster harvest function for a given stock level on a per
firm basis. A Cobb-Douglas functional form model was used to relate
firm landings to the number of traps fished and fishing intensity.
Fishing intensity was measured as percentage of traps pulled per week,
number of weeks fished, and size of the craft. Location of fishing
grounds was entered in the model to adjust for area differences in fish
ing conditions. All variables with the exception of one location vari
able were highly statistically significant. The cross-sectional harvest
model was used to estimate the profit maximizing level of traps per
firm. This value was then substituted into the bioeconoxnic industry
function for traps per firm to complete the industry analysis.
Maximum sustainable yield for the industry was approximated by
observing the range of estimated maximum industry landings as traps per
firm and then firms were increased to practical feasible limits. While
one input was varied the other was held constant at actual mean, minimum,
and maximum levels employed in the industry. The estimated range in
maximum sustained yield was between 5.9 to 8.9 million pounds. For the
purposes of ths study, 8 million pounds was defined as an extreme esti
mate of maximum sustainable yield while 6 million pounds v/as defined as
a conservative estimate.
Maximum economic yield was estimated for the industry allowing both
traps per firm and number of firms to be simultaneously determined such
that maximum economic profit would be attained. Maximum economic yield


138
big catch" would be destroyed if he were limited to a predetermined har
vest level.
An alternative approach to management, the "harvest rebate program,
was offered for further consideration. This program integrated several
features of the previously discussed traditional management programs.
Effort in the form of firms would be limited and license fee would be
required. The harvest rebate program offers the flexibility of allow
ing each firm to maximize landings. Finally, this program would allow
the market system to regulate harvest since higher license fees should
discourage inefficient fishermen. Landings regulated in this manner
could be substantially less costly to regulate due to less government
intervention than would be the case in the more traditional management
programs discussed.
The harvest rebate program was analyzed simulating the industry
behavior under various levels of traps per firm. License fees were
ranged from $17,000 to $1,000 per firm, with the optimal number of firms
ranging from 140, each fishing 1,000 traps, to 328, each fishing 429
traps. Those fishermen choosing not to fish would receive a rebate pay
ment equivalent to the average firm profit without the program for a
specified level of inputs. The increase in profit per firm for those
fishermen electing to pay the license fee ranged from 38.7 percent with
140 firms in the industry to 17.3 percent with 328 firms in the indus
try. Profits for each of the 400 firms before the management program
ranged from $5,935 for firms fishing 1,000 traps to $7,943 for firms
fishing 618 traps. Maximum revenue to the state, given the assumptions
of the analysis, ranged from $745,544 for 328 firms to $2,701,160 for
1!
140 firms.


43
from Equation 15, except that environmental, and biological differences
among fishing areas were represented by the coefficient for ej. The
objective of this analysis was to determine differences in ej . e4
among firms that influence individual firm landings and thus, production
responses to different levels of input use. A detailed summary of defi
nitions and derivations of variables that significantly influence the
typical firm harvesting process are presented in Appendix D.
A trap is defined as before to represent the unit of effort through
which the traditional factors of production are employed in the produc
tion process. Thus traps, xi, was substituted for e3, and et, in
Equation 15. In addition, the intensity at which the trap is fished
was included in the model through the inclusion of X2 (number of times
a fisherman pulls his total number of traps in one week) and X3 (the
number of weeks fished). These intensity variables adjusted trap use
between firms in a cross-sectional survey and in addition represented
additional use of traditional production variables such as labor and
capital. Variation in firm size and capital investment were included
by a proxy variable, X4, defined to be the square footage of the boat
or vessel.
Quality of fishing grounds with respect to stock and other environ
mental attributes is expected to raise or lower firm harvest and there
fore, were entered into the model using dummy variables. Fishing
grounds were broadly segregated into three different areas defined by
the sample stratification. The upper Keys region (X5) was defined as
the 44-mi.les from Key Largo to Lower Matecumbe Key. The lower Keys
region (xg) was defined as that 31-miles from Big Pine Key to Key West.
The middle Keys region, the base region, was defined as the 37-mile


lb
tionships between biological arid economic aspects of commercial fisher
ies. Carlson [11, 12] developed a theoretical yield function by inte
grating an economic production function with a biological growth model
and distinguished between firm and industry or aggregate production
functions. Van Mair [53] demonstrated that landings will exceed maximum
sustainable yield (MSY) as a result of excess effort generated in a
competitive economic system such as the George's bank haddock fishery.
To curtail effort at MSY he suggested free entry with landings quotas,
monopolistic exploitation implying the maximization of net revenue above
labor and capital cost, or quotas placed on fishing effort. A problem
inherent in all of these alternatives is defining a unit of effort.
Smith [44] developed a dynamic competitive model of the interaction
between the number of firms (investment) in a fishery and the population
of ar; exploited fish species, which included crowding externalities.
Bell's [3, 4, 5, 6] empirical research dealt primarily with
firm analysis and illustrates the use of econometric techniques in
marine research. He attempted to determine what factors influence the
rate of return and what impact their variability has on the industry.
A major criticism of his findings is that the estimates will not with
stand rigorous statistical tests primarily because of model misspecifi-
cation and lack of a randomly selected sample.
After an extensive review of literature the major revelation can
best be explained by a quote from the concluding statement of the ab
stract of a dissertation written in 1965 (Bromley [8, p. 36]) "The
presence of considerable uncertainty In a fishery, and the lack of per
fect knowledge on the part of biologists and economists, renders in sweep
ing conclusions of traditional writers in fishery, and their subsequent


TABLE OF CONTENTS (continued)
CHAPTER
IVEMPIRICAL MODEL AND DATA 36
Definitions 36
Bioeconomic Analysis 37
Firm Analysis 41
Maximum Economic Analysis (MEY) 45
Study Area and Data Acquisition 47
Sample Selection and Size 49
Survey Technique 33
VANALYSIS OF RESULTS 54
Bioeconomic Model 54
Maximum Sustainable Yield (MSY) Estimate 59
Value Marginal Product Analysis 62
Analysis of Firm Harvest Function Model 67
Firm Harvest Model 67
Estimated Parameters 71
Traps per firm? (x^) 72
Rounds per week (X2) 73
Weeks fished per season (X3) 75
Craft size (xt,) 78
Optimum Resource Allocation of the Firm ...... 80
VITHE MANAGEMENT MODEL 87
Maximum Economic Yield for the Industry 87
Evaluating MEY 89
Policy implications ?3
V


Estimation of the effect or traps on landings for the typical firm
using the firm harvest function took into consideration influences of
craft size, (X4), fishing intensity (x2 and X3) and differences in fish
ing grounds (X5 and x$). With this estimate an analysis of optimum num-
A
her of traps (xi ) was made. Then holding trap levels at this economic
optimum an estimate of the optimum number of firms was possible. Thus,
xi from the cross-sectional firm analysis was substituted for in the
time-series industry harvest function model to estimate industry land
ings assuming firms are employing the optimum number of traps. Equiva
lent notational form for the industry harvest function now became
A A
$1 62
Q = a + * + + 33X3
xi
X2
(17)
where,
Q = estimated industry landings,
J.
xi = optimal number of traps per firm estimated from firm
analysis,
X2 = number of firms in the industry,
X3 = mean seasonal surface water temperature,
ex, B2> 63 are parameters to be estimated.
HEY with respect to number of firms occurs at that point less than
MSY where the difference between total industry revenue and total indus
try cost are maximized. After deriving industry total revenue and total
cost curves, their slopes were equated and the solution for the optimal
A A
number of firms (X2 ) was determined. X2 occurred when industry margi-
A
nal revenue equals industry marginal cost of an additional firm. X2
was then substituted into the industry harvest function (Equation 17)


30
Parent Population
Figure 3. Equilibrium harvest as a
function of parent population
harvest, Y may be taken with either parent population Pa or Po. MSY
occurs at that point of equilibrium harvest curve where its slope is
zero.
Traditional Economic Productlon Model
A production function normally used in economic analysis is defined
as the relationship between physical inputs and a resulting level of
physical output, similar to the biological yield process. The difference
occurs in the type of relationship between the inputs and the resulting
output. Similarly, theory exists that explains the economic stages of
a production process in an economic system.
Production inputs or factors of production can be defined as units
of effort and consist of land, labor, capital, and management. The


137
fished 700 traps, no more than 175 firms could be allowed in the industry
in order to maintain a desired harvest level of 5 million pounds.
Licensing firms appeared to be a more manageable program for regu
lating entry of effort into the fishery than licensing traps since a
much smaller number of units (number of firms) would have to be regu
lated. The number of licenses issued would be based on the regulatory
agency's objectives and selected parameters for traps per firm, landings,
and expected prices of inputs and outputs. Furthermore, if traps were
not regulated, limiting the number of firms would not guarantee that
the desired level of landings would be achieved.
Landing quotas could be useful as a management tool for expedient
adjustments to precisely control industry landings. Since current land
ings were less than the estimated range of maximum economic yield levels
precise control of landings was not viewed as an immediate concern in
the Florida spiny lobster fishery. Consequently, an example of the in
dustry structure and behavior regulated through landing quotas was not
simulated. However, a quota fee could be assessed in a similar manner
to the firm licensing program. The major advantage of the quota system
would be that it would allow the harvesting process to operate freely
to optimally combine inputs. Free enterprise is conducive to effi
ciency and technological innovation, which could lead to reduced total
industry costs in the long run.
Conversely, disadvantages of the quota system are: (a) that an
accurate estimation of maximum sustainable yield would be needed which
could generate high research costs; (b) maximum economic yield would
not necessarily be attained since the incentives of over capitalization
still remain; and (c) the fisherman's motivation due to dreams of "the


71
increase in all inputs was positive and total landings were increasing
at an increasing rate. Homogenity of 1.87848 means that if each of the
independent variables of the harvest function are multiplied by a con
stant k, landings will change by a multiple of k1*878if 5. For example,
if XI ... Xg are all doubled (k = 2) landings will more than quadruple.
To illustrate the significance of this, assume that the State of Florida
determined that MSY had been surpassed and landings would have to be
reduced by, say, approximately 50 percent to protect the fishery stock
from irreversible damage. Given homogenity of 1.87848, all inputs would
have to be reduced by only 25 percent to obtain a 58 percent reduction
in landings per firm, and thus, for the industry, assuming homogeneous
firms.^ If the state does not have control over individual effort,
individual firms would have to be provided some inducement to voluntarily
cut back input usage, similar to the objective of the Federal Soil Bank
Program for agriculture in the 1960s. Although this type of analysis
may provide some interesting insights into management of the fishery,
it may be argued that the interpretation is non-sensical. Realistically
speaking, size of craft and number of weeks are definitely limited
beyond some point of expansion.
Estimated Parameters
The estimated coefficients (8^) of the hai'vest function presented
in Table 5 explained the percentage change in landings due to a given one
percent change in the particular input level, assuming all other inputs
^Notationally the derivation is 3S follows:
(. 75) 1 8781,8 q = .58 q
where,
q = firm harvest function (Equation 31).


95
there was an average of 701 traps per firm. Finally, the MEY analysis
using the bioeconomic industry harvest function at the beginning of this
chapter resulted in 795 traps per firm as optimum.
Industry landings (Q) ranged from 3.1 to 7.4 million pounds as the
number of firms has varied from 100 to 1,500 in Table 12. This range
represents only a 141.7 percent increase in total industry landings as
the result of a 1,400 percent increase in effort. Total costs become
greater than tctal revenues when the number of firms exceeds 966. If
the 1973-74 season level of 400 firms were in effect, landings would be
6.6 million pounds with industry profits of $3.1 million. Thus, if each
firm fished 700 traps (selected economic optimum for 1974) 225 firms
would maximize industry profits. Approximately 772 firms would likely
dissipate all industry profits, while the 400 existing firms could
operate at a total industry profit level of $3.1 million. Maximum
industry profits would occur with 225 firms, each fishing 700 traps.
This would result in landings of 5.6 million pounds.
Estimates on a per firm basis presented in Table 12 were derived by
dividing total industry estimates by the appropriate number of firms.
Estimated landings per firm (q) ranged from 4,938 to 30,646 pounds for
the alternative programs. Costs per firm were constant in Table 12.
Estimated average profits per firm ranged from $23,137 for 100 firms in
the industry to $3.00 per firm for 771 firms in the industry. Total
costs per firm were estimated to exceed total revenues per firm when the
number of firms exceeded 771. With these estimates maximum profit per
firm occurred at 121 firms while maximum industry profit occurred at
225 firms.


Table 17. Median and mean spiny lobster landing per trap for sample of firms classified according to number of traps pci' firm (Xi),
economic study of Florida spring lobster Industry
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
No.
traps
firm
(Xi)
No.
firms
fishing
(X?*)
Landings
W/0
program
(Qn)
Landings
w I 111
program
Total cost
pee firm
ProfIt8
per
f Lrm
W/0
program
(Tt/X2)
Profltb
por
f I rrn
with
program
(r/x2*)
7.
n /X2
Incl.
lie.
f IC
Maximum
state
revenue
$
$
lb.
lb.
$
$
$
7.
$
1,000
140
7.170,570
5,010,833
13,426
5,935
25,229
325.1
2,701,160
800
156
6,810,576
4,991,626
11,116
7,273
23,441
222.3
2,522,208
700
171
6,553.437
4,996,056
9,961
7,733
21,593
179.2
2,370,060
518
190
6,280,487
4,995,138
9,014
7,943
19,379
144.0
2,172,840
500
246
5,730,593
5,002,577
7,651
7,822
14,312
83.0
1,596.540
429
328
5,253,958
4,998,679
6,831
7,355
9,628
30.9
745.544
350
400
4,496,328
5,000,376
(No limited entry program needed since require
currently exist to harvest an KEY equal to 5
more firms than
million pounds.)
200
400
1,410,665
4,996,381
(No limited
currently i
entry program needed since require
exist to harvest an MEY equal to 5
more firms than
million pounds.)
117


Million pounds
56
Observed and predicted values of landings for 1963-73 are shown in
Figure 7. Since 1969, landings have varied between 4 and 5 million
pounds, with a slight exception in 1970. Maximum landings observed
within the data range occurred in 1970 at 5.24 million pounds. In 1973
landings decreased to 4.99 million pounds. Assuming current management
regulations are adequate and new technology does not occur, there is
little reason to expect landings to increase substantially above five
or six million pounds annually. This assumes that biological and
environmental factors will remain substantially unchanged.
Figure 7. Observed and predicted volume of spiny lobster landings,
1963-73 for Monroe County, Florida


107
For each of the programs analyzed the following assumptions were
made, unless otherwise specified: ex-vessel price per pound (Py) equaled
$1.08 (1974 mean price); number of firms in the industry was 400
(1973 level); traps per firm (X]) was 618 (sample survey mean); desired
level of landings (Q) equaled 5 million pounds (1973 level); and total
cost per firm equaled $1876 plus $11.55 per trap (estimated).
Licensing Traps
Licensing of traps and the charging of a fee increases costs but
appears economically and politically feasible, provided that some form
of "grandfather clause" is included which limits the number of firms in
the industry to at least those that were previously fishing.^ As the
cost of traps increases, the number of traps per firm must be reduced
to obtain higher marginal productivities so that the value of the margi
nal product can equal the higher trap cost. This would reduce effort in
the form of traps as captains attempt to maximize profits.
As a way of illustrating the effects of this program, consider the
analysis in Table 15. Total landings would be 6.28 million pounds and
average firm profits would be $7,325, if 618 traps were employed per
firm. Given assumed desired annual landings of 5 million pounds, a re
duction in average traps to 400 per firm would be required. Industry
profit would be $2.65 million after the reduction, a portion of which
may be taxed through a license to finance the management of the program.
After deducting opportunity costs in the form of captain's wages and
A "grandfather clause" refers to legislation which states that
fishermen licensed prior to the enactment of some limited entry
regulation must be allowed to remain in the fishery.


Table K1
Spiny 1bfcter Input, outputs, and values, Monroe County, Florida, 1963-73, econonic study of Florida opiny lobster industry
1973a
1972"
1971
1970
1969
1S68
1967
1966
1965
1964
1963
Total landings (lb.)
4,993,230 .
4,639.773
4,653.387
5,235,255
4,620,766
3,891,736 ;
2,719.178
3,650,142
4,37V,496
2,843,888
2,770,100
Total value ($)
5,322,836b 4,967,756
4,017,561
3,123,429
3,309,855
2,813,336 :
1,668,216
1,654,460 i
2,464,780
1,210,528 :
1,080,339
Prlc- (c/lb.)
1C6.6
107.5
86.3
59.7
71.6
72.3
61.4
45.3
56.3
42.6
39.0
Tc-ir* (gcJt)
171,240
133,044
155,229
134,300
96,935
98,500
91,800
74,550
89,700
73,353
60,050
Pounds per trap
29.16
34.87
2S.98
38.98
47.66
39.51
29.62
48.96
48.82
38.66
46.13
Dollars per trap
31.08
37.49
25.88
23.26
34.14
28.56
18.17
22.19
27.48
16.46
17.99
Kli(ier?ien: Ven l
421
370
329
251
134
323
143
104
56
08
44
Boat (reg.)
319
325
253
330
255
214
330
300
306
238
233
Casual
30
37
39
17
20
12
24
12
24
104
12
TOTAL
770
732
621
598
459
549
497
416
386
410
239
Boat b
211
2 34
192
212
176
135
224
210
188
214
162
Fishermen per boat
1.51
1.39
1.32
1.56
1.45
1.59
1.47
1.43
1.63
l.u
1.44
Vessels
188
123
130
111
£9
137
75
58
28
34
24
Fishermen par vessel
2.24
3.01
2.53
2.26
2.07
2.35
1.91
1.79
2.CO
2.00
1.33
Cron* Tannage
4,<)00t
2,874
3,243
2,491
2,135
3,433
1,189
824
308
2S0
261
Cros tonnspe per vessel
21.28
23.37
24.55
22.44
24.55
25.06
15.85
14.21
11.00
8.24
10.63
Firms (Em's and Vessels)
399
357
322
323
25
272
299
268
216
248
136
Pounds per lira
12,514
12,997
14,451
16,208
17,4.17
14,303
9,094
13,620
20,275
11,467
14,893
Dollars per. firm
13,340
13,971
12,477
9,670
12,430
10.343
5,579
6,173
11,411
4,883
5,808
Traps per fina
429.17
372.67
482.08
415.79
365.87
362.13
307.02
277.99
415.28
296.58
322.85
Water Temperature
79.09
79.62
78.57
76.62
76.35
76.94
77.79
76.64
77.91
77.52
77.45
Source: U.S. Department of Coirnerce, NOAA, NMFS, Southeast Fisheries Center, Miami, Florida.
aAdjusted for out-of-scasoo landings. Actual data recorded for Monroe County, before
adjusting for out of season landings v re: Landings 5,247,409 (1973); 4,314,013 (1972);
Total value $5,593,73b (1973); *5,176,026 (19/2).
b
973 total value eatic*.
ed ly 4,993,230 x 106.6
5,322,836.
Monroe County
Out of Season Landings
April May
1972 0 84,318
1973 36,008 83,661
June July Total
49,104 40,818 174,240
83,119 46,341 254,129
Estimated.
Water temperature was calculated from the monthly mean surface water temperaturu for August thru March of each season
The data for South Klmi and Key West station were averaged to obtain this value.


13
New traps catch better after being in the water at least five days.
Landings are higher if traps are lifted every two to three days rather
than over four days. Traps settling on the bottom collect silt and
foreign matter, which past experiences indicate reduce landings if the
exterior of the trap is not brushed every few days. Landings are higher
for traps set next to reefs or forage areas than for traps set on reefs
and in flat clean areas.
Butler and Pease [9] found that bottom temperature and salinity
were correlated with the presence of lobsters. In a range of 68-85F
more lobsters were landed than in higher bottom temperatures of the
83-85F range. Also in a total salinity range of 28-34/00 landings
were higher than at the 31-32/00 salinity level. Lobsters will not
feed when water temperatures are near freezing and will migrate from
locations with colder water temperatures to warmer water locations. A
study on surface and subsurface water temperature shows that the major
ity of the fishing area in the Florida spiny lobster fishery is iso
thermal year round (Robinson [39]). This means that in depths of less
than 50 feet the difference in the bottom temperature and surface
temperature is insignificant.
Aquaculture of spiny lobster is possible but currently not economi
cally feasible because they require very exacting care and specialized
conditions (Ting [46]). Spiny lobsters require clean, oxygenated water
with a balanced temperature and the individual lobsters kept separated.
To accomplish this requires a large volume of space and labor and thus
a large capital investment. The growth period from juvenile to market
able size is approximately three years in an artifically created envi
ronment, compared with five to seven years in the natural environment.


Table 15. Analysis cf alternative levels for number of traps per firm (X^) assuming number of firms (X2) equals 400, mean seasonal
water temperature (X3) equals 77.591F, ex-vessel price per pound (P ) equals $1.08, and trap license fee equals $1.00
per trap, economic study of Florida spiny lobster industry
Total Industry
Per Firm
Number of
Firms (X;)
Landings
(Q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
Landings
(q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
1000
7,170,570
7,744,215
5,770,440
1,973,815
17,926
19,361
14,426
4,935
eoo
6,810,576
7,355,422
4,766,400
2,509,022 .
17,026
13,389
11,916
6,473
700
6,553,437
7,077,712
4,264,400
2,813,312
16,384
17,694
10,661
7,033
618
6,280,487
6,782,926
3,852,760
2,930,166
15,701
16,957
9,632
7,325
* 557
6,025,310
6,507,335
3,546,540
2,960,795*
15,063
16,268
8,866
7,402*
500
5,730,593
6,139,041
3,260,400
2,928,641
14,326
15,473
8,151
7,322
429
5,253,958
5,674,275
2,903,980
2,700,295
13,135
14,186
7,260
6,926
400
5,010,605
5,411,454
2,758,400
2,653,054
12,527
13,529
6,986
6,633
300
3,810,626
4,115,475
2,256,400
1,859,075
9,527
10,289
5,641
4,648
* 207
1,654,139
1,786,470
1,739,540
-3,070*
4,135
4,466
4,474
-8*
Note: Asterisks highlight minimum and maximum positive profits for industry and/or firms and respective level of traps per firm (Xj).
108


85
dividing total costs by the mean number of weeks in the sample. Optimum
number of weeks was estimated at 10.3 and profit per firm was estimated
at $4,747. Optimum size of craft measured as square footage of hull was
estimated at 179.11 square feet. Factor costs were derived by dividing
total variable costs by mean craft size for the sample. At this level
of craft size profit estimated for the typical firm was $718.
This procedure was presented for illustrative purposes and its use
fulness depends on accurate estimates of factor prices. In addition,
total revenue, total cost, and resulting profits were also dependent on
levels of other inputs which in the above analysis were held at mean
levels rather than "optimal" levels. However, it is interesting to note
that the predicted level for rounds per week and weeks fished in Table
10 were both close to actual observed values in the industry, thus sug
gesting that if firms are maximizing profits, the above estimates of
factor prices for and X3 are reasonable. The factor price estimated
for craft size evidently may be a substantial error because the optimal
hull size of the typical craft was predicted at 179.11 square feet, con
siderably different from the current industry average size of 326.88
square feet. Furthermore, the predicted profit per firm of $718 does
not appear reasonable given the survey data.
At this point, one additional conclusion was indicated with respect
to variations in firm profits due to fishing areas. Fishing in the
upper (X5) and lower (xg) Keys regions produced increased profits. How
ever, only 65 was statistically significant at the 99 percent confidence
level, compared with a 56 percent confidence level for 65. Therefore,
there exists a good chance profits will be greater if firms fish above
Lower Matecumbe Key rather than fish the adjacent area down to Big Pine


TABLE 0? CONTENTS (continued)
APPENDIX
A Spiny lobster landings and dollar value, Florida and
U.S., 1952-73, economic study of Florida spiny lobster
Industry 141
B Spiny lobster capital and labor inputs, Florida west
coast, 1952-72, economic study of Florida spiny lobster
industry 142
C Input/Output. relationships, Florida west coast., 1952-72,
economic study of Florida spiny lobster industry 143
D Cross-sectional Data Computations 144
E Spiny lobster landings and dollar values, Florida east
and west coasts, and Monroe County, 1952-73, economic
study of Florida spiny lobster industry 146
F Spiny lobster landings in Florida ports caught in
foreign waters, 1964-73, economic study of Florida
spiny lobster industry 147
G Total product and marginal product equations for firm
harvest function model ^ . 148
II Comparison of spiny lobster production practices by
craft length for firms sampled, Florida Keys, 1963-74
season, economic study of Florida spiny lobster
industry 149
I Table 18 computations 150
J Spiny Lobster Firm Survey Questionnaire 152
K Spiny lobster inputs, outputs, and values, Monroe
County, Florida, .1963-73, economic study of Florida
spiny lobster industry 157
L Data used to estimate firm harvest function, 1973-74
survey of spiny lobster captains, economic study of
Florida spiny lobster industry 158
REFERENCES 3 59
BIOGRAPHICAL SKETCH
164


114
previously for the. firm licensing program. The quota limits per firm
could be set forth as a percentage of each firm's expected total reve
nues from landings. For example, in Table 12, with 400 firms fishing
700 traps each, profit per firm was $7,734 without any license fee.
Assuming that total implementation and enforcement costs of the program
would be $800,000 or $2,000 per license, firm profits would be 57.6 per
cent instead of 77.6 percent of total costs. To enhance the acceptabil
ity of the fee charge next year's license fee could be set at 11.3 per
cent of the previous year's total revenue ($2,000 v $16,320) instead of
25.9 percent ($2,000 $7,734) of the previous year's profit per firm.
Quotas could be offered for sale on a first come, first serve basis or
more efficiently by some form of auctioning. If firms exceeded their
landing quotas a fine per pound could be levied that would be severe
enough to discourage such practices.
The major advantage of a quota system is the assignment of owner
ship tG the resource. Consequently the quota system allows the free
market system to operate more easily than would the normal conditions
of a common property resource. Free enterprise is conducive to effi
ciency and technological innovation. As the marketing system operates
more freely, less government intervention is required, leading to lower
management costs. The quota system also would have the most direct con
trol over landings and, therefore, could be used for controlling landings
with minimum delay in situations where MSY has been reached or surpassed.
However, several disadvantages are associated with the quota system.
First, the quota system would require accurate information on maximum
sustainable yield levels which might necessitate considerable research
and management costs. Analytical results in this study show that current


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Fred J. Prochaska, Chairman
Associate Professor of
Food and Resource Economics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
' ) /
/./, U /<
W. W. McPherson
Professor of Food and Resource
Economics
1 certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
UZL&rXJ' .
Janies Heaney
'Associate Professo
r o/
Environmental Engineering


90
The technique used to reestimate MEY was different than the first
method which involved a simultaneous solution of the industry profit
function. In this case the assumed number of traps per firm (Xj) and
*
the estimated optimal number of firms (X2 ) required for industry profit
maximization was substituted into the original bioeconomic industry har
vest function. In the following equation landings are now defined as
maximum economic yield (MEY) for a given combination of traps per firm
(X^) and number of firms (X2) assuming a constant mean seasonal water
temperature (X3) of 77.591F:
$1 B2
MEY = a + + + $3(77.591).
X1 x2
(51)
The optimal number of firms (X2*) was defined as that number which
maximized industry profit while fishing the number of traps per firm
that was specified for the estimation of MEY. Consequently, total cost
per firm and resulting total industry cost varies according to the num
ber of traps specified.'*' Optimal number of firms was derived for each
level of traps per firm from the following equality between the value
XPV was previously defined as average total cost per firm for the
x2
industry. Alternatively, the estimated value of can be considered
X2
to be a function of the number of traps the firm fishes. The estima
tion of P using OLS regression technique was
x2
Pv = 1,876 + 11.55 X,
x2
where,
SE = 2.168; SE = 1,540; R2 = .74; SEE = 3,752; d.f. = 23 and
A J Ct
pXi $11.55.


APPENDIX F
Table FI. Spiny lobster landings in Florida ports caught in foreign
waters, 1964-73, economic study of Florida spiny lobster
industry
Total
Florida Landings
Florida Landings
Florida
From Domestic
From
Foreign
Year
Landings
Waters
Wa
ters
Quantity
Quantity
Quantity
Percent of
(Pounds)
(Pounds)
(Pounds)
Florida
1964
3,631,100
2,632,547
998,553
27.6
1965
5,714,100
4,719,847
994,253
17.4
1966
5,350,000
3,151,150
2,198,850
41.1
.1967
4,414,000
1,915,676
2,498,324
56.6
.1968
6,155,000
2,880,540
3,274,460
53.2
1969
7,582,000
4,086,698
3,495,302
46.1
1970
9,862,462
6,745,924
3,116,538
31.6
1971
8,205,803
4,669,102
3,536,701
43.1
1972
11,986,221a
5,488,338
6,497,883a
54.2
1973
12,676,188a
6,621,122
6,055,066a
47.8
Source: Foreign water landings obtained from unpublished data collected
by the Statistical Reporting Service of the National Marine
Fisheries Service, Miami, Florida.
dOut of season landings included for 1972 and 1973 were 782,974 pounds
and 1,504,480 pounds, respectively. These are landed in Florida from
foreign waters during the Florida closed season.
147


161
[25] Ferguson, C. E. The Neoclassical Theory of Production and Distri
bution, Homewoods, Illinois: Cambridge University Press,
1969.
[26] Fullenbaum, R. F. "A General Equilibrium Demand Model for Living
Marine Resources: An Application of General Equilibrium and
Common Property Resource Theory to the U.S. Seafood Sector,"
NMFS, ERD, FL No. 116, August, 1971.
[27] Gates, J. M. and V. J. Norton. "The Benefits of Fisheries Regu
lation: A Case Study of the New England Yellowtail Flounder
Fishery." Sea Grant Resource Economics, University oi Rhode
Island, Marine Technical Report No. 21, Kingston, R.I., 1974.
[28] Gordon, H. Scott. "The Economic Theory of a Common Propertv
Resource: The Fishery," Journal of Political Economy, Vol.
62, April, 1954, pp. 124-142.
[29] Herrington, William C. "Some Methods of Fishery Management and
Their Usefulness in a Management Program," U.S. Fish and
Wildlife Service, Special Scientific Report No. 18, 1943.
[30] Huq, A. M. and H. I. Hasey. "Socio-Economic Impact of Changes
In the Harvesting Labor Force in the Maine Lobster Fishery,"
NMFS, ERD, File Manuscript No. 142, January, 1973.
[31] Idyll, C. P. "Spiny Lobster of the Caribbean (Abstract)," F.A.O.
Fish Report No. 71.1, 1969.
[32] Lampe, Harlan C. "The Interaction Between Two Fish Populations
and Their Markets," Frederick W. Bell and Jared E. Hazleton
(eds.), Recent Development and Research in Fisheries Econ
omies Published for the New England Economic Research
Foundation. Dobbs Ferry, New York: Oceana Publications,
Inc.., 1967, pp. 179-195.
[33] Mendenhall, W., et al. Elementary Survey Sampling, Belmont,
California: Dunberry Press, Wcrdsworth Publishing Co., 1971,
p. 40.
[34] Nesbitt, Robert A. "Biological and Economic Problems of Fishery
Management," U.S. Fish and Wildlife Service, Special
Scientific Report No. 13, 1943.
[35] Pontecorvo, Giulio. "On the Utility of Bio-Economic Models for
Fisheries Management," Ocean Fishery Management: Discussions
and Research, U.S. Department of Commerce, NOAA and NMFS,
NOAA Technical Report NMFS CIRC-371, April, 1973.
[36] Prochaska, F. J. and J. R. Baarda. "Florida's Fishery Management
Programs: Their Development, Administration and Current
Status," Florida Agriculture Experiment Station Bulletin No.
768, University of Florida, Gainesville, 1975.


158
APPENDIX L
Table LI. Data used to estimate firm harvest function, 1973-74 survey of spiny lobster captains,
economic study of Florida spiny lobster industry
Landings
(pounds)
Traps
(xi)
Rounds
per week
(x?_)
Weeks
(X3)
Craft
size
(x4)
Area
fished
(x5,x6)
Length
Width
Landings
(dollars)
Survey
I.D.
Code
3052
140
.6240
36
154
1, 0
22
7
3336
105
14000
832
.8860
36
80
1, 0
16
5
1498
108
10254
377
1.1200
28
140
1, o
20
7
10254
110
2963
85
.7980
36
96
1, 0
16
6
3200
111
5000
448
.6750
36
154
0, 0
22
7
5350
204
6616
365
.9120
36
176
0, 1
22
8
7148
302
2996
140
.8300
36
176
0, 1
22
8
3176
305
13613
851
.6790
36
234
1, o
26
9
14566
101
22000
401
.6610
36
234
1, o
26
9
23540
109
7103
665
.7700
36
200
0, 0
25
8
7600
201
12000
560
1.0390
36
252
0, 0
28
9
12840
203
8000
260
.7620
36
240
0, 1
24
10
8560
304
16531
800
.6330
36
252
o, 1
28
9
20664
306
6171
396
.6670
36
208
0, 1
26
8
7171
307
15000
776
.5000
36
341
1, 0
31
11
16050
102
15973
597
.7950
36
408
1, 0
34
12
17055
103
17000
648
.7980
36
432
1, 0
36
12
18190
104
17000
647
.7950
36
340
1, 0
34
10
18190
106
18000
1103
.9300
15
468
0, 0
36
13
19260
202
8500
498
.5720
36
330
0, 0
33
10
9095
205
35308
1625.
1.0480
36
468
0, 0
36
13
37780
206
16333
1281
.8900
13
690
0, 0
46
15
17966
207
16575
716
1.0810
36
574
o, 1
41
.14
17520
303
16724
619
.9900
36
480
0, 1
40
12
17903
308
13979
622
1.3950
15
1045
0, 1
55
19
14800
310
APPENDIX L


APPENDIX C
Table Cl. Input/Output relationships, Florida west coast, 1952-72,
economic study of Florida spiny lobster industry
Year
Pounds
Per Trap
Dollars
Per Trap
Pounds
Per Firm
Dollars
Per Firm
1952
213
53
17,717
4,429
1953
134
27
15,887
3,177
1954
62
14
9,896
2,177
1955
93
21
18,802
4,324
1956
137
35
32,408
8,363
1957
154
42
30,957
8,437
1958
100
28
22,205
6,218
1959
78
23
14,987
4,421
1960
39
15
12,674
4,879
1961
54
18
15,010
5,148
1962
42
16
14,238
5,436
1963
46
18
14,896
5,808
1964
39
16
11,473
4,885
1965
49
28
20,301
11,423
1966
49
22
13,672
6,191
1967
30
18
9,154
5,601
1968
40
29
14,415
10,398
1969
48
34
17,360
12,406
1970
46
27
20,332
12,131
1971
32
28
14,068
12,145
1972
20
21
13,069
14,003
143


12
south in the winter. Extremely cold weather, extended periods of un
seasonable weather, or still, calm weather can cause lobsters to migrate
to deeper water (Smith [43]). This is contrary to the findings of
Butler and Pease [9] that spiny lobsters prefer placid waters. Smith
[43] also reported that spiny lobsters are believed to have migrated
over 1,000 miles but generally do not migrate over five miles.
No evidence is available to indicate whether they migrate over deep
straits, but it is believed that long movements lead to a gradual mixing
which, over time, results in an equalization of the stock. Consequently,
the biological stock of a geographical area, characterized by a deep
water perimeter, should be treated as a single unit. As such, changes in
any part of che fishery will eventually affect the whole fishery. Con
versely, as part of the fishery becomes "fished out" it will replenish
Itself if left alone for a period of time. Some evidence suggest that
maximum exploitation of most spiny lobster stocks in the Caribbean have
been reached, with the possible exception of the southern edge of the
Caribbean Sea (Idyll [31]).
The major portion of commercial lobster landings in Florida are
harvested at depths of less than 50 feet using wooden traps. At least
80 percent of annual landings are harvested in the first half of the
season which lasts from August 1 through March 31. Generally, one to
three fishermen per craft fish 200 to 1,000 traps. Length of the craft
range from 16 to 55 feet. They usually travel less than 25 miles and
return the same day. Based on the theory that a trap offers protection
it can be fished without bait. However, freshly baited traps are pre
ferred- There appears to be no difference in landings between traps
baited with cowhide, which lasts longer, and traps baited with fish.


22
August 1. The 1965 act provided that traps may be placed in the water
and baited ten days prior to the open season and must be removed within
five days after the closing of the season, though no lobsters can be
taken during the closed season.
Three types of restrictions on the condition of lobster caught in
Florida exist at present. These deal with minimum size, separation of
head and tail, and egg-bearing females. The minimum size allowed is a
three-inch carapace of a 5 1/2 inch tail, though the tail measurement is
inapplicable if the tail is separated from the body. If head and tail
are separated under required legal permit, the tail must have a minimum
length of six inches. The 1965 act prohibited the catching of egg
bearing female lobsters, and those found in traps are to be returned
alive to the ocean. Stripping eggs from them is also prohibited. That
same act required a special permit if the separation of head and tail
was to be done before landing the lobster. A permit for such separation
may be granted if the operation is so far from land that it is not prac
tical to keep the lobsters alive until landing them.
Historically, in 1929 the first size restriction was enacted, the
minimum being one pound avoirdupois. In 1953 the minimum was redefined
to be a lobster with a tail measuring six inches. The 1953 act rede
fined the minimum size by tail and carapace measurement, with a minimum
carapace measurement of three inches and tail measurement of 5 1/2
inches. Methods of measurement were also given. Finally, a 1969 act
allowed a six-inch minimum on tails separated under special permit.
Presently, no legislation has provided for limited traps per firm,
limited licenses, landings quotas or taxes on landings to restrict the
over employment of labor and capital in the fishery. Groups with common


155
TV. PRODUCTION AND EARNINGS
1. What percent of your total income is earned from lobster fishing?
2. Please complete the following table on monthly landings and values
to the best of your knowledge: (1973-74 season)
1973-74 Season: Landings & Value (August March) Total
Lobster (lbs.)
Lobster ($)
Finfish (lbs.)
Finfish ($)
Other (lbs.)
Other ($)
3. Please answer the following questions to the best of your knowledge.
Space for answers is provided in the table.
A. What is the average size of legal lobsters landed for each
month?
B. How many pounds of "shorts" do you see in your traps per trip,
on the average, for each month?
C. What is the average number of traps lost each month?
D. How many pounds of lobsters do you believe were stolen from
your traps, on the average, each month?
1973-74 (August March ) Total
Quest. A
Quest. B
Quest. C
Quest. D
4. Please check the range of your total earnings from lobster fishing
only for the 1973-74 season. (Below $2,000 to above $30,000)
5. If you fished and if you recall, what was your approximate total
season landings and total number of traps fished each season as
shown in the table.
(72-73) (71-72) (70-71) (69-70) (68-69)
Total Landings
Total Traps Fished
6. What do you feel would be the most efficient combination of the
following if you could design the ideal operation unit?
A. Vessel: Make, Length, Width, Gross Tonnage, Fabrication
B. Engine: Make, Horsepower
C. Size of crew
D. Electric Equipment
E. Hydraulic Equipment
F. Total Number of Traps
G. Approximate Cost of Complete Operation Excluding Crew and
Traps ($)
H. Given this "Dream" Operation Unit Approximately How Many
Pounds Do You Believe You Could Have Landed in 1973-74 Season?


.136
Licensing of traps appears feasible in a theoretical framework if
performed in conjunction with some form of "grandfather clause" legisla
tion. The objective would be to increase costs per trap to a level
where the level of traps fished would be such that the value of the mar
ginal product would be equal to the marginal factor cost of a trap.
Data for this analysis was obtained from the survey of spiny lobster
firms and results showed that typical firms in the industry would be
required to reduce number of traps fished. Assuming 400 firms in the
industry, firm and industry profits are maximized at 557 traps per firm.
No profits are returned if a firm fishes less than 207 traps. Further
more, if less than 400 traps per firm are fished, no regulation of traps
would be needed to maintain the desired 5 million pound level for land
ings. Licensing of traps from a pragmatic standpoint, however, may not
be feasible since policing the number of traps per firm would be diffi
cult and expensive to regulate.
The firm licensing program was essentially based on the theoreti
cal motive of increasing marginal factor costs of the firm to a level
where the value of the marginal product of an additional firm added to
the industry is equal to the marginal factor cost of the firm. Such a
program may or may not limit the number of traps fished and/or landings.
Seven-hundred traps fished and a $1000 license fee were assumed per
firm for the simulated example.
The analysis showed profit per firm was maximized with 121 firms,
while total industry profit was maximized with 211 firms in the indus
try. Total landings were 3.87 million pounds for 121 firms compared
with 5.51 million pounds for 211 firms in the industry. If more than
694 firms entered the industry no profits were earned. If each firm


60
Table 4. Estimated levels of maximum landings (Q) for given levels of
traps per firm (Xi), number of firms (X2), and seasonal water
temperature (X3), economic study of Florida spiny lobster
industry
Maximum
landings (Q)
Variable
approaching
CO
(infinity)
Level
Xl
of Variables
X2
Held Constant
x3
8,152,905
Xi

287
(MEAN)
77.59
(MEAN)
8,607,871
Xl

399
(MAX, 1973)
77.59
(MEAN)
8,121,094
Xl

399
(MAX, 1973)
79.62
(MAX, 1972)
8,450,247
Xl

287
(MEAN)
76.35
(MIN, 1969)
8,905,212
Xl

399
(MAX, 1973)
76.35
(MIN, 1969)
7,666,129
Xl

287
(MEAN)
79.62
(MAX, 1972)
5,860,742
x2
368
(MEAN)

77.59
(MEAN)
6,416,893
x2
429
(1973)

77.59
(MEAN)
6,786,218
x2
482
(MAX, 1971)

77.59
(MEAN)
6,299,442
x2
482
(MAX, 1971)

79.62
(MAX, 1972)
7,083,559
x2
482
(MAX, 1971)

76.35
(MIN, 1969)
Note: Mean, minimum, and maximum refer to values for Monroe County
time-series data, 1962-73 (Appendix K). Numbers in parentheses
represent year.
point where the bioeconomic harvest function becomes flat for all prac
tical purposes. This represents a 366 percent increase in traps per
firm and a 58 percent increase in landings. Note that the levels of
inputs required to achieve the maximum output levels in Table 4 were
totally unrealistic at levels of infinity. A 18 to 78 percent increase


100
marginal rate of technical substitution of traps per firm for firms
(MRTSV ) and is expressed in the following equation:
xlx2
mrtsy
xlx2
dXi
dx7
MP
MP
(53)
MRTS, v is the reduction in number of traps per firm necessary to
xlx2
maintain the same level of landings after an increase in the number of
firms.
Using input levels for the 1973-74 season as set forth in the time-
series data, MRTS v was estimated to be3
xlx2
MRTS
X1X2
A A
Si S2
-1
-2.69.
(54)
Increasing the number of firms in the industry (X2) from 400 to 401
would require decreasing the number of traps per firm (Xi) by three
(2.69 rounded)3to 426 traps to maintain 1973 landings of 5,253,958
pounds. This would result in a total decrease of only 774 traps in
3
the industry. Total cost per firm would decrease by $34.65. Constant
landings would result in an identical level of industry total revenue,
but the additional firm in the industry would decrease average revenue
per firm by $91.23. The reduction of 826 traps would reduce industry
total costs by $7,064 and thus increase industry total profit.
Assuming 429 Xlf 400 X2, $1.08 P TC equal to $1876 + $11.55 X2.
2
MRTS = 2.69 is rounded to 3.0 since inputs are indivisable
XiX2
thus not accurately maintaining the equality of MSY and total revenues.
3(400 x 429) (401 x 426) 774.


APPENDIX I
(Table 18 Computations)
1. Xj assumed equal to 1000, 800, 700, 618, 500, 429, 350, and 200,
A
X2 -
465,173,997.252
(4,773,480.707) 1,439,976,169
Xi
3. Q = 8,610,545.714 =
4. Q = 9,773,480.707 -
1,439,976,169 465,173,997.252
Xi
x2
5. TC/X2 = 1,876 + 11.55Xj
Qr (1.08)
6* ^/X2 = -^T TC/X2
7. tt/X
2a
400
* Q. (1-08)
- TC/X2
8. % A
1T/X2.
Column 7
Column 6
- 1
9.
10.
11.
Maximum State Revenue = (Column 10) x (Column 2)
License Fee assumed:
(Column
7) -
(Column 6)
$20,000
for
1000
traps
per
firm
18,000
for
800
traps
per
firm
15,000
for
700
traps
per
firm
13,000
for
618
traps
per
firm
10,000
for
500
traps
per
firm
5,000
for
429
traps
per
f irm
4,000
for
350
traps
per
firm
3,000
for
200
traps
per
firm
12. % A
tt/X,
A*
- [Column (7) Column (11)] : [Column (6)] 1
-A
State Revenue = (Column 11) x (Column 2)
150


129
Table 19. Analysis of landings per trap required to break-even under
the harvest rebate program for alternative levels of traps
per firm (Xj), economic study of Florida spiny lobster
industry
Number of traps
per firm
1,000
800 700
618 500
429
Q/Xi
35.79
40.00
41.74
42.54
40.67
35.02
BEC
28.17
28.49
28.39
27.74
23.43
16.90
(32.25)
(28.64)
(25.28)
(18.06)
% A
21.29
28.78
31.98
34.79
42.39
54.05
Max. No.
140
156
171
190
246
328
Firms
Note: Q/Xi is estimated landings per trap under harvest rebate program.
BEC is landings per trap required to break-even under price and
cost assumptions of harvest rebate program (break-even criterion).
% A is the percentage difference in Q/X¡ and BEC. Max. No. Firms
is the maximum number of firms allowable in the industry for
given levels of traps per firm under the harvest rebate program.
percent above BEC, respectively. For example, at 700 traps per firm BEC
was 31.98 percent below the estimated average landings per trap. At 500
traps BEC was 42.39 percent below (Q/Xj) and at 425 traps BEC was 54.05
percent below Q/X^. As traps per firm decrease, the difference between
estimated landings per trap and the breakeven level became larger. This
is due to the law of diminishing marginal rate of returns resulting in
an increasing margina] product for a trap as the number of traps per
firm decreases. Thus the program does appear realistic when compared
with expected changes in the industry structure and performance as a
result of the harvest rebate program.
One question that may be of concern about the harvest rebate program
is, "What happens if firms do not select the appropriate plan designed
for them?" Several problems could cause the estimated number of rebate
receivers and harvesters to change.


104
times 2.55, or approximately $35.00, but industry total costs increased
by $12.99. This amount is due to increased fixed costs generated by
the additional firm. Furthermore, industry total revenue remains un
changed since product price was held constant and landings were unchanged
due to substitution of inputs along the isoquant. However, total revenues
per firm decrease by approximately $101 because the same level of total
industry revenues was divided by one additional firm.
The analysis of the marginal rate of technical substitution between
inputs can also provide useful information in deciding which inputs
should be changed (limited or allowed to increase) to induce desired
changes in sustainable yield levels. For example, at 400 firms in the
fishery, MRTS v equals approximately unity (1.0108) and substituting
xlx2
either traps per firm (X^) or number of firms (X2) for the other at this
point would not significantly change total industry landings. As more
than 400 firms enter the industry, the marginal increase in industry
landings is greater if increments are made in traps per firm than if
additional firms are allowed in the industry. At 425 firms the marginal
product of traps per firm (MP ) is 14.1 percent greater than the margi-
X1
nal product of number of firms (HP.. ); and at 500 firms, MF* is 57.9
X2 Xi
percent greater than MP^ This suggests that once the number of firms
x2
exceeds approximately 425, further efficiency in industry harvesting
costs is questionable. This is assuming, of course, that proportionate
increases in costs per trap are not unreasonably higher than costs per
firm, which is highly unlikely. Therefore, if some reasonable level of
profit maximization is part of the overall management goal, no more than
425 firms should be allowed to enter the industry, based on the assump
tions of this analysis.


91
of the marginal product for number of firms (VMP^ ) and the total cost
per firm (Pv ):
X2
(52)
where,
VMP = MP *P the marginal product of firms multiplied times
X2 X2 y
the ex-vessel price per pound (P ),
P = 1,876 + 11.55 Xi, the firm total cost function, and
X2
X2 = optimal number of firms estimated.
The three levels of traps per firm (X^) selectee to reestimate MEY
were (a) the 1973 mean number of traps per firm for the industry (429),
(b) the mean number of traps per firm in the survey (618), and (c) the
optimal number of traps per firm for profit maximization estimated in
the firm analysis from cross-sectional data. The respective optimal
number of firms (X^*) estimated from Equation 51 are (a) 271 firms fish
ing 429 traps each, (b) 236 firms fishing 618 traps each, and (c) 225
firms fishing 700 traps each. The criteria for evaluation are presented
in Table 11. Comparable values can be derived for the typical firm by
dividing the table values by the appropriate number of firms.
In Table 11, landings were estimated at 4.7 million pounds given the
optimum number of firms (271) estimated from Equation 51. Each of these
firms were assumed fishing 429 traps. If all firms fished 618 traps in
stead (the cross-sectional sample mean), 236 firms would be the optimum
number required for a maximum industry profit which would be $3.8 million.


74
Table 6. Marginal products for various lengths of set periods, economic
study of Florida spiny lobster fishery
- '
Days in
Increase in landing
Fishing effort
set period
due to a one day
intensity in terms
(z)
increase in set period
(MPz)
of rounds per week
(X2>
3
2491
2.333
7
735
1.000
10
440
.700
14
271
.500
traps set four days between harvests. Likewise total landings can be
increased by 735 pounds by increasing the set period from 7 days to 8
days. Increasing from a 10 day set period to an eleven day set period
would increase total landings by 440 pounds, while a 271 pound increase
could be expected by allowing traps to set 15 days instead of 14 days.
Marginal increases in total landings due to increasing the set period
by one day can be estimated for any length of set period by the follow
ing equation:
MP = 12116 z-1*43991 (38)
z
where,
MP is the marginal product due to increasing the set period
by one day,
z is the number of days in the set period or between rounds, and
z = 7/x£.
Equivalent levels of fishing effort intensity measured as rounds per
week (X2) for the examples shown in Table 6 range from 2.333 rounds per
week for fishermen that harvest after a three day set period to .500


123
Total industry profits could increase (often including license fees) by
19.4 percent. Incomes to fishermen would be improved, resources would
be allocated in an efficient manner and the stock of spiny lobsters
would be in no danger of over-exploitation.
Number of traps per firm at 618 and 500
Assuming 618 and 500 traps per firm (Rows 4 and 5) profits per firm
and total industry profits could also be increased under the harvest re
bate program compared with the profit structure prior to the program.
However, as the number of traps per firm (Xi) would decrease profits for
each firm and for the industry would decrease (Columns 8, 12, and 15).
This situation would occur because the constant rate of increase in
total cost per firm would be greater than the rate at which the MRTS
xlx2
would decrease, thus resulting in a less steep increasing total revenue
function within the range of data. For example, if a decrease in traps
per firm were induced by regulations that limited trap numbers per firm,
total cost per trap would decrease. As the number of traps would de
crease, MRTS would increase. As MRTS v increases along the iso-
xlx2 xlx2
quant (Figure 13) the marginal productivity of a firm decreases, thus
requiring more firms in the industry to harvest 5 million pounds. More
firms increase total industry costs and thus decrease net returns
(profits) to the firms and the industry.
With the harvest rebate program, profits per firm (Column 12) in
creased 24.4 percent to $9,879 and 19.0 percent to $6,490 for firms fish
ing 618 and 500 traps, respectively.^ License fees were assumed at
Profits remaining above the license cost were derived by subtract
ing Column 11 from Column 7 in Table 17.


Table 17.Continued
Note: Assumptions: (1) Commercial fishermen are profit maximizers; (2) Ex-vessel price, P = $i.C8 per
pound; (3) Desired hardest level for MEY = 5 million pounds (or less defined by input
levels); (4) Rebate receivers are maintained at previous levels; (5) Harvesters are
maintained at least at previous profit levels; (6) Initial number of firms, Xo = 400;
(7) TC = (1,876 + 11.55X^)X2, constant per firm with or without the program; (8) Pro
gram is self-supporting.
Definition: (1) X^ ~ assumed trap per firm level; (2) X2* = maximum number of firms required to
^2
harvest MEY, given X- ; X = j ; (3) QD Industry landings before pro-
1 l p,
K MEY
X1
gram given X2 = 400 and Xp (4) = Industry landings after program, given X2* and
X. ; (5) TC/X2 = total cost per firm before and after program, given X2 = 400 and X-p
(6) tt/X2 = profit per firm before program, given X2 = 400 and X^; (7) ir/X2* profit
per remaining firms, X2*, given X^ (including cost of license fee); (8) Maximum State
Revenue = maximum amount total Xy* could pay in license fees and still maintain pre
vious profit (it) ; (9) Maximum License Fee = maximum fee per X2* and still maintain
previous profit (it); (10) License Fee = assumed license fee, given X2* and Xj¡ ;
(11) State Revenue = total state revenue generated, given license fee; (12) Admin.
Revenue = remaining revenue for administrative costs after paying rebates; (13) % A
Ind. it percentage change in total industry profit due to program; (14) X2** = number
of firms receiving rebate (non-lobster fishing firms); (15) B.E.C. = break-even
criterion for firms choosing not to fish this season, defined as average landings per
trap.
Refer to Appendix I for computations.


APPENDICES


124
$9,500 and $5,000, respectively, to cover rebate payments plus a balance
of $136,970 and $25,412, respectively, for administrative costs. At 618
traps per firm (Column 16) 210 firms received a rebate for not fishing
(Column 16). Then the number of firms decreased to 154 as traps per
firm decreased to 500 because more firms are needed to harvest the as
sumed 5 million pounds. As a result of the rebate program, total indus
try profits increased 15.9 percent with 618 traps per firm and 12.5 per
cent with 500 traps per firm.
When revenues for administrative costs (Column 14) are not adequate
to meet the $250,000 budget assumption license fees would have to in
crease (Column 11, parentheses) to a level that will generate the re
quired revenues. For example, if the harvest rebate program was imple
mented and each firm was allowed to fish 500 traps, the number of firms
choosing to fish would be 246 while the number of rebate receivers would
be 154. Maximum revenues to the state (Column 9) would be $1,596,540,
while program costs for payments to rebate receivers would be $1,204,588
(154 x $7,822). The $5,000 license fee would pay for rebate payments
but would leave only $25,412 to administer the program. To remedy this
deficit the license fee would need to be increased to $6,000, resulting
in a $271,412 budget for administrative costs, excluding rebate payments.
This situation would decrease profit per firm from 19.0 to 6.3 percent
(Column 12). In the case of 429 traps per firm the required revenues
could not be raised without decreasing profit per firm to less than 5
percent. In this case the program was not able to totally support itself
(Column 14, Row 6).


116
but in some cases it may be applicable to other fisheries. The follow
ing is an illustration of how such a program would operate and the anal
ysis of specific effects on landings, revenues, costs, profits, and
optimum input combinations.
Configuration of the Harvest Rebate Program
Establishing this program would begin with a moratorium on all lob
ster licenses. Using the "grandfather clause" approach the total number
of firms would be initially limited to the 1973 level of 400. Next, an
accurate recording of the average number of traps fished per firm (XO
would be necessary. This parameter would serve as the foundation for
the total program in a given season.
Once the optimum number of traps (x^ ) is established using the firm
harvest model (Equation 31), the maximum number of firms required to har
vest the desired level of landings (Q) would be determined. Those firms
not allowed to enter the industry would receive rebate payments.
Who would receive permits would be a difficult question to answer.
One approach is presented here. As an initial program activity, for
example, an application deadline could be established for licenses and
rebates. At this time a range of probable license fees and rebate pay
ments would be announced. After assessing the ratio of harvesters to
rebate receivers a more accurate estimate of license fees and payments
would be announced and a three-week period (arbitrary) would be allowed
for anyone wanting to change status. The consequences of too many chang
ing status should be made clear to the participants since it could be
detrimental to them. For example, too many rebate receivers could re
duce individual payments.


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
AN ECONOMIC ANALYSIS OF ALTERNATIVE MANAGEMENT STRATEGIES FOR
THE SPINY LOBSTER INDUSTRY
by
Joel Sylvan Williams
December, 1976
Chairman: Fred J. Prochaska
Major Department: Food and Resource Economics
Florida's spiny lobster fishery has achieved tremendous growth in
landings during the past two decades. However, the growth of inputs
into the fishery has lately increased at a considerably higher rate,
resulting in declining catch rates, over investment and a potential
for over exploitation of the spiny lobster stock.
This dissertation was designed to evaluate the current level of
resource use, determine the maximum sustainable and economic yield
levels, and analyse alternative lobster management programs. Bio-
economic and firm harvest analytical models were developed and esti
mated. Maximum sustainable yield was estimated to be approximately
seven million pounds while maximum economic yield was estimated to be
5.8 million pounds annually, slightly above current levels. Optimum
levels cf input use are 215 lobster firms each fishing 795 traps.
Ihese levels require a 47 percent reduction in the number of firms
in the industry with no redaction in number of traps fished.


57
The marginal effect of changes in effort on landings was determined
I/by the partial derivatives of the bioeconomic industry harvest function
(Equation 22) with respect to the specific explanatory variable measur
ing effort. The following marginal products (MP ) of the harvest func-
i
tion are partial derivatives with respect to a given explanatory
variable, x^:
1,439,976,169
2
Xi
(23)
= SL =
8X2
465,173,997
x22
(24)
>ffx3 - -235,791 (25)
The additional pounds of lobsters landed in the industry when each firm
intensifies production by adding one trap is shown by MP As each
X1
firm adds a trap total landings increase at a decreasing rate. The
MP
Xj
additional catch per firm can be calculated by for each MP .
X2 Xx
Additional catch per firm is simply the MP divided by X2. MP is
X2 X2
.also a declining function of the number of firms in the industry and
is interpreted to be the additional industry landings resulting from
adding one additional firm to the industry with the same characteristics
as all other firms in the industry.
In the empirical analysis of specific marginal products numerical
values of other variables ware held constant at their mean levels.
Traps per firm (X¡) and number of firms (X2) were held constant at 429
traps per firm and 399 firms, respectively. Mean seasonal surface water


77
off to 708 pounds and then to 42.9 pounds per week, respectively. After
the 1st of September weekly landings tended to level off dropping to
less than 200 pounds per week by December 1st. Some of the larger firms
with greater capital investments quit lobster fishing by November 1st
and go to other species. The expected net returns from netting mackerel
or long-living yellowtail snapper are evidently greater for at least
these firms. Four out of the 25 firms in. the sample did not fish the
entire season. At least three of these four were always ranked in the
top five in number of traps (xj), fishing intensity (X2X and size of
craft (X4). The cost per pound of fishing extra weeks becomes substan
tial and returns become relatively small. Smaller firms often did not
have the alternative of fishing for other species at higher net returns
and remained in the lobster fishery the entire season. On the other
hand, larger firms have a comparative advantage in other fisheries and
began leaving after the 13th week of the season when approximately 68.6
percent of total landings had been harvested.
By changing species early in the harvest season larger firms can
reduce costs substantially for several reasons. After two months the
trap lines become frayed and traps break off and are lost in hauling.'*'
Those traps not lost to frayed buoy lines require additional repairs
which reduce the efficiency of the harvesting process. Second, by late
summer the probability of ocean storms increases substantially and the
risk of losing traps to high winds and rough waters becomes high. Con
sequently, larger firms fishing in excess of 800 traps have the largest
total risk and pull out of trap fishing early in' the season in an
effort to reduce costs.
-Hauling is defined as pulling a trap out of the water.


zn
Table Bl. Spiny lobster capital and labor inputs, Florida west coast, 1952-72, economic study of Florida
spiny lobster indusLry
Fishermen
Boats
Vessels
Traps
Firms
Traps
Per Firm
On
Vessels
On Boats
Regular Casual
Total
No.
No.
Cross
Tonnage
No.
No.
No.
1952
0
71
0
71
54
0
0
4,500
54
83
1953
0
70
0
70
55
0
0
6,500
55
118
1 9 Vi
u
83
28
115
71
2
13
11,490
7 3
160
1955
4
61
10
75
61
2
14
12,700
63
202
1956
28
80
18
126
57
14
104
16,775
71
236
1957
49
138
10
197
83
25
126
21,720
103
201
1958
33
106
8
347
88
17
142
23,221
105
221
1959
30
174
20
224
159
17
134
33,612
176
291
1960
29
192
18
239
132
16
171
54,640
168
325
1961
32
170
11
213
124
16
166
38,990
140
279
1962
40
192
7
239
151
20
212
58,250
171
341
1963
44
233
12
289
162
24
261
60,050
186
323
1969
68
2 J!i
104
410
214
34
338
79,553
248
297
1965
56
306
24
386
188
23
308
89,700
216
415
1966
104
300
12
416
210
58
824
74,550
263
278
1967
14 3
330
24
497
224
75
1189
91,300
299
307
1968
323
214
12
549
135
137
34 33
93,500
272
362
1969
184
255
20
459
176
92
2185
96,955
268
362
1970
287
331
17
635
214
123
3534
150,050
337
445
1971
364
259
39
662
195
142
4184
147,037
337
436
1972
350
333
37
720
238
155
4006
174,490
393
445
Source:
National
Narine Fisheries
Service,
Fishery
Statistics
of the
United Sta
,tes, (Formerly Bureau of
Commercial Fisheries), U.S. Government Frintlng Office, Washington, D.C., Annual Issues, 1952-72.
APPENDIX B


CHAPTER VI
THE MANAGEMENT MODEL
The purpose of this chapter is to present a framework with which
decisionmakers can evaluate management policies. The framework is based
on results from the estimated time-series bioeconomic industry on firm
harvest models in the study. In the first section the analysis of maxi
mum economic yield (MEY) for the industry is presented. Next, analyses
of alternative combinations of traps per firm and number of firms are
presented. Finally, the alternative management considerations outlined
in the study objectives are analyzed.
Maximum Economic Yield for the Industry^
When the quantity of lobster harvested is such that the cost of an
additional unit of input (P ) is equal to the value of the marginal
A,
1
product (VHP ) for that input, then maximum economic yield with respect
A.
1
to the given input (MEY ) is achieved. Maximum economic yield with
Xi
respect to inputs Xj and X2 can be determined by first simultaneously
determining the optimal level of both inputs. These input levels are
then substituted into the production function (Equation 22) to predict
MEY. To determine optimum levels of Xj and X2 for the industry simul
taneously, the profit function (Equation 47) is differentiated with
Recall that capital notations for the variables represent industry
inputs and lower case type for variable notations represent firm inputs.
P represents ex-vessel product price in the firm and industry models.
87


REFERENCES
[1] Allen, Bennet M. "Notes on the Spiny Lobster (Panulirus inter
rupts) of the California Coast," University of California
publication in Zoology, Vol. 16, No. 12, 1916.
[2] Barnhart, P. S. "Notes on the Artificial Propagation of the Spiny
Lobster," California Fish and Game, Vol. 5, No. 2, 1919.
[3] Bell, Frederick W. "Estimation of the Economic Benefits to Fish
ermen, Vessels and Society from Limited Entry to the Inshore
U.S. Northern Lobster Fishery," BCF, DER, W.P. No. 36, March,
1970.
[4] _. The Economics of the New England Fishing
Industry: The Role of Technological Change and Government
Aid, Federal Reserve Bank of Boston, Research Report No. 31,
1966, 215 pp.
[5] "The Relation of the Production Function to
the Yield on Capital for the Fishing Industry," Recent Devel
opment and Research in Fisheries Economics, Frederick W. Bell
and Jared E. Hazleton (eds.), published for the New England
Economic Research Foundation, Dobbs Ferry, New York: Oceana
Publications, Inc., 1967.
[6] "The Pope and the Price of Fish," The American
Economic Review, Vol. LVIII, December, 1968.
[7] Bell, Frederick W. and Richard F. Fullenbaurn. "Economic Impact of
Alternative Management Strategies for the Northern Lobster
Fishery," NMFS, ERD, File Manuscript No. 108, August, 1972.
[8] Bromley, D. W. "Economic Efficiency in Common Property Natural
Resource Use: A Case Study of the Ocean Fishery," BCF, DER,
W.P. No. 28, July, 1969.
[5] Butler, J. A. and N. L. Pease. "Spiny Lobster Explorations in the
Pacific and Caribbean Waters of the Republic of Panama," U.S.
Department of Interior, Fish and Wildlife Service, BCF,
Fisheries Report No. 5U5, 1965.
[10] Carlson, Ernest V/. "Bio-Economic Model of a Fishery," BCF, DER,
W.P. No. J2, March, 19b9.
159


Figure 8
Spiny lobster bioeconomic industry harvest function


20
No quantitative statistical model was used and efficiency (net returns)
was the criterion for evaluation. The conclusions were that previous
regulations of limiting effort have led to economic inefficiencies but
that economic conditions outside the fishery have had an even greater
impact on its present structure.
Regulatory Management Programs
For Florida Spiny Lobster:
Florida laws are designed to regulate the spiny lobster fishing
industry for the purposes of insuring and maintaining the highest pos
sible production of lobster, or in other words, the maximum sustainable
yield. These laws have basically represented biological goals and atti
tudes, but in recent years the need for economic considerations in man
agement schemes has been recognized by .all concerned. During the nearly
4C years prior to 1965, Florida management was mainly concerned with the
conservation of the spiny lobster population through controls on minimum
size and fishing seasons. These regulations are still of importance in
the total management program. Although most of the earlier regulations
have been revised and new regulations added since 1965, gear regulations
were first emphasized in the 1965 legislation. Perhaps more important
in the 1965 legislation was the emphasis on the need for effective
policing policies through the use of marketing by permit number, and
gear and boat identification for surveillance.
The regulations discussed here are as of March 31, 1976. A more
detailed discussion of the present laws and historical pattern of
Florida spiny lobster regulations can be found in a review by
Prochaska and Baarda [36].


53
Initial fishermen contacts were acquired through the Southeastern
Fisheries Center in Miami and a local chapter of Organized Fishermen of
Florida (O.F.F.).1 In July 1974 the research project was presented and
a questionnaire pretested at a local O.F.F. Chapter meeting in the area.
Possible benefits to the fishermen were explained as well as soliciting
their cooperation for interviews to be conducted in the fall. Also,
names of fishhouse managers that would cooperate in encouraging their
local lobster fishermen to be interviewed were obtained.
In October 1974 the interviewing began using a thirteen page ques-
2
tionnaire with those fishermen that agreed to cooperate the past July.
Once this source of interviews was exhausted, various cooperating fish-
houses were then contacted. Managers were asked to recommend fishermen
that they felt would cooperate and that were needed to complete the
various strata as specified by the sample design. Interviewing con
tinued for three weeks until all observations required in the sample as
stratified were collected. Twenty-eight questionnaires were completed
and after editing for inconsistencies and incompleteness, twenty-five
were used in the analysis. Additional observations were collected for
those strata that were weighted heavier to assure completeness. Data
comparisons of study projections with industry output characteristics
suggest the sample was representative.
The author is indebted to Mr. Lloyd Johnson and Mr. Pete Maley,
agents of the Southeastern Fisheries Center, NOAA, NMFS; and the of
ficers of the Lower Keys Chapter of O.F.F. located in the Summerland
Key area.
2
Appendix J includes the survey questionnaire.


1
2
3
4
5
6
7
8
9
10
11
12
13
LIST OF FIGURES
Growth curve for a fishery stock
Page
26
Number of mature progeny as a function of parent
population levels
Equilibrium harvest as a function of parent population
Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to landings
Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to number of firms
The Florida spiny lobster fishery
Observed and predicted volume of spiny lobster
landings, 1963-73 for Monroe County, Florida 56
Spiny lobster bioeconomic industry harvest function 61
Value marginal product of traps per firm (Xj) divided
by the maximum number of firms observed (399) in the
industry in 1973 64
Value marginal product of firms (X2) 66
Firm harvest functions with respect to effort measured
as gear (X3), fishing intensity (X?, X3), firm size (X4),
and adjusted for fishing grounds (X5, Xg) 69
Marginal product curve for spiny lobster craft size
(HP ) 80
x4
Spiny lobster harvest isoquants and ridge lines defining
expansion paths where returns equal total costs, (assum
ing ex-vessel price per pound (P) equals $1.08, industry
total cost equals $1,876 plus $11.55 per trap per firm '
(X¡), and mean seasonal water temperature (X3) equals
77.591F)
xi
102


156
V. ABOUT THE CAPTAIN AND HIS VIEWS ON MANAGEMENT AND REGULATION
1. Toe Captain
A. Age (years)
B. Years lobster fishing (years)
C. Father's occupation
D. What generation lobster fisherman are you
E. Education (grade school, high school, college)
2. Is your lobster operation considered single firm, partnership, or
Corporation?
3. Is there any cooperative activity with other fishermen (i.e. sharing
of labor)? Explain.
4. Do you find that the size of lobsters has decreased over the years?
Yes. No. If so, by how much or in what manner?
5. What are the major factors used by you to determine when and where
to fish certain areas? (i.e. with respect to such things as tides,
month, wind, moon, temperature, barometer readings, etc.)
6. If the landing of shorts \ you have landed in the 1973-74 season in addition to the legal
lobsters you landed? (lbs.)
7. How many pounds of shorts do you feel were landed in your area in
the 1973-74 season? (lbs.)
8. If you were not a lobster fisherman x^hat other occupation would you
have chosen based on your qualifications.
A. Other fishing (specify) Estimated income ($)
B. Non-Fishing (specify) Estimated income ($)
9. What kind of regulation or management xrould you recommend xcith
respect to the following:
A. How long should the season be? Why?
B. What months should the season include? Why?
C. Should the number of licenses be limited? If so, how and to
whom?
D. What is the maximum amount you are x^illing to pay for a license?
E. What should a lobster's legal carapace length be set at? (inches)
F. Other comments.


19
additive structural production function is specified as an average pro
duct function. From the estimation a simple parabolic yield function
was derived. Number of traps was the measure of a unit of effort.
Bell and Fulienbaum [7] developed a production function which was de
rived from an integration of a logistic growth function, an industry
production function and an industry revenue relationship. The model
includes a biomass variable over time, environmental constraints, total
industry cost, a technology variable and other parameters to be esti
mated, such as catching power of a unit of effort. Variables for which
data are lacking are either assumed away or are assumed to be represented
by some proxy and ultimately the whole model collapses into a simple
second degree polynomial equation presented in Bell's earlier publica
tions, The model appears to be considering all the necessary components
of a total bioeconomic system when, in fact, Bell does not have direct
measures of all independent variables in his first model. Dow, Bell,
and Harriman [24] utilized this model and incorporated undated data for
the bioeconomic model and some biological information on the Northern
American lobster such as history, migration, disease, etc.
Huq [30] analyzed labor mobility and social transfer costs of three
representative lobster fishing communities in Maine. Huq concluded that
substantial immobility and limited employment opportunities exist in the
fishery and thus the human element must be seriously considered in de
signing ary management program.
Finally, DeWolf [23] investigated Canada's lobster fishery. Bio
logical and economic bases of fishery regulations were examined. Also
examined were the economic effects of regulations on the fishery, such
as total industry value, total landings, and net return per fisherman.


76
beginning at various dates within the season can be estimated using the
marginal product of weeks, expressed as follows:
MP = 1093.46 x3--6279 (39)
x3
The second partial derivative of the harvest function for weeks fished
showed MP^ diminishing at an increasing rate.
= -686.58 x3-1-6279 (40)
9x3
Estimated marginal products are presented in Table 7 for various periods
A
throughout the harvest season. g3 was statistically significant at the
86 percent confidence level.
Table 7. Weekly landings expected for given dates within the spiny
lobster season, economic study of Florida spiny lobster
industry
Beginning date of Week
(x3>
Weeks fished
Change in landings
for each addition
week fished (MP )
x3
August
7
1.00
1,093
14
2.00
708
31
4.43
429
September
15
6.57
335
30
8.71
281
October
31
13.14
217
November
30
17.43
182
December
31
21.86
158
February
28
30.29
128
March
31
36.14
115
An additional week of fishing after August 7 would return approxi
mately 1,093 pounds. By the third and fourth week, landings would drop


4
annual total revenue per firm increased 23 percent from $11,423 to
$14,003 (Appendix C).
During the 1952-72 period when total revenue increased at a de
creased rate, costs of inputs used in the fishery steadily increased
due to upward shifts in the demand for inputs. But, in recent years,
input costs skyrocketed primarily due to rapidly increasing inflation
which has been shown by changes in the consumer price index (CPI) for
major inputs used in this fishery (Barnhart [2]). The CPI (1967 base)
for petroleum products was 108.9 in 1972 and increased 109.5 points
between 1973 and 1974. For wood products, the CPI was 144.3 in 1972
and increased 11.8 points between 1973 and 1974. CPI representing
engines used in the fishery was 117.9 in 1972 and increased 31.0 points
from 1973 to 1974.
Information on costs of inputs and returns for the 1973-74. spiny
lobster season was acquired in a survey of captains of spiny lobster
boats and vessels/- In 1959 the average spiny lobster craft ranged from
fourteen-foot wooden skiffs that were either rowed or powered by an out
board motor, to larger wooden-hulled craft ranging in length from 26 to
36 feet and powered by 125 to 150 horsepower gasoline and diesel engines.
Average cost of the skiff began at $150 while average cost of the engine
and hull of larger craft ranged from $3,000 to $10,000. From the 1974
survey, average cost of only the engine was $8,257. This was based on a
range from $500 for a 40 h.p. outboard motor to an excess of $60,000 for
AThe survey of 25 captains was completed in October, 1974. The
random sample was stratified according to length of boat and area of
fishery with confidence levels of 90 percent. Individual strata were
weighted according to landings from these areas and size of boats in
these areas.


26
Figure 1. Growth curve for a fishery
stock
relationship between the parent population, the mature progeny, and the
influence of the environment on this biological process. The following
implicit relationship is suggested:
S g(Sj, S2, S3) (2)
where
S ~ stock
£j = population of mature progeny,
So = parent population, and
S3 = environmental attributes affecting the biological
behavior of the stock.
The population of mature progeny (S¡) is a function of the parent popu
lation (S2) and the environment (S3). Also determining the level of
mature progeny is the number of young or recruitment; the rate of growth


APPENDIX D
CROSS-SECTIONAL DATA COMPUTATIONS
Definitions:
x\ = (TR) average number of traps fished for the season.
X2 = (PWK), average number of rounds per week for the season.
X3 = (WK), number of weeks fished during season (36 maximum).
X4 = (LOWD), size of hull in square feet; computed as hull length
(LO) times hull width (WD).
X5 = (DU), dummy variable for upper Keys; DU = e if included
and 1 if excluded.
xg = (DL), dummy variable for lower Keys; DL e if included
and 1 if excluded.
i = months, 1, 2, ... 8 (August March).
PULL = pulling a trap out of the water once (also termed hauling).
TOTAL PULLS = total number of times a trap was pulled (P) out of
the water (could be same or different trap(s)).
ROUND = pulling all traps fished, once.
R. = total rounds per month i.
x
TOTAL ROUNDS = total number of times all traps fished were pulled
(R).
SET PERIOD = length of time a trap sets between pulls (SP).
SF^ = set period for month i.
D, = days per month i.
LG = hull length.
WD = hull width.
T^ = traps fished in month i.
DATA COLLECTED (or known): T SPj[> D x3, LO, WD, x5, and x6.
144


32
value. Thus, the integration of biological and economic considerations
is needed to accurately estimate the relationship between that level of
product which reaches the market (i.e., pounds landed) and those vari
ables that determine that level of product. This process is necessary
to insure that the equilibrium harvest level is both biologically and
economically sufficient.
Bioeconomlc Model
Variables of the yield function (Equation 1) and the production
function (Equation 3) were integrated to form the bioeconoroic model or
the harvest function:
YgE MS, E).
Substituting equations
ybe h(Sj . s
(2) and (4) into (6) gives
3 Ei . E4),
where,
(6)
(7)
Yt, is defined as the bioecoaomic equilibrium yield.
D£j
The biological yield model and the production model provide the
basic foundation from which proper management policies are designed.
Management policies consider equilibrium harvest (Y ) that does not
i)
endanger the parent population (So) while allowing maximization of har
vest ('/ ) for a given level cf inputs. This approach to managing a
fishery is known as maintaining maximum sustainable yield (MSY). MSY
was previously defined as the greatest equilibrium yield possible
without damaging the parent stock and varies in the long-run as a result
of effort, biological changes in the stock, and environmental induce
ments. MSY is an important variable in designing accurate management
policies.


59
changes such as storms and weather fronts. These weather changes often
create lower temperatures and partially explain the inverse relation
ship of this parameter.
Maximum Sustainable Yield (MSY) Estimate
One of the initial objectives in this study was to address the
question of "the status of the spiny lobster fishery with respect to
maximum sustainable yield (MSY)." The industry bioeconomic harvest
model indicated that industry landings are approaching a maximum sustain
able yield. The bioeconomic empirical model based on a theoretical cur
vilinear harvest function fitted the data very well (R2 = .75). Explan
atory variables were individually highly significant and the total
"accounted for" variation was significant. At current levels of effort
the percentage increase in landings was much less than the percentage
increases in inputs.
These conclusions were reached observing the range in landings as
inputs were increased to an infinitely large number as shown in Table 4.
Inputs were held constant at 1973 mean values while the remaining vari
ables were varied. Landings were also analyzed with seasonal water
temperature (Xj) which was held constant at its mean, minimum, and
maximum observed values.
The range of maximum landings was from 5.9 million to 8.9 million
pounds. Illustrated in Figure 8 is the harvest function as it reaches
a maximum of 7.89 million pounds with 2,000 traps per firm (Xj), holding
total number of firms (X2) at the 1973 level of 399 and seasonal water
temperature (X3) at its mean of 77.59. Although some fishermen are
fishing 2,000 traps, this number was chosen to illustrate the approximate


67
respectively (Equation 30, Figure 10). The difference between industry
total value of landings in 1973 for 399 firms fishing compared with 400
firms fishing was $3,154 at a product price of $1.08. In order to gen
erate a net profit to the industry, the addition to industry total cost
from the 400th firm fishing must be less than $3,154.
Analysis of Firm Harvest Function Model
Time-series data on firms included both part-time and full-time
commercial fishermen. Some of these firms fish in more productive fish
ing grounds than others which can significantly influence the firm har
vest rate. Fishing power and intensity of this power varies substan
tially between firms which influences the firm harvest rate. Aggregate
data measuring explanatory variables such as firms and traps have all of
these production input differences confounded in their estimated effects,
thus making the interpretation of estimated coefficients very difficult
and incomplete. Therefore, one objective of the cross-sectional anal
ysis was to obtain partial estimates adjusted for these other influences.
A second objective was to develop cost estimates which would be used
with the time-series bioeconcmic model to determine maximum economic
yield for given measures of effort. That analysis is presented in this
section along with a brief analysis of optimum resource allocation for
the firm at a given fishery stock level.
Firm Harvest Model
The harvesting process for the typical spiny lobster firm was esti
mated using a Cobb-Douglas functional form. The empirical data must lie
in Stage II of production since diminishing marginal returns are indi
cated by less than unity values estimated for the parameters. The


9 VI
Table FI. Spiny lobster landings and dollar values, Florida east and vest coasts, and Monroe County, 1952-73, economic study of Florida spiny
lobster industry
Y?d r
FTOPIfiA
FAST COAST
WEST
COAST
MOSROE
COUNTY
Pound*
Dollnrs
c/lb.
Founds
On]lnra
C/Jb.
Pounds
Pollnra
C/lb.
2 Florida
lbs. Dollars
Founds
Dollars
c/lb.
2 Vest
lbs.
Co%st
Dollars
1552
1.612,400
403.100
25.0
655.700
163,925
25.0
956,;o0
739,175
25.0
59
59
447,396
Na
NA
47
NA
1 VO
1.975.000
397,000
20.0
1,171,200
224.740
20.0
M73,MOO
174,760
21.0
44
44
573.847
NA
NA
66
NA
1534
1.947,300
428,406
22.0
1,223,300
269,126
22.0
/24,000
159,280
22.0
37
37
722,444
NA
NA
100
NA
1555
2.295,400
527,942
23.0
1,079,400
24B.262
23.0
1,216,000
279,680
23.0
53
53
1,210,109
NA
NA
100
NA
1956
3,113,000
825,056
26.5
793,800
227,818
28.5
2,314,200
597,238
25.6
74
72
2,308,836
NA
Na
100
NA
1957
4,039.800
1,123,545
27.8
651,300
200,112
30.7
3,388,500
923,433
27.3
84
82
3,333,541
NA
NA
100
NA
1 VO
2.954,J07
834,451
28.3
677,787
383,772
29.3
7 "ll 570
f 9
28.0
79
78
2,328,406
NA
NA
100
NA
1959
3,180,733
954,605
30.0
542,9/9
176,468
32.5
2,637,754
776,137
29.5
83
82
2,635,118
NA
NA
100
NA
I960
2,848.540
1,100,284
38.6
719,344
280,544
39.0
2,129,19.;
819,740
38.5
75
75
2,126,349
813,664
38.5
100
100
1961
2,803,439
969,303
34.6
702,041
248,523
35.4
2,101,398
720,700
34.3
75
74
2,099,829
720,241
34.3
100
ICO
1942
3.107,000
1,187.177
38.2
672,400
259,546
38.6
2,434,600
927,581
38.1
78
73
2,434.148
929 3 '* *
53.2
100
100
1663
3.585,194
1,407,746
39.3
814,604
327,377
40.2
2,770,590
1,080,369
39.0
77
77
2,770,100
1,080,339
39.0
100
100
1964
3,631,130
1,562,163
43.0
735,718
350.537
44.6
2,845,412
1,211,576
42.6
78
78
2,843,888
1.21G.928
42.6
100
ICO
1965
5,714,093
3,219.741
56.3
1,328,998
751,851
56.6
4,385,095
2.467,390
56.3
77
77
4,379,496
2,464,780
56.3
100
100
1966
5,350,266
2.468,969
46.1
1,686,333
809,852
48.0
3,664.12.3
1,659,117
45.3
68
67
3,650,142
1,654,460
45.3
100
100
196 7
4,413,567
2,732,724
61.9
1,676,595
1,053,000
63.1
2,736,972
1,674,724
61.2
62
61
2,719,173
1,668,216
61.4
99
100
15o5
6,155,036
4,403,569
71.6
2,234,177
1,530,336
70.7
3,920,359
2,823,183
72.1
64
64
3,891,736
2,313,336
72.3
59
99
1969
7,581,133
5.257,542
69.4
2,928,569
1,932,852
66.0
4,652,564
3,324,690
71.5
61
63
4,620,746
3,309,355
71.6
99
100
16 70
9.669,462
5,913,479
60.0
3,017,745
1,330,199
60.
6,851,717
4,008,280
59.7
69
69
5,235,225
3,125.429
59.7
76
76
1971
8,205.S03
7,066,538
86.0
3,417,767
2,932,268
85.8
4,783,036
4,124,270
86.1
58
58
4,653,137
4,017,561
86.3
97
97
1972
10,633,808
10,986.294
103.3
5,736,746
5,721,281
99.7
4,857,062
5,265,013
107.5
46
48
NA
NA
NA
NA
NA
1973
9,667,228
10,221,242
105.7
4,371,265
4,556,980
104.2
5,295,943
5,664,262
107.0
55
55
NA
NA
NA
NA
NA
1572a
11,416,782
11,771,425
103.1
6,267,480
6,254,188
99.8
5,149,302
5,517,237
107.1
45
47
4,314,013
5,176,026
107.5
93
94
1573a
11,171,708
11,661,141
104.4
5,621,636
5,747,531
102.2
5,550,072
5,913,610
106.6
50
51
5,247,409
NA
NA
95
Includes out of season landings. See Footnote a, Table A1, Appendix A
APPENDIX E


Relationships between the size of the parent population in one
time period and the number of mature progeny in the. following time
period may be summarized as in Figure ? (Prochaska [36]). The 45 line
OA, represents the level of mature progeny necessary tc maintain the
parent population at its present level. That is, OA traces out the
number of mature progeny, measured on the vertical axis, necessary to
replace the parent population measured on the horizontal axis. The
curve, OM, represents the actual number of mature progeny that will be
produced by each parent population level. For example, a mature progen
of Mi, will maintain a parent population of PjS but parent population P
will produce and the total fish stock will increase. This process
will continue in nature until the actual production of mature progeny
Parent population
Figure 2. Number of mature progeny as a
function of parent population
levels


CHAPTER V
ANALYSIS OF RESULTS
Estimated coefficients and tiieir interpretation for the industry
and firms' harvest functions are presented in this chapter. Information
from the industry harvest model was used to derive estimates of MSY and
MEY. Optimum input levels and related costs at current stock levels for
the "typical" firm were derived from the firm harvest model. Informa
tion obtained from both analyses was then integrated to analyze alterna
tive fishing practices.
Bioeconomic Model
As previously mentioned, the reciprocal function was selected for
the time-series estimation because of its theoretical characteristics
and its simplicity. Recall that current management programs such as
size limits and protection of berried females suggested the model to be
realistic. The management program protects the young until they reach
minimum size. Thus, assuming continuous fishing pressure it is possible
that (a) there is a lvel of pounds landed which is a function of the
weight of minimum-sized lobsters and (b) increased effort alone will
not cause total landing to decrease because of present size and sex
regulations.
The reciprocal function allows landings to reach a maximum limit
but does not allow total landings to decrease with increased effort.
54


23
interests in and recent concern for the welfare of the fishery have
expressed a need for information describing the benefits and conse
quences of such regulation.


126
landings without the program would have ranged from 7.1 to 1.4 million
pounds, assuming all 400 firms in the industry fished (Columns 3 and 4).
No limit on the number of fishermen was required when fishermen were
limited to 350 or less traps each. Firms were limited to 328 if each
fished 429 traps and to 140 if each fished 1000 traps (Column 2). Net
profits for this group increased in the range from 17.3 to 38.7 percent
(Column 12), for 429 and 1000 traps per firm, respectively.
Total program cost ranged from $2.3 million (1000 traps per firm)
to $0.5 million (429 traps per firm) and was paid for by iicesne fees
ranging from $17,000 for firms fishing 1000 traps each to $1,535 for
firms fishing 429 firms each (Columns 11 and 14). Except for a $26,000
deficit assuming each firm fishing 429 traps the program was totally self
supporting and firms receiving rebate payments were maintained at their
previous incomes. The increase in total industry profit with the program
ranged from 7.3 percent assuming 429 traps per firm to 48.8 percent as
suming 1000 traps per firm.
Assuming the harvest rebate program would be feasible, individual
firms, in many cases, would require a careful evaluation of their opera
tions to determine if a license should be purchased or a rebate payment
received. To aid in this decision making process a breakeven criterion
was developed as a result of this study.
Breakeven Criterion
Using the time-series data and primary data obtained from the cross-
sectional survey, an estimate was developed to provide an indication of
which firms might elect to receive payments for not fishing, given the
structure of the industry for a particular season. The breakeven


28
26
24
22
20
18
16
14
12
10
b
6
4
2
O'
2S,892
^ - X?
100
200
300
Firms (X2)
500
cn
o
10. Value marginal product of firms (X2)


CHAPTER I
INTRODUCTION
The Florida spiny lobster (Panulirus argus) is produced in the
warmer ocean waters and is easily distinguished from its northern, cold-
water cousin, the American lobster (Homarus americanusl by its lack of
claws and relatively smaller size. Over the past forty years the
Florida spiny lobster has developed from a casual food source of the
habitants of the Florida Keys to an important commercial food resource.
Second only to shrimp as a seafood, spiny lobster landings in Florida
exceeded 11 million pounds in 1973 with an estimated retail value of
ever AC million dollars. Over 1,100 licensed fishermen landed lobsters
in 1971. Florida represents approximately 98 percent of U.S. spiny
lobster landings (Appendix A). The Florida spiny lobster fishery is
experiencing an ever increasing number of problems that require imme
diate attention by the legislature, regulatory agencies, and researchers
One of the basic underlying forces creating problems within this
fishery is consumer demand given the relatively fixed supply of stock.
Spiny lobster is now a preferred item in seafood markets and restaurants
An increasing tendency for U.S. consumers to eat in restaurants has
created upward shifts in demand. The demand for spiny lobster is highly
income elastic but inelastic with respect to its own-price elasticity
of demand (Allen [1]). U.S. consumption currently accounts for approxi
mately SO percent of the world spiny lobster production. Canada and
1


81
This analysis was expanded to determine the optimum allocation of inputs
for each size of craft classified by the sample stratification.
Optimum level of input usage is customarily determine by solving
a system of equations determine from the first order conditions. In
this case . x4 can be considered as factors of production and X5
and xg are simply area adjustment factors. Notationally, the equilibrium
between value marginal product (VMP ) and marginal factor price for
Xi
each input (x^) can be represented as
VMP = P (42)
x. x.
1 X
Thus the optimum solution for . X4 is determined by simultaneously
solving Equations 43-46.
67.85
-.2423 = p
J X1
(43)
5557.06
5601 = p
X2 r
x2
(44)
1180.39
-.6279 = p
d x3
(45)
602.67
x -.6912 = p
x4
(46)
The terms on the left of Equations 43-46 represent the value marginal
products for the individual factors determined at the means of the other
independent: variables and at a product price of $1.08 per pound. Un
fortunately the factor prices (P ) were not unique exogenous prices.
1.
They were interdependent and thus presented problems in arriving at a
unique solution. Factor price estimates of a trap (P ) are possible
xi
and were the primary concern in this analysis. As ment Lotted earlier,
the traps (x^) variable was the. principle factor through which all


CHAPTER II
LITERATURE REVIEW
Introduction
Previous empirical spiny lobster (Panulirus argus) research is
summarized and some major theoretical and empirical bioeconoxnic manage
ment studies are capsuled in this chapter. This information is the
minimum necessary to understand biological and psychological relation
ships considered in the design of management programs. Furthermore,
existing laws must be understood before alternative programs can be
considered and thus they are reviewed in this chapter. None of the
empirical bioeconomic studies consider the spiny lobster fishery, but
they do include analyses of management strategies which may be appli
cable to the spiny lobster fishery. Severa] recent bioeconomic studies
such as Eromley [8], Fullenbaum [26], and Van Meir [53] contain extensive
and thorough reviews of past theoretical and empirical studies. This
chapter contains a review of selected theoretical concepts and empirical
studies directly applicable to this study. The reader is referred to
the more extensive reviews where appropriate.
Spiny Lobster Research
There is a lack of economic analysis concerned with management of
the spiny lobster (Panulirus argus). Several empirical studies deal
primarily with biological characteristics, environmental conditions
and physical production analysis of fishing craft, gear, and techniques.
9


79
Table 8. Marginal products of craft size (X4) for sample sizes
observed, economic study of Florida spiny lobster industry
Change in landings for
Craft size (X4)
(length x width)
Length
Width
each additional square
foot increase in craft
size (MP )
X4
80
16
5
27.00
96
16
6
23.80
140
20
7
18.34
154
22
7
17.17
176
22
8
15.66
200
25
8
14.33
208
26
8
13.95
234
26
9
12.86
240
24
10
12.63
252
28
9
12.22
330
33
10
10.14
340
34
10
9.93
341
31
11
9.91
408
34
12
8.76
432
36
12
8.41
468
36
13
7.96
480
40
12
7.82
574
41
14
6.91
675
45
15
6.18
1045
55
19
4.57
of return. After X4 reached 350 square feet (approximately 34 feet long
times 10 feet wide) returns to increasing the size of the craft began to
level off. For example, in Table 8 marginal product of craft size de
creased by 48 percent compared with a 156 percent increase in craft
size, as the square footage increased from 408 (34 feet x 12 feet) to
1,045 (55 feet x 19 feet). The implications were that marginal decreases
in landings due to increases in the size of the craft were smaller for
larger firms than for smaller firms at mean levels of various inputs.
In summary, the estimated firm harvest model fitted the data well
and all individual explanatory variables were highly significant statis
tically. The model indicated that firms were operating In stage II of


Table 16. Analysis of alternative levels for number of firms (X2) assuming traps per firm (Xj) equals 700, mean seasonal
water temperature (X3) equals 77.591F, ex-vessel price per pound equals $1.03, and license fee per firm equals
$1,000, economic study of Florida spiny lobster industry
Total Industry
Per Firm
Number of
Firms (X2)
Landings
CQ)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(1!)
Landings
(q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
* 121
3,871,959
4,181,715
1,326,281
2,835,434
32,000
34,560
10,961
23,599*
175
5,058,235
5,462,894
1,918,175
3,544,719
28,904
31,217
10,961
20,256
* 211
5,511.756
5,952,696
2,312,771
3,639,925*
26,122
28,212
10,961
17,251
249
5,843,203
6,3)6,059
2,729,289
3,536,770
23,487
25,366
10,961
14,405
400
6,553,437
7,077,712
4,384,400
2,693,312
16,384
17,694
10,961
6,733
400
6,786,024
7,328,906
5,480,500
1,848,406
13,572
14,658
10,961
3,697
* 694
7,046,092
7,609,780
7,606,934
2,846*
10,153
10,965
10,961
4*
966
7,234,825
7,813,611
10,588,326
-2,774,715
7,489
8,089
10,961
-2,872
Note; Asterisks highlight
minimum and maximum profits for firms and/or industry and respective number of firms (X2).
111


clerical activities performed during this study. Ms. Jennie Lou Carroll
arduously accomplished the transformation of this dissertation from a
longhand manuscript into its present form. For this feat she has earned
my gratitude and admiration for her considerable ability and perseverance.
Jii


68
estimated equation is
a .7577 .43991 .37211 .30876 .44455 .13063
q = 4.09000 X2 X3 X4 X5 Xg (31)
Equation 31 was estimated in log linear form using ordinary least
square methods. This entails minimizing the sum of squares of the
logarithms of residuals. The assumptions of BLUE estimaters are still
valid.
Landings per firm (q) were measured in pounds. Average traps
fished per firm (xj) was a weighted average of traps fished per firm.
Tills variable considered the initial number of traps fished at the
beginning of the season, the number of traps lost during each month of
the season, and the number of times a trap was fished before lost.
Rounds per week (X2) was a measure of effort intensity and was defined
as the season average proportion of traps pulled per week for the season.
A round was defined as a single pulling of all traps. Total number of
weeks fished (X3) was another measure of effort intensity. In Florida
a maximum of 36 weeks is allowed in the season by law. Fishing power
of the firm (X4) was taken into consideration by including a size vari
able. The square area of the hull was used as a proxy for size. Influ
ences on harvest levels due to quality differences in fishing grounds
were accounted for by including dummy variables X5 and xg which broadly
characterized the firms into the three areas previously defined.^
The R2 corrected for small sample size showed that the harvest
function explained 82 percent of the variation in a typical firm's
"^Derivations and detailed definitions of the explanatory variables
are presented in Appendix D. Appendix G contains the estimating
equations for landings (q) and marginal products (MP ). Appendix L
contains the data used to estimate the firm harvest Xi function.


51
in Table 2, the following stratified sample illustrated in Table 3 was
drawn. Total number of samples drawn was 25 rather than the required
21 in order to round the desired number of samples to whole numbers
after stratification.
Table 2. Stratified population of boats and vessels, defined as
firms, economic study of Florida spiny lobster industry
Length (feet)
Area
<21
21-30
31-40
>40
Total
Upper Keys
8
28
6
2
44
Middle Keys
33
33
14
10
90
Lower Keys
37
25
18
9
89
TOTAL
78
86
38
21
223
(35%)
(39%)
(17%)
(9%)
(100%)
Table 3. Stratified sample of boats and vessels, defined as firms,
economic study of Florida spiny lobster industry
Length (feet)
Area
<21
21-30
31-40
>40
Total
Upper Keys
2
2
2
0
6
Middle Keys
3
3
2
1
9
Lower Keys
3
3
3
1
10
TOTAL
8
8
7
2
25
The following
formula was
used to
determine the
number of
observa-
tions to be sampled in each strata:
C, c,,
i ij
ij N N
n
(20)


33
MSY expresses a physical relationship and has provided the basis
for conservation programs of U.S. fisheries with little concern about
the economic consequences on the fishermen or society (SoLoloski [45]).
In recent years this philosophy of management practices lias changed and
economics has entered the arena of fishery resource management. Such
things as factor prices, product prices, costs, and other pecuniary at
tributes of the "bioeconomic system" must be considered for proper
management of a fishery. To many policy makers maximum economic yield
(MEY) is now considered the objective of "proper" management as is
assumed throughout this dissertation. MEY occurs at a level of landings
which are less than those suggested by the MSY criterion and thus
requires less fishing pressure.
MEY is defined as that yield where net revenue (NR) is maximized
for the fishery. Net revenue for the industry is at a maximum whe^e the
greatest positive difference occurs between total revenue (TR) and total
cost (TC), as illustrated in Figure 4. MEY occurs where the slopes of
the TR curve and TC curve are equal and can be expressed as follows:
BE
EE
0
(8)
where
represents additional or marginal revenue to the industry
tor additional landings, and
9TC
represents additional or marginal cost to the industry for
BE
additional landings.
Industry total revenue (TR) is derived by multiplying the harvest
function (YRt;) by ex-vessel price per pound (P). As ex-vessel price


Table 17. Continued
(10)
(U)
(12)
(13)
(14)
(15)
(16)
(17)
Maximum
license
fee
License
fee
7. 4
ir/X2
Excl.
lie.
fee
State
revenue
Admin.
revenue
loan
rebate
payments
7. A
Total
ind.
profit
No.
firms
rcc1d.
rebate
(X2**)
Break
even
harvest
per
trap
(3EC)
$
$
7.
$
$
7.
No.
lb.
IV, 2*34
17,000
38.7
2,380,000
836,900
48.8
260
28.17
16,168
13,500
36.7
2,106,000
331,388
25.7
244
28.49
13,860
11,500
30.5
1,966,500
195,643
19.4
229
28.39
(11,820)
(26.4)
(2,021,220)
(250,363)
(32.25)
11,435
9,500
24.4
1,805,000
136,970
15.9
210
27.74
(10,100)
(16.8)
(1,919,000)
(250,970)
(28.54)
6,490
5,000
19.0
1,230,000
25,412
12.5
154
23.43
(6,000)
(6.3)
(1,476,000)
(271,412)
(25.28)
2,273
1,000
17.3
328,000
-201,560
7.3
72
16.90
(1.535)
(5.0)
(503,480)
(-26,080)
(18.06)
(No limited
entry program needed
since require more
firms than currently
exiat to harvest
an MEY equal
to 5 million pounds.)
(Ho limited
entry program needed
since require more
firms than currently
exist to harvest
an KEY equal
to 5 million pounds.)
118


CHAPTER III
THEORETICAL MODEL
This study dealt with the management of a living marine resource
and the consequences of management strategies on the resources and its
uses. The production of living marine resources differs from tradi
tional production processes in that it requires the capture of a wild
animal without the more traditional production, cultivation and/or
manufacturing of the products involved. Biological behavior of the
animal, changes in its environment and economic factors of production
(labor, capital, management, and land) influence the success of capture
or amount of product entering the market.^ This relationship between
the product, defined as landings, and the above factors or variables
that influence landings, was defined as a harvest function. The
analyses presented in this study were based on the estimated harvest
function for the Florida spiny lobster resource. The theoretical frame
work of a fishery harvest function is presented in this chapter, A
biological growth model of a fishery was combined with the influence of
man in the form of fishing effort and termed a bioeconomic model.
Finally the procedure in which the bioeconomic model was used to
satisfy the remaining objectives of the study is presented.
^Assuming all that is captured enters the market.
2 4


34
Figure 4. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to landings
increases the TR curve shifts up and conversely TR shifts down s ex
vessel price decreases. Industry total cost (TC) is defined to be a
function of the exogeneous variables of the harvest function (Y^) and
their related prices. TR and TC may be expressed as
TR = Ybe x P (9)
TC = h(S,E) (10)
One fishermans harvest function is theoretically interdependent
with all other fishermen's harvest functions. Landings for one fisher
man are affected by what other fishermen catch from a given stock.
Consequently, as the number of firms in the industry increase, each
firm's production function constantly shifts downward while the asso
ciated cost functions shift upward. Per unit costs increase for the
same amount of effort expended because of fewer landings per unit of



PAGE 1

AM ECONOt-lIC ANALYSIS OF ALTERNATIVE MANAGEMENT STRATEGIES FOR THE SPIKY LOBSTER INDUSTRY by JOEL SYLVAN WILLIAMS A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL CF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOP THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF Yl OR I PA 1976

PAGE 2

ACKNOWLEDGMENTS My debt of gratitude for assistance during my graduate career exceeds my ability to provide acknowledgment. I trust that my many unrecognized benefactors will assume my great appreciation and thanks. The greatest debt should be acknowledged first. Mine is to my wife, Susan, for her moral support, understanding, and patience. Fred Prochaska served as Chairman of my Supervisory Committee, academic and professional advisor, and friend. Joe Havlicek provided substantial guidance during stages of the final draft. W. W. McPherson provided a wellspring of experience from which I have freely drawn as a student and as author of this dissertation. Jim Cato provided a comprehensive critique that greatly improved the overall quality of the final draft. Jim Heaney end Gary Lynne also provided constructive criticism of the study. For these contributions, as well a? many left unmentioned, I am grateful and wish to thank the members of my Supervisory Committee. I wish to thank Leo Polopolus, Chairman of the Food and Resource Economics Department of the University of Florida, for providing financial assistance during my graduate career. In addition, 1 wish to extend my appreciation tc Lloyd Johnson and Pete Maley of NMFS and to members of the Summerland Key Chapter of O.F.F. for their contributions during the survey of spiny lobster captains. I am also indebt ed to Ms. Sandy Waters and Ms. Carolyn Almeter Cor their indispensable' help in the voluminous typing task and numerous li

PAGE 3

clerical activities performed during this study. Ms. Jennie Lou Carroll arduously accomplished the transformation of this dissertation from a longhand manuscript into its present form. For this feat she has earned my gratitude and admiration for her considerable ability and perseverance ill

PAGE 4

TABLE OF CONTENTS ACKNOWLEDGMENTS ii LIST OF TABLES viii LIST OF FIGURES xi ABSTRACT xii CHAPTER I INTRODUCTION 1 Objectives 6 Scope 7 II LITERATURE REVIEW , 9 Introduction 9 Spiny Lobster Research 9 General Bioeconomic Management Research 14 Bioeconomic Lobster Research 18 Regulatory Management Programs for Florida Spiny Lobster 20 III THEORETICAL MODEL . 2k Biological Theory of a Fishery 25 Traditional Economic Production Model 30 Bioeconomic Model .... 32 Summary , 35 iv

PAGE 5

TABLE OF CONTENTS (continued) CHAPTER IV EMPIRICAL MODEL AND DATA Definitions * Bioeconomic Analysis Firm Analysis . . . * • Maximum Economic Analysis (MEY) Study Area and Data Acquisition Sample Selection and Size Survey Technique • • V ANALYSIS OF RESULTS . Bioeconomic Model Maximum Sustainable Yield (MSY) Estimate Value Marginal Product Analysis Analysis of Firm Harvest Function Model Firm Harvest Model • • Estimated Parameters . . . Traps per firm? (x^ Rounds per week. (X2) Weeks fished per season (X3) Craft size (xt,) , . . . . Optimum Resource Allocation of the Firm VI THE MANAGEMENT MODEL . . . Maximum Economic Yield for the Industry Evaluating MEY Policy implications ....

PAGE 6

TABLE OF CONTENTS (continued) CHAPTER VI Discrete Analysis of Alternative. Combinations of Firms and Traps Per Firm 9 Number of traps per firm ac 429 125 Number of traps per firm at 350 and 2C0 .... 125 Overall summary of analysis (Table 17) l2 -> Breakeven Criterion 1 31 VII SUMMARY AND CONCLUSIONS lJJ vi

PAGE 7

TABLE 0? CONTENTS (continued) APPENDIX A Spiny lobster landings and dollar value, Florida and U.S., 1952-73, economic study of Florida spiny lobster industry 141 B Spiny lobster capital and labor inputs, Florida west coast, 1952-72, economic, study of Florida spiny lobster industry ^ C Input/Output relationships, Florida west coast, 1952-72, economic study of Florida spiny lobster industry 143 D Cross-sectional Data Computations • • • 1^4 E Spiny lobster landings and dollar values, Florida east and west coasts, and Monroe County, 1952-73, economic study of Florida spiny lobster industry 146 F Spiny lobster landings in Florida ports caught in foreign waters, 1964-73, economic study of Florida spiny lobster industry 14 G Total product and marginal product equations for firm harvest function model LSO H Comparison of spiny lobster production practices by craft length for firms sampled, Florida Keys, 1963-74 season, economic study of Florida spiny lobster . , 149 industry ^ y I Table 18 computations "0 J Spiny Lobster Firm Survey Questionnaire 152 K Spiny lobster inputs, outputs, and values, Monroe County, Florida, 1963-73, economic study of Florida spiny lobster industry "7 L Data used to estimate firm harvest function, 1973-74 survey of spiny lobster captains, economic study of Florida spiny lobster industry 158 REFERENCES ...... o 359 BIOGRAPHICAL SKETCH 164 vii

PAGE 8

LIST OF TABLES Table Pa g e Industry harvest function variables in theoretical model and reduced form, economic study of Florida spiny lobster industry Stratified population of boats and vessels, defined as firms, economic study of Florida spiny lobster industry Stratified sample of boats and vessels, defined as firms, economic study of Florida spiny lobster industry Estimated levels of maximum landings (Q) for given levels of traps per firm (Xi), number of firms (X 2 ), and seasonal water temperature (X3) , economic study of Florida spiny lobster industry Regression statistics for the cross-sectional firm harvest function model, economic study of Florida spiny lobster industry 39 51 51 60 70 6 Marginal products for various lengths of set periods, economic study of Florida spiny lobster fishery 7 Weekly landings expected for given dates within the spiny lobster season, economic study of Florida spiny lobster industry ^6 8 Marginal products of craft size (X1+) for sample sizes observed, economic study of Florida spiny lobster industry ^9 9 Optimum levels of trap usage per firm and resulting levels of profits, total revenue, total cost, and landings given trap cost, economic study of Florida spiny lobster industry 10 Optimum levels of adjustment factors (X2, X3, and xi^) resulting levels of profits, total revenue , total cost, and landings per firm, economic study cf Florida spiny lobster industry 83 84 viii

PAGE 9

LIST OF TA3LES (continued) Table Pa g e 11 Maximum number of firms (X 2 *) , landings, revenues, and costs for industry profit maximization given desired management levels of traps per firm (X] ) , economic study of Florida spiny lobster industry 92 12 Analysis of alternative levels for number of firms (X2) assuming traps per firm (Xj) equals 700, mean seasonal water temperature (X3) equals 77.591°F, and ex-vessel price per pound (Py) equals $1.08, economic study of Florida spiny lobster industry 96 13 Analysis of alternative levels for number of traps per firm (Xi) assuming number of firms (X 2 ) equals 400, mean seasonal water temperature (X3) equals 77.591°F, and ex-vessel price per pound (Py) equals $1.08, economic study of Florida spiny lobster industry 93 14 Marginal rate of technical substitutions (MRTS X x ) of traps per firm (Xi) for number of firms 1 2 (Xx) holding traps per firm constant at 700, economic study of Florida spiny lobster industry 103 15 Analysis of alternative levels for number of traps per firm (Xi) assuming number of firms (X 2 ) equals 400, mean seasonal water temperature (X3) equals 77.591°F, ex-vessel price per pound (Py) equals $1.08, and trap license fee equals $1.00 per trap, economic study of Florida spiny lobster industry 108 16 Analysis of alternative levels for number of firms (X 2 ) assuming traps per firm (X] ) equals 700, mean seasonal water temperature (X3) equals 77.591°F, exvessel price per pound equals $1.08, and license fee per firm equals $1,000, economic study of Florida spiny lobster industry HI 17 Median and mean spiny lobster landings per trap for sample of firms classified according to number of traps per firm (Xj), economic study of Florida spiny lobster industry H7 13 Median and mean spiny lobster landings per trap for sample of firms classified according to number of traps per firm (Xj), economic study of Florida spiny lobster industry . 128 ix

PAGE 10

LIST OF TABLES (continued) Table 19 Analysis of landings per trap required to breakeven under the harvest rebate program for alternative levels of traps per firm (X^), economic study of Florida spiny lobster industry

PAGE 11

LIST OF FIGURES Figure 1 Growth curve for a fishery stock 2 Number of mature progeny as a function of parent population levels 3 Equilibrium harvest as a function of parent population 4 Maximum economic yield (MEY) for the industry is illustrated as the greatest distance between industry total revenue (TR) and industry total cost (TC) with respect to landings 6 The Florida spiny lobster fishery Page 26 28 30 34 Maximum economic yield (MEY) for the industry is illustrated as the greatest distance between industry total revenue (TR) and industry total cost (TC) with respect to number of firms ^1 48 7 Observed and predicted volume of spiny lobster landings, 1963-73 for Monroe County, Florida 56 8 Spiny lobster bioeconomic industry harvest function 61 9 Value marginal product of traps per firm (Xj) divided by the maximum number of firms observed (399) in the industry in 1973 64 10 Value marginal product of firms (X 2 ) 66 11 Firm harvest functions with respect to effort measured as gear (X^, fishing intensity (X?, X 3 ) , firm size (Xi ( ) , and adjusted for fishing grounds (X 5 , X 6 ) 69 12 Marginal product curve for spiny lobster craft size (MP ) 80 x 4 13 Spiny lobster harvest isoquants and ridge lines defining expansion paths where returns equal total costs, (assuming ex-vessel price per pound (P.,) equals $1.08, industry total cost equals $1,876 plus $11.55 per trap per firm (Xi), and mean seasonal water temperature (X3) equals 77.59J°F) 102

PAGE 12

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN ECONOMIC ANALYSIS OF ALTERNATIVE MANAGEMENT STRATEGIES FOR THE SPINY LOBSTER INDUSTRY by Joel Sylvan Williams December, 1976 Chairman: Fred J. Prochaska Major Department: Food and Resource Economics Florida's spiny lobster fishery has achieved tremendous growth in landings during the past two decades. However, the growth of inputs into the fishery has lately increased at a considerably higher rate, resulting in declining catch rates, over investment and a potential for over exploitation of the spiny lobster stock. This dissertation was designed to evaluate the current level of resource use, determine the maximum sustainable and economic yield levels, and analyse alternative lobster management programs. Bioeconomic and firm harvest analytical models were developed and estimated. Maximum sustainable yield was estimated to be approximately seven million pounds while maximum economic yield was estimated to be L«.S million pounds annually, slightly above current levels. Optimum levels cf input use are 21 c lobster firms each fishing 795 traps, 'ihase levels require a 4? percent reduction in the number of firms in the industry with no reduction in number of traps fished. xii

PAGE 13

Political and social considerations often make the maximum econom yield not a feasible management alternative. In this case an analysis of input (firm and trap) substitution was completed and presented for alternative input and output levels. Resulting cost, revenue and profit levels were determined for alternative program levels. Specific management programs considered in the analysis include licensing, quotas and a harvest rebate program. For each program, maximum yield levels, costs, revenues and profits were determined. Fo the harvest rebate program alternative levels of administrative costs and related sources of revenue were analyzed. xiii

PAGE 14

CHAPTER I INTRODUCTION The Florida spiny lobster (Pa nulirus argus) is produced in the warmer ocean waters and is easily distinguished from its northern, coldwater cousin, the American lobster ( Homarus araericanus) by its lack of claws and relatively smaller size. Over the past forty years the Florida spiny lobster has developed from a casual food source of the habitants of the Florida Keys to an important commercial food resource. Second only to shrimp as a seafood, spiny lobster landings in Florida exceeded 11 million pounds in 1973 with an estimated retail value of over mC million dollar.". Over 1,100 licensed fishermen landed lobsters in 1971. Florida represents approximately 98 percent of U.S. spiny lobster landings (Appendix A). The Florida spiny lobster fishery is experiencing an ever increasing number of problems that require immediate attention by the legislature, regulatory agencies, and researchers. On*, of the basic underlying forces creating problems within this fishery is consumer demand given the relatively fixed supply of stock. Spiny lobster is now a preferred item in seafood markets and restaurants. An increasing tendency for U.S. consumers to eat in restaurants has created upward shifts in demand. The demand for spiny lobster is highly income elastic but inelastic with respect to its own-price elasticity of demand (Allen [1]). U.S. consumption currently accounts for approximately SO percent of the world spiny lobster production. Canada and 1

PAGE 15

Europe account for approximately 10 to 15 percent while the small amount remaining is domestically consumed in the producing countries. Between 50 to 60 countries produce and export spiny lobster tails to the U.S. The top four spiny lobster producing countries are Australia, Cuba, South Africa, and New Zealand. These countries produce approximately 65 percent of world landings while fifth ranked U.S. produces about 7 percent of the world total (U.S. Department of Commerce [48] Retail prices have increased substantially in recent years. In 1960 the retail price of spiny lobster tails was $1.50 per pound and the U.S. consumed 53 percent of the world production. By the 1970s U.S. consumption increased to over 80 percent of the world production of spiny lobsters. The 1970 retail price for spiny lobster tails was $3. A3 per pound and reached $5.40 per pound in 1972. Currently, spiny lobster tails are retailed for as high as 59.27 per pound. 1 In roughly ten years retail price doubled and has almost tripled in the last five years. Rising retail prices have encouraged increased exploitation of spiny lobster stocks. This has resulted in an increasing number of biological and economic problems in the Florida spiny lobster fishery. Somti of these problems could also be credited to the nature of this industry or fishery. Unlike most economic enterprises the spiny lobster fishery is a common property natural resource which is characterized by unlimited entry. As such, the fishery generates excess use of inputs to maximize catch without any economic incentive to conserve or replenish the resource for future use. January 24, 1975, average retail price for three seafood re callers in Gainesville, Florida.

PAGE 16

The spiny lobster fishery is currently subject to some limited form of fishing regulation. Conservation directed regulations presently prohibit stripping eggs from females, specify trap dimensions so small undersized lobsters are released, close areas believed to be nursery areas, and specify a season which protects recruitment. An investigation of the possible excessive use of resources in the industry gives reason for concern. 1 In the last 20 years the number of firms, defined as the sum of vessels and boats, increased from 54 in 1952 to 394 in 1972 (Council of Economic Advisors [18], Bell [3]). Number of vessels began increasing at an increasing rate around 1965. Simultaneously capital and labor inputs began to increase. From 1965 to 1972 firm members increased over 80 percent. Use of other inputs since 1965 also increased substantially: Number of traps by 242 percent; number of traps per firm by 60 percent; and number of fishermen by 101 percent (Appendix B, U.S. Department of Commerce [49], [50]). Landings increased from 956,000 pounds in 1952 to over 5 million pounds in 1972. However, since 1965 landings have increased only 4.4 million pounds or 16 percent. Pounds landed per trap averaged 213 pounds in 1952, 49 pounds in 1965, and 20 pounds in 1972. From 1965 to 1972 dollars generated per trap decreased from $28 to $21; annual landings per firm decreased from 20,301 pounds to 13,069 pounds; and 1 Until 1975 approximately 50 percent of spiny lobster landings in Florida were harvested from the Florida domestic fishery. The remaining 50 percent were harvested in foreign waver fisheries, primarily the Bahamian fishery. Approximately 10.0 percent of these landings were reported as Florida "east coast" statistics. In 1975 the Bahamian government closed its fishery to U.S. fishermen. Due to this U.S. landings were down approximately 25 percent in 1975 compared to 1974 landings.

PAGE 17

annual total revenue per firm increased 23 percent from $11,423 to $14 , 003 (Appendix C) . During the 1952-72 period when total revenue increased at a decreased rote, costs of inputs used in the fishery steadily increased due to upward shifts in the demand for inputs. But, in recent years, input costs skyrocketed primarily due to rapidly increasing inflation which has been shown by changes in the consumer price index (CPI) for major inputs used in this fishery (Barnhart [2]). The CPI (1967 base) for petroleum products was 108.9 in 1972 and increased 109.5 points between 1973 and 1974. For wood products, the CPI was 144.3 in 1972 and increased 11.8 points between 1973 and 1974. CPI representing engines used in the fishery was 117.9 in 1972 and increased 31.0 points from 1973 to 1974. Information on costs of inputs and returns for the 197374. s^xn, lobster season was acquired in a survey of captains of spiny lobster boats and vessels. 1 In 1959 the average spiny lobster craft ranged from fourteen-foot wooden skiffs that were either rowed or powered by an outboard motor, to larger wooden-hulled craft ranging in length from 26 to 36 feet and powered by 125 to 150 horsepower gasoline and diesel engines. Average cost of the skiff began at $150 while average cost of the engine and hull of larger craft ranged from $3,000 to $10,000. From the 1974 survey, average cost of only the engine was $8,257. This was based on a range from $500 for a 40 h.p. outboard motor to an excess of $60,000 for The survey of 25 captains was completed in October, 1974. The random sample was stratified according to length of boat and area of fishery with confidence levels of 90 percent. Individual strata were weighted according to landings from these areas and size of bouts in these areas.

PAGE 18

5 diesel engines approaching 500 h.p. Average cost of the hull for this sample was $8,748. The range was from $400 for a sixteen-foot fiberglass skiff to over $20,000 for wooden and fiberglass vessels with a maximum length of 55 feet. In 1959 a wooden lath trap complete with buoy and line cost an average of $6.00 each. In 1974 average cost of materials alone for a wooden lath trap was $11.00. The cost was a few dollars more if the trap was used for deep-water fishing. Average cost of fishheads used for bait was 5 cents per pound in 1959 compared vzith 11 cents per pound in 1973. The prime interest rate increased from approximately 6 percent in 1959 to 9.5 percent in 1973 signaling a substantial increase in the cost of capital. Spiny lobster captains surveyed in 1974 claimed the costs of petroleum based products, such as polyethlene rope, styrofoam buoys and fuel, were triple 1973 prices. Engine costs were increasing at the rate of 15 tc 25 percent per year. Fiberglass boats were increasing in cost at similar rates. Because of the shortage of cypress lumber the cost of cypress lath for trap construction was also increasing. In addition, the introduction of sonar and other fish locating devices, hydraulic pullers, and ot.her harvesting improvements, has substantially increased the capital investment which the commercial lobster fisherman must make to remain competitive. The increase in number of traps used per fisherman represents a substantial increase in investment. One problem that appears to exist in the fishery is a resource allocation problem . . . "over-investment" in capital (gear and craft) and labor (fishermen). Too many inputs are employed to produce a relatively fixed supply of spiny lobsters. This is reflected in the substantial

PAGE 19

6 increases in inputs (traps, vessels, and gross tonnage) compared with the increase in landings. The broad over-investment problem of the fishery begins with the fishermen. Capital and labor investments increase at the fishermen's level due to (1) a struggle to overcome a severe price-cost squeeze; and (2) interdependencies in the production function creating negative externalities to the fishing firm or producer As a consequence of this increaseing level of effort, a second problem of the fishery that may be occurring is one of "over-exploitation" of the fishery stock. Decreasing stock levels can cause serious long-term damage to the fishery and welfare of fishermen. Ob j ec t ives The overall problem is defined as one of resource allocation. The general objective is focused upon the determination of an optimal allocation of resources for selected price, cost, and fishery management alternatives. Optimal allocation may entail protecting the stock from reaching a level beyond recovery as well as regulating economic factors of the fishery. The specific objectives are (1) To identify the major factors affecting the quantity of spiny lobster harvested, and to estimate the harvest function of the Florida spiny lobster fishery; (?.) To evaluate the potential substitution between specific resources used to harvest spiny lobster in Florida; (3) To determine an optimal combination of inputs for the Florida spiny lobster fishery; and

PAGE 20

(4) To evaluate the impact of selected management programs on resource allocation in the fishery and on the optimum combination of inputs used by firms. Specific programs considered are limiting licensing of firms and traps, establishing landings quotas, and a harvest rebate program. The results of this study will provide a basis for establishing guidelines for managing the Florida spiny lobster fishery. The focus is on the analysis of management strategies which might help reduce the cost and difficulties of regulating effort. In addition, study results can be conceivably viewed as a case study applicable, at least in approach, to other marine resource allocation problems. Finally, individual fishermen may use the results of the production analysis as a basis for both long and short-run decision making. Scop e Spiny lobsters landed in Florida are harvested from the domestic. Florida spiny lobster fishery and foreign water spiny lobster fisheries More than 95 percent of spiny lobster landings harvested from the domes tic fishery are landed in Monroe County. These landings comprise approximately 50 percent or more in past years of all spiny lobster landed in Florida. Without the Bahamian fishery, landings from Monroe County make u P over 90 percent of U.S. spiny lobster landings. Consequently, although the scope of this study is defined as the Florida spiny lobster fishery, the data for the empirical analysis are delineated as that of the Florida Keys or Monroe County, Florida. Hhc majority (approximately 90%) of foreign water landings were lost as a result of the 1975 closing of the Bahamian fishery.

PAGE 21

8 A literature review of theoretical and/or applied bioeconomic research is presented in the next chapter. The theoretical model is presented in Chapter III while the data and empirical model are presented in Chapter IV. Results of the analyses and their practical interpretation are given in Chapter V. Four management alternatives and resulting policy implications are reviewed in Chapter VI. Chapter VII, the final chapter, includes a summary, conclusions, and suggestions for further research.

PAGE 22

CHAPTER II LITERATURE REVIEW In troduction Previous empirical spiny lobster ( Panulirus argus) research is summarized and some major theoretical and empirical bioeconomic management studies are capsuled in this chapter. This information is the minimum necessary to understand biological and psychological relationships considered in the design of management programs. Furthermore, existing laws must be understood before alternative programs can be considered and thus they are reviewed in this chapter. None of the empirical bioeconomic studies consider the spiny lobster fishery, but they do include analyses of management strategies which may be applicable to the spiny lobster fishery. Several recent bioeconomic studies such as Eromley [8], Fullenbaum [26], and Van Meir [53] contain extensive and thorough reviews of past theoretical and empirical studies. This chapter contains a review of selected theoretical concepts and empirical studies directly applicable to this study. The reader is referred to the more extensive reviews where appropriate. Spiny Lobster Research There is a lack of economic analysis concerned with management of the spiny lobster (Panulir us argus ) . Several empirical studies deal primarily with biological characteristics, environmental conditions and physical production analysis of fishing craft, gear, and techniques.

PAGE 23

10 Scientific research in the U.S. on spiny lobster began as early as 1916 (Allen [1], Barnhart [2], and Crawford [19]), but it was not until 1944 that an investigation of the Florida spiny lobster fishery was conducted by the Marine Laboratory at the University of Miami (Smith [42, 43]). A review of studies since 1948 provides considerable information that may be useful in explaining the behavior of landings (Smith [42, 43], Cope [17], 3utler and Pease [9], Dees [22], Chislett and Yesaki [15], and Ting [46]) . Smith's publication in 1958 [43] provides a most complete discussion of the Florida spiny lobster fishery including taxonomy, biological cultivation, fishing gear and methods, dollar value and importance of the fishery, and state regulations of the fishery. Several other studies published since 1958, including Butler and Tease [9], Chislett and „ . , r-,^i n _,_ 1-171 T# •> tact ,,T>A*fr>A oone of Smith ' s findings. YesaKi [15], Cope LI'Jj I* 0 !* upa^cea t>ji-e . oui.li.li ^ Butler and Pease [9], and Chislett and Yesaki [15] determined the feasibility of developing spiny lobster fisheries off coasts of Panama and Jamaica, respectively. Although they primarily compared types of gear and fishing techniques, some biological and environmental observations were documented. Cope [17] analyzed alternative gear and fishing techniques in the Florida fishery. Finally, a recent study by Ting [46] analyzed the potential for spiny lobster cultivation from a physical production standpoint but alluded to economic implications. The information obtained from these studies is briefly summarized. The Florida spiny lobster (Pa nulirus arg us) is one of 30 species distributed nearly world wide in tropical and sub-tropical waters. They differ from the Northern cold-water lobster (Komardie family) in that they lack claws and have long antennae for sensing food and danger.

PAGE 24

IX They are smaller and have numerous spines covering their back (cape) for protection against many natural enemies. The average legal size landed in Florida weighs approximately one and a quarter pounds and is 10 inches long, although in 1968 maximum lengths of 17 inches and weights in excess of 10 pounds were not infrequent (Dees [22]). Spiny lobsters generally feed at night on a wide variety of feeds, primarily small crustaceans. They also forage. During the day they hide in rocks, coral, and other marine growth but are known to resort to cannibalism when crowded. Growth is primarily dependent upon the environment. As body weight of the spiny lobster increases the hard outer shell is sheddedThis shedding of the shell is called molting and occurs several tines throughout the life cycle. The body weight increases approximately 5 percent during each molting stage. Although younger lobsters molt inure frequently, it takes approximately five years for them to reach legal size. Female spiny lobsters do net begin reproducing until they reach a length of eight to nine inches. An eight-inch spiny lobster can produce approximately 50,000 eggs compared with 500,000 eggs produced by a 14inch lobster. In Florida, mating occurs February through June in shallow waters. The eggn are hatched in deeper water three weeks later. It takes the young larvae three to six months to conform to the shape oi the adult lobster. At this stage the young lobster drops to the ocean floor; and is approximately 7/8 inch long. The mortality rate, from hatching to this stage is hypothesized to be over 99 percent. Water temperature, food supply, reproduction and weather influence thft migration of splay lobsters. Usually migration occurs between deep and shallow water bat sometimes migration is north in the summer and

PAGE 25

12 south in the winter. Extremely cold weather, extended periods of unseasonable weather, or still, calm weather can cause lobsters to migrate to deeper water (Smith [43]). This is contrary to the findings of Butler and Pease [9] that spiny lobsters prefer placid waters. Smith [43] also reported that spiny lobsters are believed to have migrated over 1,000 miles but generally do not migrate over five miles. No evidence is available to indicate whether they migrate over deep straits, but it is believed that long movements lead to a gradual mixing which, over time, results in an equalization of the stock. Consequently, the biological stock of a geographical area, characterized by a deep water perimeter, should be treated as a single unit. As such, changes in any part of the fishery will eventually affect the whole fishery. Conversely, as part of the fishery becomes "fished out" it will replenish Itself if left alone for a period of time. Some evidence sugfec.Jw tmii. maximum exploitation of most spiny lobster stocks in the Caribbean have been reached, with the possible exception of the southern edge of the Caribbean Sea (Idyll [31]). The major portion of commercial lobster landings in Florida are harvested at depths of less than 50 feet, using wooden traps. At least £0 percent of annual landings are harvested in the first half of the season which 'lasts from August 1 through March 31. Generally, one to three fishermen per craft fish 200 to 1,000 traps. Length of the craft range from 16 to 55 feet. They usually travel less than 25 miles and return the same day. Based on the theory that a trap offers protection it can be fished without bait. However, freshly baited traps are preferred. There appears to be no difference in landings between traps baited with cowhide, which lasts longer, and traps baited with fish.

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13 New traps catch better after being in the water at least five days. Landings are higher if traps are lifted every two to three days rather than over four days. Traps settling on the bottom collect silt and foreign matter, which past experiences indicate reduce landings if the exterior cf the trap is not brushed every few days. Landings are higher for traps set next to reefs or forage areas than for traps set on reefs and in flat clean areas. Butler and Pease [9] found that bottom temperature and salinity were correlated with the presence of lobsters. In a range of 68°-85°F more lobsters were landed than in higher bottom temperatures of the 83°-85°F range. Also in a total salinity range of 28°-34°/00 landings were higher than at the 31°-32°/00 salinity level. Lobsters will not feed when water temperatures are near freezing and will migrate from locations with colder water temperatures to warmer water locations, ft study on surface and subsurface water temperature shows that the majority of the fishing area in the Florida spiny lobster fishery is isothermal year round (Robinson [39]). This means that in depths of less than 50 feet the difference in the bottom temperature and surface temperature is insignificant. Aquaculture of spiny lobster is possible but currently not economically feasible because they require very exacting care and specialized conditions (Ting [46]) . Spiny lobsters require clean, oxygenated water with a balanced temperature and the individual lobsters kept separated. To accomplish this requires a large volume of space and labor and thus a large capital investment. The growth period from juvenile to marketable size is approximately three years in an artifically created environment, compared with five to seven years in the natural environment.

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14 General Bice co no mic Manag em ent Research Researchers have been contemplating bio-economic management of the fisheries at least as far back as the 1920's as evidenced by Rich's [38] work on the Gulf of Maine fishing grounds in 1929 and Russell's [40] work in 1931 titled "Some Theoretical Considerations on the 'Overfishing' Problem." In 1943, Herrington [29] considered alternative methods of fishing management and Nesbitt [34] investigated the biological and economic problems in management of fisheries. Major theoretical contributions emerged in the early 1950 's in the writings of Schaefer [41], Gordon [28], Christy and Scott [16], Crutchfield and Zellner [21], and Turvey [47]. These antecedents of the past twenty years are generally credited with developing the fundamental bioeconomic theory. Their differences can be briefly analyzed on the. basis of four management objectives. Schaefer 's biological approach was concerned with maximizing production from the sea in a strictly physical production framework. The others were oriented toward the maximum economic yield concept but differed to a slight degree. Gordon, and Scott and Christy actually defined a monopoly situation as optimum with an objective of maximum economic yield above costs. Crutchfield and Zellner' s approach was the same but excluded returns due to monopolistic practices in order to maintain consistency with federal regulations on monopolies. Turvey also maximized economic yield excluding returns to monopolistic practices but, in addition, attempted to maximize consumer surplus. More recent research deals with the empirical application of the above concepts and with some refinements to the theory. Latnpe [32] used a dynamic model of the Cobweb form to investigate the interrela-

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15 tionships between biological and economic aspects of commercial fisheries. Carlson [11, 12] developed a theoretical yield function by integrating an economic production function with a biological growth model and distinguished between firm and industry or aggregate production functions. Van Meir [53] demonstrated that landings will exceed maximum sustainable yield (MSY) as a result of excess effort generated in a competitive economic system such as the George's bank haddock fishery. To curtail effort at MSY he suggested free entry with landings quotas, monopolistic exploitation implying the maximization of net revenue above labor and capital cost, or quotas placed on fishing effort. A problem inherent in all of these alternatives is defining a unit of effort. Smith [44] developed a dynamic competitive model of the interaction between the number of firms (investment) in a fishery and the population of an exploited fish species, which included crowding externalities. Bell's [3, 4, 5, 6] empirical research dealt primarily with firm analysis and illustrates the use of econometric techniques in marine research. He attempted to determine what factors influence the rate of return and what impact their variability has on the industry. A major criticism of his findings is that the estimates will not withstand rigorous statistical tests primarily because of model misspecification and lack of a randomly selected sample. After an extensive review of literature the major revelation can best be explained by a quote from the concluding statement of the abstract of a dissertation written in 1969 (Bromley [8, p. 36]) — "The presence of considerable uncertainty in a fishery, and the lack of perfect knowledge on the part of biologists and economists, renders in sweeping conclusions of traditional writers in fishery, and their subsequent

PAGE 29

16 policy recommendations, particular-/ vulnerable to incrudelity. " Since the time of this statement considerable documentation of theoretical and empirical marine research has accumulated, yet one has to agree that the quoted statement can still carry conviction today. This is not to imply that the research is not useful, but rather that a need still exists for data, authenticated tools, and methodologies for research applicable to the bioeconomic management of today's marine resources. Many of the works to date develop interesting statistical investigations while others hinge on highly abstract optimization criteria. The major reason that the success achieved in traditional agricultural research, particularly in estimating production functions, has not been achieved in marine economics research is partly due to basic underlying problems that have yet to be solved in analyzing marine resources. These problems relate to the techniques, assumptions, and empirical limitations (i.e., lack of biological, environmental and economic data) and are characteristic of the common property nature of bioeconomic resources. The very few exceptions to this lack of success have occurred with species existing in what may be termed "closed systems," in which the researcher had considerable control over the individual variables. Very often the problems are related to inadequate specification of the theoretical bioeconomic structure of the fishery, lack of appropriate biological and economic data, lack of multidisciplinary research cooperation in designing models oriented towards a systems approach, misunderstanding the needs of counterparts in a multidisciplinary team, and often defining objectives dissonant to the researchers or policy makers .

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17 This is evidenced in a recent publication edited by Sokoloski [45] in which several researchers addressed the issues and problems encountered when dealing with research directed toward managing marine resources. Sokoloski defined a critical area of marine resources research to be the measurement of the gap between the "optimum" management solution for a given fishery and current management arrangements. To emphasize the relative lack of success with this objective, he listed several critical issues that have been complicating current research efforts. They were characterized as empirical and conceptual in nature and multidiscipliv-ary in scope. One conclusion drawn after reviewing this publication is the fact that substantial uncertainty exists with respect to the reliability of results in marine economics research and accordingly the proposed management programs. Many of these problems need to be solved before sound management programs can be developed for many of the species. Determination of optimal solutions will require considerable time, effort, and financial resources. Pontecorvo [35] pointed out in his work with Pacific red salmon that the costs of improving information may exceed the benefits. This should be taken into account when deciding the value of increasing the sophistication of models designed for direct applicability in managing a particular fishery. Consequently, when a researcher is given the task of developing management alternatives for a currently existing real problem as in the case of the Florida spiny lobster fishery, he is often not allowed the luxury of exhausting all methodological possibilities in his investigation due to the reasons previously discussed. Because of this he uses what resources are available, such as traditionally acceptable or validated theories in economics and marine biology. For

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18 example, such resources include production functions exhibiting diminishing marginal rates of return, downward sloping demand for a commodity, and the bio-mass or population of a fish species which is in part dependent upon its environment and thus exhibiting a semi-sphere-shaped yield curve. Given lack of data, particularly biological data, and lack of precise models which lend themselves to rigorous statistical testing, it would appear that a reasonable criterion for model building would be "Occum's razor," — the simpler the better. This may not be too unreasonable since statistical testing may be more efficient, the results are timely, completion of the project remains within the limits of the budget, and it is questionable whether more sophisticated models requiring more resources would improve the results. In light of these observations, the approach for this project presented in the next chapter does not attempt to improve the theory or apply overly-sophisticated empirical models or models requiring inapplicable assumptions or data which are not available. Bioeconomic Lobster Research Bioeconomic research related to the Northern American Lobster fishery. Bell, 1970 [3]; Bell and Fullenbaum, 1972 [7]; Dow, Bell and Harriman, 1973 [24]; Huq, 1973 [30]; and DeWolf, 1974 [23] were considered in the development of the present models. The latter two publications by Bell are extensions of his early work on the American lobster industry. All three of Bell's publications analyze impacts of different types of management programs through changes in a ger.eral equilibrium model. In Bell's first publication [3], a linearly

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19 additive structural production function is specified as an average product function. From the estimation a simple parabolic yield function was derived. Number of traps was the measure of a unit of effort. Bell and Fullenbaum [7] developed a production function which was derived from an integration of a logistic growth function, an industry production function and an industry revenue relationship. The model includes a biomass variable over time, environmental constraints, total industry cost, a technology variable and other parameters to be estimated, such as catching power of a unit of effort. Variables for which data are lacking are either assumed away or are assumed to be represented by some proxy and ultimately the whole model collapses into a simple second degree polynomial equation presented in Bell's earlier publications. The model appears to be considering all the necessary components of a total bioeconomic system when, in fact, Bell does not have direct measures of all independent variables in his first model. Dow, Bell, and Harriman [24] utilized this model and incorporated undated data for the bioeconomic model and soma biological information on the Northern American lobster such as history, migration, disease, etc. Huq [30] analyzed labor mobility and social transfer cost.*; of three representative lobster fishing communities in Maine. Huq concluded that substantial immobility and limited employment opportunities exist in the fishery end thus the human element must be seriously considered in designing any management program. Finailv, DeWolf [23] investigated Canada's lobster fishery. Biological and economic bases of fishery regulations were examined. Also examined were the economic effects of regulations on the fishery, such as total industry value, total landings, and net return per fisherman.

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20 No quantitative statistical model was used and efficiency (net returns) was the criterion for evaluation. The conclusions were that previous regulations of limiting effort have led to economic inefficiencies but that economic conditions outside the fishery have bad an even greater impact on its present structure. Re gulato r y Management Programs For Florida Spiny Lobste r 1 Florida laws are designed to regulate the spiny lobster fishing industry for the purposes of insuring and maintaining the highest possible production of lobster, or in other words, the maximum sustainable yield. These laws have basically represented biological goals and attitudes, but in recent years the need for economic considerations in management schemes has been recognized by all concerned. During the nearly 4C years prior to 1965, Florida management was mainly concerned with the conservation cf the spiny lobster population through controls on minimum size and fishing seasons. These regulations are still of importance in the total nianagement program. Although most of the earlier regulations have been revised and new regulations added since 1965, gear regulations were first emphasized in the 1965 legislation. Perhaps more important in the 1965 legislation was the emphasis on the need for effective policing policies through the use of marketing by permit number, and gear and boat identification for surveillance. The regulations discussed here are as of March 31, 1976. A more detailed discussion of the present laws and historical pattern of Florida spiny lobster regulations can be found in a review by Prochaska and Baarda [36].

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21 A $50 permit is required for all persons intending to catch more than 24 lobsters per day. The permit must be carried on the person at all times and can be suspended or permanently revoked upon the arrest and conviction of a permit holder for violation of any of the lobster fishing laws. Florida's management program includes two regulations pertaining to the gear and craft. The first is that all gear (traps and buoys) and the craft must be permanently identified by the permit number and/or color code assigned to the fisherman upon receipt of his permit. The figures on the craft must be at least three inches high to permit, easy identification from the air. The second regulation pertains to the specific gear requirements. Wooden traps, ice cans, drums, and other similar devices may be used provided that they are not equipped with grains, spears, grabs, hooks, or similar devices. The traps must be designed out of wooden slats not to exceed 3x2x2 feet or the cubic equivalent. Only the sides of the traps may be reinforced with 16 gauge, one inch poultry wire. Any gear vised to capture lobsters must be marked by a buoy. Up to twenty traps can be attached to a trot-line, and the line is marked at each end by the attachment of a flag buoy. Buoys used must be of sufficient strength and buoyancy to remain continuously afloat. Any device not conforming to the specifications listed, or not carrying a valid permit number, may be seized and destroyed by enforcement officials. It is unlawful to interfere with anyone's traps or markers without the owner's permission. In 1953 the closed season was set between April 15 and August 15, and in 1955 it was placed at its present interval of March 31 to

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22 August 1. The 1965 act provided that trapt; may be placed in the water and baited ten days prior to the open season and must be removed within five days after the closing of the season, though no lobsters can be taken during the closed season. Three types of restrictions on the condition of lobster caught in Florida exist at present. These deal with minimum size, separation of head and tail, and egg-bearing females. The minimum size allowed is a three-inch carapace of a 5 1/2 inch tail, though the tail measurement is inapplicable if the tail is separated from the body. If head and tail are separated under required legal permit, the tail must have a minimum length of six inches. The 1965 act prohibited the catching of eggbearing female lobsters, and those found in traps are to be returned alive to the ocean. Stripping eggs from them is also prohibited. That same act required a special permit if the separation of head and tail was to be done before landing the lobster. A permit for such separation may be granted if the operation is so far from land that it is not practical to keep the lobsters alive until landing them. Historically, in 1929 the first size restriction was enacted, the minimum being one pound avoirdupois. In 1953 the minimum was redefined to be a lobster with a tail measuring six inches. The 1953 act redefined the minimum size by tail and carapace measurement, with a minimum carapace measurement of three inches and tail measurement of 5 1/2 inches. Methods of measurement were also given. Finally, a 1969 act allowed a six-inch minimum on tails separated under special permit. Presently, no legislation has provided for limited traps per firm, limited licenses, landings quotas or taxes on landings to restrict the over employment of labor and capital in the fisherv. Groups with common

PAGE 36

23 interests in and recent concern for the welfare of the fishery have expressed a need for information describing the benefits and consequences of such regulation.

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CHAPTER III THEORETICAL MODEL This study dealt with the management of a living marine resource and the consequences of management strategies on the resources and its uses. The production of living marine resources differs from traditional production processes in that it requires the capture of a wild animal \;ithout the more traditional production, cultivation and/or manufacturing of the products involved. Biological behavior of the animal, changes in its environment and economic factors of production (labor, capital, management, and land) influence the success of capture or amount of product entering the market. 1 This relationship between the product, defined as landings, and the above factors or variables that influence landings, was defined as a harvest function. The analyses presented in this study were based on the estimated harvest function for the Florida spiny lobster resource. The theoretical frame work of a fishery harvest function is presented in this chapter. A biological growth model of a fishery was combined with the influence of man in the form of fishing effort and termed a bioeconomic model. Finally the procedure in which the bioeconomic model was used to satisfy the remaining objectives of the study is presented. Assuming all that is captured enters the market. 24

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25 Biologica l Theory of a Fishery 1 The harvest function, or yield function. (Equation 1) form a biological point of view represents the. level of biomass (or stock of fish) that can be harvested. The equilibrium level of biomass is that which can be harvested without changing or damaging the parent stock. The yield function may be expressed as Y f (Stock) (1) B where, \' = the amount of biomass available for harvest, and B Stock = the total biomass of fish. This system is exclusive of the influence of man. Biological theory states that the change in the stock of a fishery will follow an S-shaped curve as shown in Figure 1. This theory has been supported by findings from population studies of deer and insects. Additional support is presented in a recent study by Gates and Norton [27] who estimated an Sshaped curve for the yellowtail flounder fishery of New England. An S-sbaped curve suggests that the population increases (a) slowly at lower levels, limited by the reproductive capabilities of smaller numbers and the smaller number of fish that are actually growing: (b) rapidly in the intermediate range, as larger numbers of fish produce more eggs than can survive and food supplies are adequate; and finally, (c) slowly at higher levels where pressure from limited food supplies impedes the population growth in an equilibrium manner and deaths just offset births. Therefore, stock is a function of the biological The material in this section was primarily developed from the following references: Bromley [8], Carlson [10], Christy and Scott [16], Cheung [14], and Prochaska and Bharda [36].

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26 Figure 1. Growth curve, for a fishery stock relationship between the parent population, the mature progeny, and the influence of the environment on this biological process. The following implicit relationship is suggested: S = g(S!, S 2 , S 3 ) (2) where S « stock Sj population of mature progeny, S ? parent population, and S-j = environmental attributes affecting the biological behavior of the stock. The population of mature progeny (Sj) is a function of the parent population (3-,) and the environment (S3). Also determining the level of mature progeny is the number of young or recruitment; the rate of growth

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27 of the progeny; and the natural mortality rate clue to diseases or duo to changes in the biological process. Parent population is a function of the environment, growth rates, and mortality rates. The response of the parent population to the variables may differ for various levels of parent stock. Numerous environmental factors significantly affect the biological process. Significant factors are the food supply, predators other than man and hydrographic characteristics including water temperature, salinity, bottom conditions, currents and atmospheric conditions. The relation between the number of mature offspring and the parent population may be derived from these basic biological relationships The recruitment of nature progeny is of particular interest since that is an important policy variable used in developing management schemes that will maintain seme equilibrium level of catch. The relationship between mature progeny and parent population is a function of the same variable affecting growth. At very low parent population levels recruitment is low because the number of spawners is small. As the parent population increases, the level of recruitment increases. After some population level is reached, recruitment levels decline for reasons due to the environment and biology of the species, such as unhealthy fish stocks, an inadequate ecological niche, declining growth rates, increasing mortality races, severe competition for food, and adverse hydrographic conditions. Thus, at some intermediate population level, the ability cf spawners to rectuit progeny into the standing population is a maximum. At low population levels, growth rates are relatively low, but beyond some population level, the growth rates decline and natural mortality rates are relatively high.

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2S Relationships between the size of the parent population in one time period and the number of mature progeny in the following time period may be summarized as in Figure ? (Prochaska [36]). The 45° line OA, represents the level of suatuve progeny necessary tc maintain the parent population at its present level. That is, OA traces out the number of mature progeny, measured on che vertical axis, necessary to replace the parent population measured on the horizontal axis. The curve, OM, represents the actual number of mature progeny that will be produced by each parent population level. For example, a mature progen of Mi, will maintain a parent population of P}, but parent population I will produce M2 and the total fish stock will increase. This process will continue in nature until the actual production of mature progeny Parent population Figure 2. Number of mature progeny as a function of parent population levels

PAGE 42

29 just equals that necessary to maintain a stable parent population, at P 3 where the lines intersect. At population P 2 , total production of mature progeny is a maximum, and at Pi, the excess of mature progeny over that necessary to maintain the parent population is greatest. The introduction of successful fishing effort while the parent stock is P 3 , will reduce the parent population since there is no net recruitment with parent stock P 3 . The reduction of parent stock in the. initial time period results in an increase in the production of mature progeny in the following time periods. Increased fishing effort may continue to reduce the parent stock until parent stock, P x , is reached. Parent stock, P lt will produce the largest marketable surplus defined as equilibrium harvest and represented as M 2 Mi in Figure 2. Maximum marketable surplus is not at the parent population level which produces the maximum mature progeny (M 3 ) . If in any time period more than the equilibrium harvest is taken, the parent population will move Po and again the equilibrium in following periods will be reduced. If the level of fishing is that which exactly takes the excess over the needed replacement each season, parent population, Pi will be maintained. This is defined as maximum sustainable yield (MSY) . The equilibrium harvest shown as the area between the mature progeny curve, 0:1, and the replacement line, OA, in Figure ?, may be expressed in Figure 3. Points P 0 , Pi, ?2 and P 3 correspond with population levels in Figure 2. The maximum sustained yield, Y , is produced from population Pi which corresponds to ?\ in Figure 2. Except at the maximum sustained yield the same equilibrium harvest may be taken at different levels of parent population. For example, equilibrium .

PAGE 43

30 Maximum Sustainable Yield 7 \ \ 0 P 0 *1 ? 2 P 3 Parent Population Figure 3. Equilibrium harvest as a function of parent population harvest, Y , may be taken with either parent population P 0 or P 2 . HSY B2 occurs at that point of equilibrium harvest curve where its slope is zero. Tr aditional Economic Product ion_Mqdel A production function normally used in economic analysis is defined as the relationship between physical inputs and a resulting level of Physical our put, similar to the biological yield process. The difference occurs in the type of relationship between the inputs and the resulting output. Similarly, theory exists that explains the economic stapes of a production process in an economic system. Production inputs or factors of production can be defined as units of effort and consist of land, labor, capital, and management . The

PAGE 44

31 production process can be defined as Y E f (E) E g(E l5 E 2 , E 3 , En) (3) (4) such that, Y E f(E 1} E 2 , E 3 , E^) (5) where, Y output as a result of effort, E E = effort = combined unit of inputs, Ej . . . E^, E| = land, E 2 = labor, E3 = capital, and E4 = management. The assumed objective for firms in the industry is profit maximization. All firms are assumed to operate in a rational economic manner with production occurring under conditions of decreasing returns. The industry is assumed to have an atomistic structure with constant factor prices and independent production processes.*" The biological yield function (Equation 1) is actually a physical relationship between the various exogenous biological and environmental attributes and the available fish stock for harvesting. The production function (Equation 3) is a physical relationship between output and exogenous variables representing effort. Biological models of fishery populations without economic considerations are of little value as a tool for developing useful policy for fisheries management. Likewise, an economic model devoid of biological considerations is also of little The. reader is referred to Ferguson [25] or Carlson [13] for a complete presentation of production economics.

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32 value. Thus, the integration of biological and economic considerations is needed to accurately estimate the relationship between that level of product which reaches the market (i.e., pounds landed) and those variables that determine that level of product. This process is necessary to insure that the equilibrium harvest level is both biologically and economically sufficient. Bioeconomic Mode l Variable of the yield function (Equation 1) and the production function (Equation 3) were integrated to form the bioeconomic model oi the. harvest function: Y RE = h(S, E) . (5) Substituting equations (2) and (4) into (6) gives Y BE " k(Sl • • • s 3» E! . . . E U ), (7) where, Y t ,,, is defined as the bioeconomic equilibrium yield. BE Tne biological yield model and the production model provide the basic foundation from which proper management policies are designed. Management policies consider equilibrium harvest (Y g ) that does not endanger the parent population (So) while allowing maximization of harvest (/..,) for a given level cf inputs. This approach to managing a t. fishery is known as maintaining maximum sustainable yield (MSY) . MSY was previously defined as the greatest equilibrium yield possible without damaging the parent stock and varies in the long-run as a result of effort, biological changes in the stock, and environmental inducements. MSY is an important variable in designing accurate management policies .

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33 MSY expresses a physical relationship and has provided the basis for conservation programs of U.S. fisheries with little concern about the economic consequences on the fishermen or society (Sokoloski [45]). In recent years this philosophy of management practices has changed and economics has entered the arena of fishery resource management. Such things as factor prices, product prices, costs, and other pecuniary attributes of the "biceconomic system" must be considered for proper management of a fishery. To many policy makers maximum economic yield (MEY) is now considered the objective of "proper" management as is assumed throughout this dissertation. MEY occurs at a level of landings which are less than those suggested by the MSY criterion and thus requires less fishing pressure. MEY is defined as that yield where net revenue (NR) is maximized for the fishery. Net revenue for the industry is at a maximum where the greatest positive differerce recurs between total revenue (TR) and total cost (TC) , as illustrated in Figure 4. MEY occurs where the slopes of the TR curve and TC curve are equal and can be expressed as follows: WY m 8TR_ _ 3TC_ = (8) 3Y BE 3Y BE where DTK 0 BE ~~— reorestnts additional or marginal cost to the industry for additional landings. Industry total revenue (TR) is derived by multiplying the harvest function (Y n£ .) by ex-vessel price per pound (P) . As ex-vessel price represents additional or marginal revenue to the industry for additional landings, and

PAGE 47

34 Landings Figure 4. Maximum economic yield (MEY) for the industry is illustrated as the greatest distance between industry total revenue (TR) and industry total cost (TC) with respect to landings increases the TR curve shifts up and conversely TR shifts down as exvessel price decreases. Industry total cost (TC) is defined to be a function of the exogeneous variables of the harvest function ( Y gg) an d their related prices. TR and TC may be expressed as TR = Y x P (9) TC = h(S,E) (10) One fisherman's harvest function is theoretically interdependent with all other fishermen's harvest functions. Landings for one fisherman are affected by what other fishermen catch from a given stock. Consequently, as the number of firms in the industry increase, each firm's production function constantly shifts downward while the associated cost functions shift upward. Per unit costs increase for the same amount of effort expended because of fewer landings per unit of

PAGE 48

35 effort. Costs per unit of output eventually rise to a level where entry into the industry ceases. Crutchfield [20, p. 12] identified the consequence of such a situation when he said, "... such a market, unregjlated, will destroy itself either economically or biologically." Or in Carlson's [11, p. 7] words, "In common property resource, the 'invisible hand' guarantees that the market will arrive at a solution that is suboptimal." Summary Biological and economic theory suggests the following bioeconomic harvest model". Y fiE = f(Si, S 2 , S 3 , Ei, E 2 , E 3 , Ei,). (11) Major focus of this analysis entailed determining the appropriate input level and subsequent landings where the greatest net revenue is generated to the fishery. Net revenues for various levels of effort such as number of firms in the industry and number of traps were compared. The feasibility of alternatives for limiting effort were assessed by considering the impacts these have on net revenues per firm, number of displaced firms, total revenues to the state from user fees, cost and time of implementation and enforcement of regulations, and expected public acceptability. Development of the theoretical model for this study has resulted in an examination of the biological theory of a fishery resource and a brief discussion of production theory. Models of these two theoretical frameworks were integrated into a bioeconomic model used to explain the theoretical constructs of management goals, namely MSY and MEY. The empirical model and data analysis are presented in the next chapter.

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CHAPTER IV EMPIRICAL MODEL AND DATA The empirical model and estimation procedure are presented in this chapter in three parts. Types of data used are included in the presentation of each structural equation. Delineation of the study area and the method of data acquisition is presented in the final section. Estimation and theoretical analysis of the industry harvest function are presented in the first part of the chapter. The second part of the analysis is concerned with estimation of a firm harvest function and associated optimum resource allocations for the firm at estimated fishery stock levels. Implicit industry factor prices and costs were derived in the firm analysis. The final part of the analysis involved integrating the results from the industry and firm analyses to estimate maximum economic yield (MEY) for the industry. Definitions A few definitions at this point may help clarify relationships within the model. The industry hardest function was estimated using secondary time-series data for 20 years from 1952-71. The firm harvest function was estimated using primary cross-sectional data obtained from a survey conducted in 1974 of 25 full-time spiny lobster fishermen. Capital letters are used to represent variables relating to the industry harvest function, while lower case letters are used to represent variables related to the firm harvest function. The only exception to this 36

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37 is P , which is always used as the ex-vessel product price per pound for the industry and for the firm. Industry landings are represented by Q and firm landings are represented by q. Variables representing inputs into the industry harvest function are Xi, X 2 , and X 3 . Firm harvest function input variables are x l5 x 2 , x 3 , x^, x 5 , and x 6 . In only one case does a variable from the industry harvest function and the firm harvest function represent a similar measure of inputs, number of traps. Xi, from time-series data, represents average number of traps per firm in the industry for a given year, while x 1( from cross-sectional data, represents the number of traps fished by a given firm. An asterick (*) superimposed on a variable, for example x x * , denotes the variable as an optimum solution and facilitates its identification when substituted in different equations. Bioeconomic Analysis Time-series analysis is necessary to determine the direct and indirect effects of increased effort on catch. Resulting effects of the traditional economic production relationships are defined as direct. Indirect effects are the influences on landings from variations in the fish stock due to variations in effort. Time-series analysis is necessary because an analysis for only one point in time will only consider the effect of effort on landings for the given fishery stock in existence at that time. Evaluating effort over time also allows for the consideration of expanding effort on the extensive margin — more firms in the industry. The bioeconomic model set forth earlier can be restated as Y gE h(E lf E 2 , E 3 , E„, S l9 S 2 , S 3 ) (12)

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33 In the lobster fishery E± (land) is not a factor, therefore, Ej drops out of the theoretical equation. E 2 (labor) and E k (management) are transformed into output in the production process through the fishing traps (the primary type of gear used in Florida). Therefore, Xj, traps per firm, is substituted for E 2 and E4 . The remaining production factor E 3 (capital) is represented by both number of traps per firm and number of firms (measured by number of boats and vessels) X 2 . Thus X 2 is substituted for E 3 . The biological factors population of mature progeny (S x ) and parent population (S 2 ) are not available from secondary data. However both have been shown to be a function of environmental factors, (S 3 ), in the previous chapter. Water temperature is one of the many variables which can be used to represent the environment. Water temperature however has been shown as a significant factor affecting lobster landings (Bell [3]) and thus was used in this study as a pro'-; for S 3 and is denoted as X 3 . Thus with these assumptions and substitutions Equation 12 can be rewritten as Q = f(X ls X 2 , X 3 ) ( 13 > Variables in the reduced form equation for the industry harvest function (Equation 13) are compared to variables in the theoretical harvest function (Equation 7) in Table 1. The reciprocal form of the yield function was selected because it is consistent with current conditions and regulations in the industry. Management regulations such as minimum size limits, gear restrictions, prohibition of egg stripping and a fishing season set after spawning, insures some, maximum level of stock. The reciprocal function allows landings to reach a maximum level but does not allow total production

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39 Table 1. Industry harvest function variables in theoretical model and reduced form, economic study of Florida spiny lobster Industry Variable Variable In Theoretical Model In Reduced Form Notation Definition Notation Definition Y BE El bioeconomic yield land (area of fishing) Q total industry landings E-? labor X] traps per firm E 3 capital x 2 number of firms E 4 management Xi traps per firm Si population of mature progeny S 2 parent population s 3 environmental attributes x 3 surface water temperature to decline with additional fishing effort. In addition, the reciprocal function exhibits diminishing marginal returns which is consistent with the stage of production in which firms are expected to operate. The Industry harvest yield function can be expressed in reciprocal form as Bi 3? Q = a + -— + y~ + B3X3 < U > The industry harvest function is used to determine an estimate of maximum sustainable yield (MSY) to serve as a guideline in developing management programs. Since the reciprocal function only approaches a maximum, the MSY analysis considers "approximate" or "practical" maxima. These maxima are estimated using various combinations of explanatory

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AO variables at reasonable maximum levels within the range of the data to determine a range for MSY. Maximum economic yield (MEY) for the industry was also determined from the industry harvest function (Equation 14). Total revenue (TR) was computed by multiplying the estimated harvest function (Equation 14) by product price (P ) . P y is assumed constant and representative of current prices. P y was computed as the current average ex-vessel price per pound. 1 Time-series cost data were unavailable. To determine MEY it was necessary to develop an industry cost function from primary data. A cross-sectional survey of spiny lobster firms was used to obtain the necessary data and is presented in a later section. From these data an industry total cost function was developed. Total industry cost (TC) was derived by computing the average total cost per firm (ATC) for the firms in the sample and then multiplying ATC per firm by the total number of firms (N) in the industry. Together, these functions were used to determine MEY as shown in Figure 5 . Derivation of MEY begins with the determination of the level of firms 2 at which the. slopes of the TR and TC curves (Figure 5) are equal. This is determined by equating industry marginal revenue (partial derivative of TR with respect to X 2 ) with industry marginal cost (derivative of TC with respect to X2) and then solving for the number of P was compared by dividing annual total industry value of landings by' annual total industry landings. Any input that serves as a policy variable for management purposes is applicable in place of firms. Number of firms is preferred for reasons to be liter discussed in this section.

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41 TC Firms (X 2 ) Figure 5. Maximum economic yield (MEY) for the industry is illustrated as the greatest distance between industry total revenue (TR) and industry total cost (TC) with respect to number of firms firms in the industry which is necessary for industry profit maximiza* 1 * tion, X? • The optimum number of firms, X 2 , is substituted into the industry harvest function to determine Q , defined as MEY. Firm Analysis The primary purposes of the cross-sectional survey and subsequent firm analyses were to (a) provide cost estimates required to determine MEY, (b) d fit ermine an optimum allocation of specified inputs for profit Hlotationally the derivation of X 2 is a solution of the following equalities : (a) industry marginal revenue industry marginal cost, 3TR 3TC (b) 7x7 = i"xT ' and (c) P v • H= P Y is price of X 2 . y oX 2 >>. 2

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42 maximization for the firm, and (c) incorporate the analysis of optimum firm input levels into the MEY analysis and related analysis of management alternatives. The firm harvest function is defined as the physical relationship between landings and various units of effort. Effort may be generally categorized as related to labor, capital, management, and fishing area or location (geographical locations). From Equation 11, the general theoretical harvest function, the typical firm harvest function can be defined as q = f(ei, e 2 , e 3 , ei, , s l5 s 2 , S3) (15) where, q = quantity harvested by the typical firm, ei = attributes of the fishing process related to fishing area (somewhat similar to land factor input), U2 " labor, e 3 = capital, eif = management, s\ = mature progeny, 52 parent population, and 53 = environmental attributes. Environmental and biological influences within a given area were assumed constant for this analysis, since the data represent the lobster harvest ing process at a given period in time. Thus, sj, S2> and S3 were deleted "'"Strictly speaking returns to land are to "ownership" of the resource and has little relevance to geographical . locat ion in most instances. Returns to area in fishing is similar to saying a type of soil is better than another in reference to agricultural production, which has no relationship with "ownership" of tne various soil types.

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A3 from Equation 15, except that environmental and biological differences among fishing areas were represented by the coefficient for ej. The objective of this analysis was to determine differences in ei . . . ei, among firms that influence individual firm landings and thus, production responses to different levels of input use. A detailed summary of definitions and derivations of variables that significantly influence the typical firm harvesting process are presented in Appendix D. A trap is defined as before to represent the unit of effort through which the traditional factors of production are employed in the production process. Thus traps, xj , was substituted for e2 > ej, and et, in Equation 15. In addition, the intensity at which the trap is fished was included in the model through the inclusion of x 2 (number of times a fisherman pulls his total number of traps in one week) and X3 (the number of weeks fished). These intensity variables adjusted trap use between firms in a cross-sectional survey and in addition represented additional use of traditional production variables such as labor and capital. Variation in firm size and capital investment were included by a proxy variable, x^ , defined to be the square footage of the boat or vessel. Quality of fishing grounds with respect to stock and other environmental attributes is expected to raise or lower firm harvest and therefore, were entered into the model using dummy variables. Fishing grounds were broadly segregated into three different areas defined by the sample stratification. The upper Keys region (X5) was defined as the 44-miles from Key Largo to Lower Natecumbe Key. The lower Keys region (xg) was defined as that 31-miles from Big Pine Key to Key West. The middle Keys region, the base region, was defined as the 37-mile

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44 stretch between the above two areas. If a one is entered for x 5 and a zero for x 6 the firm was fishing in the upper Keys region and viceversa for a firm fishing in the lower Keys region. If both x 5 and x 6 are zeros, the firm was fishing in the middle Keys region. These dummy variables allow the intercept or position of the harvest function to vary for different fishing areas. Underlying bioeconomic theory for the firm does not specify curvilinearity in the firm harvest function since the stock of lobsters, or sustainable yield, is assumed constant for a given period in time. Thus the Cobb-Douglas functional form was selected which allows for either increasing, constant, or decreasing returns. 1 An additional reason for the selection of the Cobb-Douglas form was that it requires fewer degrees of freedom to derive the interactive effect among the independent variables. The summary of these considerations and the final model for estimation is represented by Equation 16. a . 3i 32 3 3 3t+ 3 5 3 6 q axi X2 X3 Xi t X5 X6 vlo) where, q ~ estimated landings (harvest) for the typical firm, x, = number of traps, x 2 = average number of times a fisherman pulls his total number of traps in one week, x 3 ~ number of weeks fished, x^ = measure of craft size, A detailed discussion of the Cobb-Douglas function is presented in Carlson [13] .

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45 X5 = dummy variable representing upper Keys region (one represents upper Keys and zero represents middle Keys), xg = dummy variable representing lower Keys region (one represents lower Keys and zero represents middle Keys) , and a, gj, . . . Bg are parameters to be estimated. Optimum levels of inputs were determine at the point of profit maximization for the typical firm. The same computational procedure used in the time-series analysis was used to derive TR and TC for the firm and optimal level of input use. Maximum Economic Analysis (MEY) The final part of the estimation procedure involved integrating information obtained in the cross-sectional analysis into the timeseries model which estimated the industry harvest function. This was then used to estimate maximum economic yield (MEY) . A recognized short-coming of the industry harvest function model is that the assumption of homogeneity among fishing firms or "fishing effort" does not prevail in the real world. Firms differ in fishing power due to such factors as size of craft, fishing intensity, and amount of gear. However, note that Equation 16 representing the firm harvest function and based on cross-sectional data adjusted for these differences. Size of craft was accounted for by x^, fishing intensity by x 2 and x 3 , and amount of gear by xj . With these adjustments it was assumed that the firms were homogeneous. The dummy variables, X5 and xg, further influenced this conclusion.

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46 Estimation of the effect of craps on landings for the typical firm using the firm harvest function took into consideration influences of craft size, (x^), fishing intensity (x 2 and x 3 ) and differences in fishing grounds (x 5 and X6>. With this estimate an analysis of optimum number of traps (xi ) was made. Then holding trap levels at this economic optimum an estimate of the optimum number of firms was possible. Thus, X} from the cross-sectional firm analysis was substituted for Xi in the time-series industry harvest function model to estimate industry landings assuming firms are employing the optimum number of traps. Equivalent notational form for the industry harvest function now became 3l 32 Q = a+ — + — + 3 3 X 3 < 17 ) xi 2 where , Q = estimated industry landings, xi = optimal number of traps per firm estimated from firm analysis , X2 = number of firms in the industry, X3 = mean seasonal surface water temperature, c> 3l» B 2 » S3 are parameters to be estimated. MEY with respect to number of firms occurs at that point less than MSY where the difference between total industry revenue and total industry cost are maximized. After deriving industry total revenue and total cost curves, their slopes were equated and the solution for the optimal number of firms (X 2 ) was determined. X 2 occurred when industry margi* nal revenue equals industry marginal cost of an additional firm. X 2 was then substituted into the industry harvest function (Equation 17)

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47 and the solution of Q was equal to MEY with respect to X 2 for a given level of X l5 X 2 , and X 3 , expressed as follows: (18) Bl P2 MEY = Q = a + — + — I + &3 X 3 Xl* X 2 " Thus, traps per firm, estimated from the firm analysis was used as the constant exogenous variable to characterize firms in the industry harvest function model. Ordinarily least squares regression techniques were used to estimate the parameters. S tudy Area and Data Acquisition The Florida spiny lobster fishery primarily consists of the area known as the Florida Keys region. This region is made up of two counties (Dade and Monroe) and is located in the southernmost portion of the state. Spiny lobsters are landed in small amounts in other counties, mostly Pinellas, but these are usually caught in foreign waters. Monroe County was selected for the study area for several reasons. A trend analysis of the Florida spiny lobster fishery was conducted using secondary data for 1952-71 (Williams and Prochaska [54]). From this analysis the Florida landings were estimated to be approximately 95 percent of total U.S. landings in recent years. Approximately 50-60 percent in the last five years of Florida landings were caught in foreign waters (Appendix E) . The majority (over 90 percent of these foreign lobsters) were landed in Dade County. Of the remaining 40-50 percent of total Florida landings (which came from domestic, waters) approximately 80-90 percent were landed in Monroe County (Appendix F) . Monroe County is geographically located in the middle of the domestic spiny lobster fishery (Figure 6). A final consideration is that the impact of confining

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48 Figure 6. The Florida spiny lobster fisheryall domestic spiny lobster fishermen to the Keys region can be addressed."'' For these reasons the study area was delineated to include only Monroe County. In addition, it is realistic to include only that area of the fishery over which the state of Florida has jurisdiction since one of the ultimate objectives is to consider management alternatives . "At the time of this final writing the Bahamian government was proposing to limit its fishing grounds to only its citizens. This will moan that future Florida landings will be made up almost exclusively of domestic stock.

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49 Department of Commerce secondary data on landings, total value of landings, and effort for 1963-73 were used for the time-series analysis [18], [49]. Measurer, of effort for the industry during this period were total number of traps; total number of vessels; total number of boats; total number of fishermen classified as, on vessels or casual; and total gross tonnage of vessels in the industry. Gross tonnage was measured only for vessels greater than 5 gross tons and was loosely defined as a measure relating to the net capacity of the craft. Water surface temperature data was acquired from Ocean Survey Branch of NOAA [52]. It was assumed that surface water temperature and bottom water temperature vary in proportion in this study. This assumption was based on findings from a study by Robinson [39] that concluded no thermoclines exist, or the water is isothermal in Lhe delineated stady area, Temperature data for the study period was in the form of mean, minimum, and maximum monthly temperatures for three stations located at South Miami, Marathon, and Key West. Sample Selection and Size A sample of the population was drawn since surveying the total population was impractical from a cost and time standpoint. Sample size was determined using the following formula: 1 NS 2 _ (19) n = 7 (N 1) D -IS where , n = sample siz?. , ^This formula was obtained from Mendenhall [ 33 j

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50 N » population size, o S = estimate of the population variance, 2 D = B /4, and B = bound on the error of estimation (i.e., 10 percent on each side) . Data from a sample of 15 observations on 1973-74 landings by individual boats (9) and vessels (6) for sizes ranging from 26 feet to 40 feet in 2 length were obtained for estimating the population variance (S ) [51]. 2 The sample was classified into six vessels and nine boats. S , a pooled variance (within craft class) was estimated from the actual survey data to be 30,129,877.77. B was selected at 10 percent on each side of the population mean to be estimated. N was equal to 226 and was calculated from a list of commercial craft registrations provided by the Florida State Department of Natural Resources. Criteria used to include a firm in the population was (a) that the address of the craft owner be Monroe County; and (b) that lobster fishing was listed as the primary (dollar value) species harvested. A major limitation of this sampling technique was that fishermen may live out of the county and fish in the study area and vice-versa. Sample size, N, was calculated to be 21. Stratification of the sample was based on length of craft and location of home port. Proportions in each sample strata were equal to proportions of the population in each strata. Boat length strata were less than 21 tent, 21-30 feet, 31-40 feet, and greater than 40 feet. In the stratification of the study area upper Keys was defined as that area from Key Largo to Lower Matecumbe Key. Middle. Keys was defined as that area from Craig Key to Bahia Honda Key and lower Keys was the. area from Big Pine Key to Key Went. Based on the population as stratified

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51 in Table 2, the following stratified sample illustrated in Table 3 drawn. Total number of samples drawn was 25 rather than the requi 21 in order to round the desired number of samples to whole number after stratification. Table 2. Stratified population of boats and vessels, defined as firms, economic study of Florida spiny lobster industry Length (feet) Area <21 21-30 31-40 >40 Total Upper Keys 8 28 6 2 44 Middle Keys 33 33 14 10 90 Lower Keys 37 25 18 9 89 TOTAL 78 86 38 21 223 (35%) (39%) (17%) (9%) (100%) Table 3. Stratified sample of boats and vessels, def ined as firms , economic s tudy of Florida spiny lobster industry Length (feet) Area <21 21-30 31-40 >40 Total Upper Keys 2 2 2 0 6 Middle Keys 3 3 2 1 9 Lower Keys 3 3 3 1 10 TOTAL 8 8 7 2 25 The following formula was used to determine the number of observations to be sampled in each strata: C C N « _i . -11 . n (20) ij N N

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52 where, N = sample size of strata ij , ij C. = number of craft of length class i, C = number of craft of length class i in area j , ij n = total sample size to be drawn, and N = total population of craft. Su rvey Technique Observational units within each strata were not drawn randomly in the usual sense. The data were collected in a very precarious environment, at a very difficult time. Florida spiny lobster fishermen, like most fishermen, are very independent and generally do not divulge information. So, there was first a problem of locating a fisherman that would cooperate. A second problem frequently encountered was that many cooperative fishermen lacked adequate records, particularly costs, so much of the information was "best estimates." To complicate the matter, at the time of the survey the Internal Revenue Service was investigating Florida fishermen because a recent court ruling had changed the tax regulation, retroactively, and thus information was highly guarded. Also it was felt by many that a substantial amount of undersized lobster were "blackmarketed" from this area. In addition, any list of fishermen was usually out of date because of the highly mobile nature of fishermen. Given these circumstances, it was impossible to collect data on a strictly random basis. Thus, the samples represent fishermen who would cooperate. Personal interviews were conducted until th< quired number of observations within each strata was accomplished, le re-

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53 Initial fishermen contacts were acquired through the Southeastern Fisheries Cenuer in Miami and a local chapter of Organized Fishermen of Florida (O.F.F.)1 In July 1974 the research project was presented and a questionnaire pretested at a local O.F.F. Chapter meeting in the area. Possible benefits to the fishermen were explained as well as soliciting their cooperation for interviews to be conducted in the fall. Also, names of fishhouse managers that would cooperate in encouraging their local lobster fishermen to be interviewed were obtained. In October 1974 the interviewing began using a thirteen page ques2 tionnaire with those fishermen that agreed to cooperate the past July. Once this source of interviews was exhausted, various cooperating fishhouses were then contacted. Managers were asked to recommend fishermen that they felt would cooperate and that were needed to complete the various strata as specified by the sample design. Interviewing continued for three weeks until all observations required in the sample as stratified were collected. Twenty-eight questionnaires were completed and after editing for inconsistencies and incompleteness, twenty-five were used in the analysis. Additional observations were collected for those strata that were weighted heavier to assure completeness. Data comparisons of study projections with industry output characteristics suggest the sample was representative. The author is indebted to Mr. Lloyd Johnson and Mr. Pete Maley, agents of the Southeastern Fisheries Center, NOAA, NMFS; and the officers of the Lower Keys Chapter of O.F.F. located in the Summerland Key area. 2 Appendix J includes the survey questionnaire.

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CHAPTER V ANALYSIS OF RESULTS Estimated coefficients and their interpretation for the industry and firms' harvest functions are presented in this chapter. Information from the industry harvest model was used to derive estimates of MSY and MEY. Optimum input levels and related costs at current stock levels for the "typical" firm were derived from the firm harvest model. Information obtained from both analyses was then integrated to analyze alternative fishing practices. Bioeconomic Mod el As previously mentioned, the reciprocal function was selected for the time-series estimation because of its theoretical characteristics and its simplicity. Recall that current management programs such as size limits and protection of berried females suggested the model to be realistic. The management program protects the young until they reach minimum size. Thus, assuming continuous fishing pressure it is possible that (a) there Is a lvel of pounds landed which is a function of the weight of miriinutn~:jizcd lobsters and (b) increased effort alone will not cause total landing to decrease because of present size and sex regulations . The reciprocal function allows landings to reach a maximum limit but does not allow total landings to decrease with increased effort. 54

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55 It also allows decreasing marginal returns to fishing effort.^" The following spiny lobster harvest function is the statistical model estimated using time-series data: Q = a + f$ 1 ^-+$2ir + S 3 X 3 + e. (21) " 1 A 2 The estimated coefficients and standard errors are presented in Equation (22): Q = 28,379,136 1,439,976,169 — 465,173,997 (365,878,684) (216,457,337) 239,791 X 3 . (170,321) (22) Overall the model was statistically significant at the .01 level (F 3j 7 = 9.16). The coefficient of determination, R 2 and R 2 (which was R2 corrected for degrees of freedom) indicated that the model explained 80 and 75 percent of the variation in annual landings, respectively. A Durbin-Watson value of 2.38 indicated the model hinges on the border 2 between no autocorrelation and inconclusiveness range of the test. The coefficients for traps per firm, 3i> and number of firms traps in the industry, $2» were found to be statistically different from zero at the .01 and .07 levels ue significance, respectively. As a check on the logic, of using the reciprocal form of the function other functions were considered, but none of these yielded "better" results. For the second degree polynomial function, negative signs were estimated for the parameters but the coefficients estimated were not significantly different from zero. 2 Durbin-Watson statistic, is not calculated for less than 15 observations. Therefore DW was not used to test in this case. However, there was no apparent pattern of the residuals.

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56 Observed and predicted values of landings for 1963-73 are shown in Figure 7. Since 1969, landings have varied between 4 and 5 million pounds, with a slight exception in 1970. Maximum landings observed within the data range occurred in 1970 at 5.24 million pounds. In 1973 landings decreased to 4.99 million pounds. Assuming current management regulations are adequate and new technology does not occur, there is little reason to expect landings to increase substantially above five or six million pounds annually. This assumes that biological and environmental factors will remain substantially unchanged. Figure 7. Observed and predicted volume of spiny lobster landings, 1963-73 for Monroe County, Florida

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57 The marginal effect of changes in effort on landings was determined l/by the partial derivatives of the bioeconomic industry harvest function (Equation 22) with respect to the specific explanatory variable measuring effort. The following marginal products (MP ) of the harvest function are partial derivatives with respect to a given explanatory variable, x . : i MP = _ 1,439,976,169 (23 ) *1 "l Xl 2 Xl 2 MP = 19 !L = 46^173^97 (24) X 2 ^ X 2 2 X 2 2 MP Y = ||= B 3 = -239,791 (25) X3 <3X3 The additional pounds of lobsters landed in the industry when each firm intensifies production by adding one trap is shown by MP . As each x l firm adds a trap total landings increase at a decreasing rate. The additional catch per firm can be calculated by — — for each MP . X 2 X} Additional catch per firm is simply the MP divided by X 2 . MP is X 2 x 2 also a declining function of the number of firms in the industry and is interpreted to be the additional industry landings resulting from adding one additional firm to the industry with the same characteristics as all other firms in the industry. In the empirical analysis of specific marginal products numerical values of other variables were held constant at tiv;!r mean levels. Traps per firm (X^) and number of firms (X 2 ) were held constant at 429 traps per firm and 399 firms, respectively. Mean seasonal surf ace' water

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58 temperature was 77.591°F. Evaluating MP V (Equation 23) at 1973 input x l levels gi^es 1,439,976,169 , DO/ , , 0 ,s MP = — * 1 % = 7,824 pounds. (26) (429) As each firm in the industry increases the number of traps it fishes by one, total landings for the industry increases by 7,824 pounds. A one trap increase per firm is equivalent to a 399 total trap increase for the industry and an increase of 19.59 pounds per trap. Evaluating the effect of changing the number of firms in the industry (Equation 24) gives MP = 465,173,99 7 „ 2>Q22 pQundSj (27) (399) Holding traps par firm and water temperature constant and increasing the number of firms by one increases total industry landings by 2,922 pounds. Increasing the number of firms by one unit and holding traps per firm constant, brings 429 new traps into the industry. The fishing power of an additional trap to the industry may be greater if it is the first trap for a new firm compared to an additional trap for a firm already fishing. However, the marginal analysis as set forth will not allow for this difference. Evaluating the effect of changes in water temperature (Equation 25) gives m x 3 " 63 = ~ 239 ' 7yi P°' jnds (28) For every one degree increase in the mean surface water temperature for the season, total industry landings will decrease by 239,791 pounds or about 5 percent of total landings in 1973. A general concensus among fishermen is that landings increase shortly after meteorological

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59 changes such as storms and weather fronts. These weather changes often create lower temperatures and partially explain the inverse relationship of this parameter. Maximum Sustainable Yi eld ( MSY) Estimate One of the initial objectives in this study was to address the question of "the status of the spiny lobster fishery with respect to maximum sustainable yield (MSY)." The industry bioeconomic harvest model indicated that industry landings are approaching a maximum sustainable yield. The bioeconomic empirical model based on a theoretical curvilinear harvest function fitted the data very well (R 2 = .75). Explanatory variables were individually highly significant and the total "accounted for" variation was significant. At current levels of effort the percentage increase in landings was much less than the percentage increases in inputs. These conclusions were reached observing the range in landings as inputs were increased to an infinitely large number as shown in Table 4. Inputs were held constant at 1973 mean values while the remaining variables were varied. Landings were also analyzed with seasonal water temperature (Xj) which was held constant at its mean, minimum, and maximum observed values. The range of maximum landings was from 5.9 million to 8.9 million pounds. Illustrated in Figure 8 is the harvest function as it reaches a maximum of 7.89 million pounds with 2,000 traps per firm (Xi), holding total number of firms (X2) at the 1973 level of 399 and seasonal water temperature (X3) at its mean of 77.59. Although some fishermen are fishing 2,000 traps, this number was chosen to illustrate the approximate

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60 Table 4. Estimated levels of maximum landings (Q) for given levels of traps per firm (X^), number of firms (X 2 ) , and seasonal water temperature (X3), economic study of Horida spiny lobster industry Maximum landings (Q) Variable approaching 00 (infinity) Level Xl of Variables X 2 Held Constant x 3 8,152,905 Xl — 287 (MEAN) 77.59 (MEAN) 8,607,871 Xl — 399 (MAX, 1973) 77.59 (MEAN) 8,121,094 Xl — 399 (MAX, 1973) 79.62 (MAX, 1972) 8,450,247 Xl — 287 (MEAN) 76.35 (MIN, 1969) 8,905,212 Xl — 399 (MAX, 1973) 76.35 (MIN, 1969) 7,666,129 Xl — 287 (MEAN) 79.62 (MAX, 1972) 5,860,742 x 2 368 (MEAN) 77.59 (MEAN) 6,416,893 x 2 429 (1973) 77.59 (MEAN) 6,786,218 x 2 482 (MAX, 1971) 77.59 (MEAN) 6,299,442 x 2 482 (MAX, 1971) 79.62 (MAX, 1972) 7,083,559 x 2 482 (MAX, 1971) 76.35 (MIN, 1969) 1!£££ : Mean, minimum, and maximum refer to values for Monroe County time-series data, 1962-73 (Appendix K) . Numbers in parentheses represent year. point where the bioeconomic harvest function becomes flat for all practical purposes. This represents a 366 percent increase in traps per firm and a 58 percent increase in landings. Note that the levels of inputs required to achieve the maximum output levels in Table 4 were totally unrealistic at levels of infinity. A 18 to 78 percent increase

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61 c o G

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62 in landings would require an infinite percentage increase in inputs. The same point is illustrated in Figure 8 but traps per firm is presented in a more realistic range. Predicted landings increase by 40 percent, from 5.62 to 7.89 million pounds, as a result of a 115 percent increase in the number of traps per firm (from the maximum observed in the data of 482 to 2,000). Estimates of MSY chosen for analysis in this study ranged between six million and eight million pounds with a realistic estimate probably in the range of six to seven million pounds. This is not to imply that landings cannot increase above these figures, but rather that these figures are the levels estimated at which landings could be maintained from year to year — maximum sustainable harvest (yield) , ceteris paribus . Actually, the limiting factor probably is that the typical firm does not have the capacity to reach the required trap level. In summary, maximum harvest levels considered here are quite liberal for several reasons. Some illustrations used extremely unrealistic levels of inputs to achieve the maximum levels of harvest and more importantly, some input levels were beyond the range of data. Estimated landings may be beyond maximum economic yield, discussed in the next section. In addition, substantial input increases of this nature may cause irreversible effects on the population, not directly observable in the existing data on which the analysis was based. Therefore, the realistic MSY level was concluded to be in the range of six to seven million pounds annually. Value Marginal Pro d uct Analysis A mere comprehensive analysis of maximum economic yield (MEY) is presented in the section integrating results from the cross-sectional

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63 and time-series analyses, but cone, knowledge of levels of expenditures and profit maximization can be gained using results of the time-series industry analysis thus far. Value marginal products for given inputs were derived by multiplying constant product price times the respective marginal physical product. The value marginal product equation for traps per firm (X^) is 1 Pi VMP = P MP V = P ( r) (?-9) Xi y Xi y _ 2 where, P = annual average dockside price per pound of lobster, y assumed constant; — = marginal product of Q with respect to input Xi (Equation xi : 23) VMP is the addition to industry total revenue as a result of a margiX] nal increase in traps fished per firm. VMP was divided by the number of firms in the industry in 1973 (399) to demonstrate the effect of price changes on an individual firm (Figure 9). 2 Product prices per pound used in the analysis were $1.08, $1.25, $1.50, and $2.00. In this price range the value marginal product ranged from approximately $4.81 to $140.00 as traps per firm vary from approximately 900 to 168, respectively. At a product price of $1.08 and traps per firm at the mean level for 1952-71 (368) the VMP V was $2.3.77. If Xi the cost for an additional trap were $28.77, this would be the profit VMP is with respect to the subscript (x.) denoted in Equation 29, 2 Mean ex-vessel price of $1.08 per pound was obtained from a . survey of 25 lobster boat captains taken in 1973.

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64 n s H U *H i4_( U-i *§ g 0 B 3 0 .p-i X c3 d p 4-1 n '0 CD T) •H > H r i « — / p P i| 'H OH 0\ A] M« r-* H DO V— 1 (rt M u 4-' m <~i U 1 Q H >-< 4J U 01 O -d 4-1 o vj c •H rH o\ c «H CI H 13 O > 0) u 01 H (0 id ,n o

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65 maximization level of output. Thus as long as the cost of fishing a trap was less than $28.77 it would pay to expand. At dockside prices of $1.25, $1.50, and $2.00, marginal cost per trap could increase to $33.31, $39.97, and $53.30, respectively, before the input level for profit maximization would be reached. With traps per firm (Xj) at the 1973 level of 429, VMP„ ranged from $21.16 (assuming a product price of $1.08 per pound) to $39.22 (assuming a product price of $2.00 per pound) . Maximum level of traps per firm observed was 482 in 1971. At this level VMP„ ranged from $16.77 to $31.07 for product prices ranging x l from $1.08 to $2.00 per pound. These values exceed trap costs and encourage intensification of traps fished per fisherman. Value marginal product for an additional firm was also analyzed while holding traps per firm (Xj) constant. Value marginal product for the firm was expressed as VMP = P ( o) (30) X 2 > X2 2 where, — j = marginal product of Q (Equation 24) with respect to firms X 2 (X 2 ), holding X^ constant. Estimates of VMP for the mean, minimum, maximum, and 1973 levels of X 2 firms are presented in Figure 10 at the product prices used earlier. Profit maximization will occur with 399 firms in the industry when the total cost for the typical firm reaches $;>,i54, $3,652, $4,383, or $5,844, given product prices of $1.08, $1.25, $1.50,or $2.00, respectively Cost of an additional trap includes fixed costs for construction and craft, and variable expenses incurred to fish the trap such as fuel, bait, and labor.

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66

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67 respectively (Equation 30, Figure 10). The difference between industry total value of landings in 1973 for 399 firms fishing compared with 400 firms fishing was $3,154 at a product price of $1.08. In order to generate a net profit to the indu&try, the addition to industry total cost from the 400th firm fishing must be less than $3,154. Analysis of Firm H arvest Function Model Time-series data on firms included both part-time and full-time commercial fishermen. Some of these firms fish in more productive fishing grounds than others which can significantly influence the firm harvest rate. Fishing power and intensity of this power varies substantially between firms which influences the firm harvest rate. Aggregatedata measuring explanatory variables such as firms and traps have ail of these production input differences confounded in their estimated effects thus making the interpretation of estimated coefficients very difficult and incomplete. Therefore, one objective of the cross-sectional analysis was to obtain partial estimates adjusted for these other influences A second objective was to develop cost estimates which would be used with the time-series bioeconomic model to determine maximum economic yield for given measures of effort . That analysis is presented in this section along with a brief analysis of optimum resource allocation for the firm at a given fishery stock level. Firm Harvest Model The harvesting process for the typical spiny lobster firm was estimated using a Cobb-Douglas functional form. The empirical data must lie in Stage II of production since diminishing marginal returns are indicate'.; by Jess than unity values estimated for the parameters. The

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68 estimated equation is .7577 .43991 . 3721 1 . 30876 .414455 . 13063 q = A. 09000 xj x 2 x 3 x 4 x 5 x 6 (31) Equation 31 was estimated in log linear form using ordinary least square methods. This entails minimizing the sum of squares of the logarithms of residuals. The assumptions of BLUE estimaters are still valid . Landings per firm (q) were measured in pounds. Average traps fished per firm (xj) was a weighted average of traps fished per firm. This variable considered the initial number of traps fished at the beginning of the season, the number of traps lost during each month of the season, and the number of times a trap was fished before lost. Rounds per week (x 2 ) was a measure of effort intensity and was defined as the season average proportion of traps pulled per week for the season. A round was defined as a single pulling of all traps. Total number of weeks fished (x 3 ) was another measure of effort intensity. In Florida a maximum of 36 weeks is allowed in the season by law. Fishing power of the firm (x^) was taken into consideration by including a size variable. The square area of the hull was used as a proxy for size. Influences on harvest levels due to quality differences in fishing grounds were accounted for by including dummy variables X5 and xg which broadly characterized the firms into the three areas previously defined.^" The R 2 corrected for small sample size showed that the harvest function explained 82 percent of the variation in a typical firm's "^Derivations and detailed definitions of the explanatory variables are presented in Appendix I). Appendix G contains the estimating equations for landings (q) and marginal products (MP ). Appendix L contains the data used to estimate the firm harvest X i function.

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69 o o o o S fl> 0", spunoJ pupsnoqx O ITi O to C — t •H X 00 H '4-1 rt CJ M to 0 4-1 CO 03 tj 11 TJ u di CO > i 3 ^ rn CO ""Ci R) til Gj (3 ™j C i-' t6 »•< O # in 'M .* a ; c a) N 4--' •H a 09 a) 0 n M CJ •H u in ,c 1-1 •H CO to EJ CM o X •H 4-> a >^ C 4J — * •H 10 DO X C 1J OJ r M 4J in C) a X > •H ^—^ M (0 c •a •H c a 3 Of) O •H H V-i 4-1 DO a.' •H

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70 landings (Table 5) . The range in error of estimated landings was computed by expressing the antilog of the standard error of the estimate (SEE) as a percentage of the total estimated value. For Equation 31 landings varied from 31.5 percent above to 24.0 percent below the estimated harvest values. Table 5. Regression statistics for the cross-sectional firm harvest function model, economic study of Florida spiny lobster industry Independent Estimated Standard Significance Variables (x.) l Coefficient (B^ Error t-Ratio Level of Probability Constant (u) A. 09000 1.2500 1.128 Traps per firm (Xi) .75770 .1099 6.895 .9999 Rounds per week (x 2 ) .43991 .2772 1.587 .8700 Weeks fished (x 3 ) .37211 .2400 1.550 .8615 Craft size .30876 .1358 2.274 .9645 Upper Keys area (x 5 ) .44455 .1493 2.977 .9919 Lower Keys area (x 6 ) .13063 .1653 .790 .5603 Note: R 2 = .8223, R 2 = .9310, d.f. 18, SEE = .2742, F 6>18 = 19.514. The relationship of landings to effort (xj, x 2 , X3 and,Xi,) for the firm is presented in Figure 11. Adjustments to the firm harvest function for the influence of different fishing grounds is also illustrated. An analysis of the estimated effort coefficients (Equation 31) indicated that the function is homogeneous of degree 1.87848 and thus defined an industry exhibiting increasing returns to scale. The theoretical interpretation was that the marginal returns to a simultaneous

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71 increase in all inputs was positive and total landings were increasing at an increasing rate. Homogenity of 1.87848 means that if each of the independent variables of the harvest function are multiplied by a constant k, landings will change by a multiple of k 1 ' 8781,8 . For example, if xi . . . x 6 are all doubled (k = 2) landings will more than quadruple. To illustrate the significance of this, assume that the State of Florida determined that MSY had been surpassed and landings would have to be reduced by, say, approximately 50 percent to protect the fishery stock from irreversible damage. Given hcniogenity of 1.87848, all inputs would have to be reduced by only 25 percent to obtain a 58 percent reduction in landings per firm, and thus, for the industry, assuming homogeneous firms.'' If the state does not have control over individual effort, individual firms would have to be provided some inducement to voluntarily cut back input usage, similar to the objective of the Federal Soil Bank Program for agriculture in the 1960s. Although this type of analysis may provide some interesting insights into management of the fishery, it may be argued that the interpretation is non-sensical . Realistically speaking, size of craft and number of weeks are definitely limited beyond some point of expansion. Estimated Parameters The estimated coefficients (B/) of the harvest function presented in Table 5 explained the percentage change in landings due to a given one percent change in the particular input level, assuming all other inputs ^"Notationally the derivation is as follows: (>75) 1. 87848 . q = .58 q where, q = firm harvest function (Equation 31).

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72 constant. These were defined as output elasticities and can also be expressed as ratios of marginal and average productivities. Partial differentiation of the harvest function (Equation 31) with respect to given explanatory variables, gave the marginal products as follows : 3a * * Bi-1 3? 33 Bi+ 3s 3g fvn X! 3x x A, A. A A A A 3q * * 3?-2 Bi 33 3 1+ 3s 36 nil MP = I 3 = a 3 2 x 2 2 x^^^xit H x 5 D x 5 UJJ x 2 3x 2 /\ a /s A A 3q "2 3 3 -l 3i 3 2 Bit 3s 36 (r>A\ MP = -~= a B3X3 d X! x x 2 z xij H x 5 3 x 6 U
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number fished. The marginal return to an additional trap was positive and also greater than the marginal return for any of the other three forms of effort. Rounds per week (x?) As the firm increased its trap pulling rate by one percent (i.e., decreases its set period), landings increased by 44 percent (6 2 = .43991) Rounds per week is an index measuring fishing intensity as defined in Appendix D. B 2 was statistically significant at the 87 percent confidence level. The marginal product of x 2 was expressed as MP x2 5317 x 2 --5601 (3?) As x 2 increased the rate of increase in landings decreased. For example, assume the firm is pulling all of its traps once per week. The marginal product (Equation 37) of increasing this rate to twice per week would be approximately 4,500 pounds. Useful information contained in this index is the expected gain in landings due to increasing the number of days a fisherman's traps set between harvest periods. 1 Rounds per week (x 2 ) was computed by dividing the average number of days in a set period for the season into seven days of a week. By substituting this definition for rounds per week into the firm harvest function (Equation 31) the marginal product of increasing the set period an additional day was calculated (Table 6). For example, a fisherman previously harvesting his traps after the third day can increase his total harvest by 2491 pounds by letting his 3 This is often referred to as "set period" among fishermen.

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74 Table 6. Marginal products for various lengths of set periods, economic study of Florida spiny lobster fishery Days in set period (z) 3 7 10 14 Increase in landing due to a one day increase in set period (MP z ) 2491 735 440 271 Fishing effort intensity in terms of rounds per week (x 2 ) 2.333 1.000 .700 .500 traps set four days between harvests. Likewise total landings can be increased by 735 pounds by increasing the set period from 7 days to 8 days. Increasing from a 10 day set period to an eleven day set period would increase total landings by 440 pounds, while a 271 pound increase could be expected by allowing traps to set 15 days instead of 14 days. Marginal increases in total landings due to increasing the set period by one day can be estimated for any length of set period by the following equation: MP = 12116 z-1-^3991 ( 38 ) z where, MP is the marginal product due to increasing the set period z by one day, z is the number of days in the set period or between rounds, and z = 7/x2Equivalent levels of fishing effort intensity measured as rounds per week (X2) for the examples shown in Table 6 range from 2.333 rounds per week for fishermen that harvest after a three day set period to .500

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75 rounds per week for fishermen that pull all their traps every two weeks . Interpretation of these estimates of MP must be treated with x 2 care. First, the data represent seasonal mean levels of landings related to rounds per week which vary greacly from week to week throughout the season. During -August, the first month of the season, the mean set period for the 25 total firms in the sample was 5.8 days. By March, the last month of the season, the mean was .13.3 days. The March mean was for only 20 of the 25 sample firms since some of the larger, multiple specie fishermen usually stop lobster fishing by the end of December. Although this question was not specifically asked in the interview a considerable amount of information was volunteered that indicated the maximum level of set period, relative to poaching and vandalism, was correlated with location of fishing ground to populated areas, distance from shore, and depth cf water. The remarks indicated that approximately four days was the maximum length of time traps could set between harvest periods, particularly at the beginning of the season. This could be extended to six days if either the traps were in sight of land or firir.s banded together in groups to fish an area several miles from shore. Weeks fis hed per season ( x 3) Landings increased very rapidly the first few weeks of the season, then leveled off. Recall that in Figure 11 it was shown that approximately 54.5 percent of total landings for the 36-week season arc harvested within the first six weeks. This was supported by the estimated output elasticity for weeks. 3 3 shows that landings increase .37 percent for a one percent increase in weeks fished. Expected weekly landings

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76 beginning at various dates within the season can be estimated using the marginal product of weeks, expressed as follows: MP = 1093.46 x 3 -6279 (39) The second partial derivative of the harvest function for weeks fished showed MP diminishing at an increasing rate. ^V -686.58 X31 ' 6279 (40) a 2 3x 3 Estimated marginal products are presented in Table 7 for various periods throughout the harvest season. f5 3 was statistically significant at the 86 percent confidence level, Table 7. Weekly landings expected for given dates within the spiny lobster season, economic study of Florida spiny lobster industry Beginning date of Week (x 3 ) Weeks fished Change in landings for each addition week fished (MP ) *3 Augus t 7 1.00 1,093 14 2.00 708 31 4.43 429 September 15 6.57 335 30 8.71 281 October 31 13.14 217 November 30 17.43 182 December 31 • 21.86 158 February 28 30.29 128 March 31 36.14 115 An additional week of fishing after August 7 would return approximately 1,093 pounds. By the third and fourth week, landings would drop

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77 off to 708 pounds and then to 429 pounds per week, respectively. After the 1st of September weekly landings tended to level off dropping to less than 200 pounds per week by December 1st. Some of the larger firms with greater capital investments quit lobster fishing by November 1st and go to other species. The expected net returns from netting mackerel or long-living yellowtail snapper are evidently greater for at least these firms. Four out of the 25 firms in the sample did not fish the entire season. At least three of these four were always ranked in the top five in number of traps (xj), fishing intensity (x 2 ), and size of craft (x^). The cost per pound of fishing extra weeks becomes substantial and returns become relatively small. Smaller firms often did not have the alternative of fishing for other species at higher net returns and remained in the lobster fishery the entire season. On the other hand, larger firms have a comparative advantage in other fisheries and began leaving after the 13th week of the season when approximately 68.6 percent of total landings had been harvested. By changing species early in the harvest season larger firms can reduce costs substantially for several reasons. After two months the trap lines become frayed and traps break off and are lost in hauling."'' Those traps not lost to frayed buoy lines require additional repairs which reduce the efficiency of the harvesting process. Second, by late summer the probability of ocean storms increases substantially and the risk of losing traps to high winds and rough waters becomes high. Consequently, larger firms fishing in excess of 800 traps have the largest total risk and pull out of trap fishing early in" the season in an effort to reduce costs. 'Hauling is defined as pulling a trap out of the water.

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78 Craft size (x^) Craft size, defined as the square area of the hull, was the most significant of several measures developed from characteristics of the craft. It is reasonable to assume that the effect of craft size (3i+) is confounded. There is decreased speed but increased size which allows more traps to be transported and relocated. 3i+ was statistically significant at the 97 percent confidence level. From it was concluded that landings increased .31 percent for each one percent increase in craft size and the marginal product of craft size increased at a decreasing rate. This was the smallest response of all the measures of effort. The range of craft size in the sample was from 80 to 1,045 square feet, while the mean of the sample was 326.88 square feet. Number of craft and hull lengths in each group of the sample were: seven, 16-20 feet; seven, 21-30 feet; seven, 31-40 feet; and four, 40-55 feet. Appendix H further elaborates various characteristics and practices classified according to length, for the lobster firms surveyed. Marginal returns for increases in square footage of the hull (xtj) are presented in Table 8 and were estimated using the following equation: MP = 558.29 Xl+ -69121 ' (41) Xlt Marginal product (MP ) due to a foot increase in the hull size ranged from 27.00 pounds for craft 80 square feet in size to 4.57 pounds for craft 675 square feet in size. At levels of x^ less than 350 square feet the marginal product decreased at a greater rate per unit of increase in square footage of hull than for craft greater than 350 square feet. This was determined by the slope of the marginal product curve in Figure 12, being less than zero. This indicated a decreasing rate

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79 Table 8. Marginal products of cralt size (x u ) for sample sizes observed, economic study of Florida spiny lobster industry Change in landings for Craft size (x 4 ) (length x width) Length U-i A tVi W -LU U 11 each foot size additional square increase in craft (MP ) Xk 4 80 ID -J 27.00 y o 1 f. ± 0 23.80 j 40 l u 7 18.34 154 79 /.. — 7 17.17 1/6 90 Z. £ 8 15.66 200 fi U 14.33 O AQ z. U 8 13.95 0 *3 /. 2349 12.86 O /. A 240 z.<4 10 12.63 252 28 9 12.22 330 33 10 in i l 340 34 10 9.93 341 31 11 9.91 408 34 12 8.76 432 36 12 8.41 468 36 13 7.96 480 40 12 7.82 574 41 14 6.91 675 45 15 6.18 1045 55 19 4.57 of return. After x H reached 350 square feet (approximately 34 feet long times 10 feet wide) returns to increasing the size of the craft began to level off. For example, in Table 8 marginal product cf craft size decreased by 48 percent compared with a 156 percent increase in craft size, as the square footage increased from 408 (34 feet x 12 feet) to 1,045 (55 feet x 19 feet). The implications were that marginal decreases in landings due to increases in the size of the craft were smaller for larger firms than for smaller firms at mean levels of various inputs. In summary, the estimated firm harvest model fitted the data well and all individual explanatory variables were highly significant statistically. The model indicated that firms were operating in stage II of

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80 4 0 100 200 300 400 500 600 700 square feet (x^) Figure 12. Marginal product curve for spiny lobster craft size (MP ) the production process, defined by diminishing marginal returns to the inputs. Number of traps (xi) exhibited the largest returns to increased input usage, and had the highest statistical significance level of all explanatory variables. Estimates of rounds per week (x 2 ) revealed that marginal returns to more frequent pulls or longer set periods would be positive. Number of weeks fished (x 3 ) by law is limited to 36, although the ana Lysis of weeks fished indicated that the economic feasibility of fishing beyond the 13th week is questionable. The diminishing marginal rate of returns to a firm was smaller for larger firms than smaller firms. Optimu m Resource Allocation of the Firm The analysis and results of determining the level of inputs where profit was maximized for the typical firm are presented in this section.

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81 This analysis was expanded to determine the optimum allocation of inputs for each size of craft classified by the sample stratification. Optimum level of input usage is customarily determine by solving a system of equations determine, from the first order conditions. In this case xj . . . x 4 can be considered as factors of production and x 5 and x 6 are simply area adjustment factors. Notations lly, the equilibrium between value marginal product (VMP ) and marginal factor price for i each input (x^) can be represented as VMP = P (42) x. x. 1 l Thus the optimum solution for xj . . . x 4 is determined by simultaneously solving Equations 43-46. 67.85 X] 2 ' 423 = P (43) 5557.06 x 2 -56C:! = P (44) 1180.39 x 3 ~' 6279 = P (45) 602.67 Xtt -G912 = P (46) The terms on the left of Equations 43-46 represent the value marginal products for the individual factors determined at the means of the other independent: variables and at a product; price of $1.08 per pound. Unfortunately the factor prices (P ) were not unique exogenous prices. They were interdependent and thus presented problems in arriving at a unique solution. Factor price estimates of a trap (P ) are possible "i and were the primary concern in this analysis. As mentioned earlier, the traps (xj) variable was the. principle factor through which all

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82 inputs were translated into fishing effort. Although analyses of variables measuring effort intensity (x 2 , x 3 , and x, t ) have provided useful production information, the principle reason for specification of these in the model was to allow for partial estimates of the trap effect. This model adjustment was required because the data base represented a cross-section of firms which varied with respect to x 2 , x 3 , and x 4 . Thus an optimum solution in this analysis will be limited to (a) determination of optimal trap use for given (mean) levels of the adjustment variables and (b) discussion of possible or feasible levels of x 2 , x 3 , and x^. The price of an additional trap fished (P ) is not simply the price of the trap but is the price of the trap and the cost of fishing the additional trap. This latter component presented difficulty in determining F . Total cost per firm was regressed on the number of traps fished per firm. OLS regression technique assuming BLUE estimators was used to estimate the total cost function (TC) expressed in Equation 47: TC $1,876 + $11.55 X! (47) The coefficient of determination corrected for small sample size (R 2 ) was .53 and the estimated coefficient ($11.55) for traps per firm was statistically significant at the 99 percent confidence level (t-value equal 5.328). The constant term ($1,876) was interpreted to represent fixed costs which do not vary with level of trap use. The coefficient, $11.55, represented the marginal factor price of an additional trap fished. Total costs were used for estimation rather than variable cost because a large component of trap cost was included in fixed cost

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83 through depreciation. The estimate of optimum number of traps per firm (Xi) using this factor cost estimate is presented in Table 9 with respective landings, profit levels, total revenue, and total cost. Table 9. Optimum levels of trap usage per firm and resulting levels of profits, total revenue, total cost, and landings given trap cost, economic study of Florida spiny lobster industry Optimum level of trap use Trap factor price (P ) Total revenue (TR) Total costs (TC) Profits (n) Landings (q) (pounds) $11.55 1,491 $22,742 $17,221 $3,863 21,057 The optimum level of traps given a factor price of $11.55 was 1,491 Relatively small variations in the factor price of a trap produce signif icant changes in the estimated optimum level of traps. The highly variable nature of the optimum solution is significant in that it offered a possible explanation for the rapid increase in trap usage in the industr Relatively small changes in product price (P ) or factor price of a trap (P ) resulted in considerable expansion of fishing effort on trap usage This finding justifies further consideration of trap usage in management considerations in the following chapter. Before closing this chapter consideration of the remaining incepend ent variables is warranted, given the earlier significant estimates of their marginal effects. One crude method for estimating the factor pric for X2, X3, and x^ involves dividing total cost or total variable for each by the mean input levels of each of these factors. Estimates of Traps have an average life expectancy of three years.

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84 total cost (TC) , total revenue (IK.) , firm profit (II), landings (q) , and optimal levels x 2 , x 3 , and x^, given the crude factor estimates of P x , P and P are presented in Table 10. The remaining variables used in x 3 Xl+ the estimation procedure are assumed constant at their sample mean. Table 10. Optimum levels of adjustment factors (x 2 , x 3 , and x l( ) and resulting levels of profits, total revenue, total cost, and landings per firm, economic study of Florida spiny lobster industry Optimum Factor Estimated Total Total Profits Landings level of price factor revenue costs (II) factor deriprice (TR) (TC) use vation (P ) X. X (dollars) (dollars) (dollars) (dollars) (pounds) .834 P J™. 6,149.88 12,084 5,129 6,955 11,189 *2 x 2 10.30 P _TC 273.00 7,559 2,812 4,747 6,999 179.11 P =IXc 17.70 9,690 2,991 718 8,972 Xl^ x^ Optimum number of rounds per week, or total percentage of traps pulled was .834. The imputed factor cost for rounds per week was derived by dividing average total variable cost per firm from the sample by the mean level of rounds per week for the sample. Co incidentally , the optimum level of rounds per week (x 2 ) was equal to the mean of rounds per week from the sample (x 2 ) which resulted in a $6,955 profit for the typical firm. Imputed factor costs for weeks were derived by Length of set period, measured as days, is derived as follows: Days set period = — , Xo

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85 dividing total costs by the mean number of weeks in the sample. Optimum number of weeks was estimated at 10.3 and profit per firm was estimated at $4,747. Optimum size of craft measured as square footage of hull was estimated at 179.11 square feet. Factor costs were derived by dividing total variable costs by mean craft size for the sample. At this level of craft size profit estimated for the typical firm was $718. This procedure was presented for illustrative purposes and its usefulness depends on accurate estimates of factor prices. In addition, total revenue, total cost, and resulting profits were also dependent on levels of other inputs which in the above analysis were held at mean levels rather than "optimal" levels. However, it is interesting to note that the predicted level for rounds per week and weeks fished in Table 10 were both close to actual observed values in the industry, thus suggesting that if firms are maximizing profits, the above estimates of factor prices for x 2 and x 3 are reasonable. The factor price estimated for craft size evidently may be a substantial error because the opuimal hull size of the typical craft was predicted at 179.11 square feet, considerably different from the current industry average size of 326.88 square feet. Furthermore, the predicted profit per firm of $718 does not appear reasonable given the survey data. At this point, one additional conclusion was indicated with respect to variations in firm profits due co fishing areas. Fishing in the upper (x 5 ) and lower (x 6 ) Keys regions produced increased profits. However, only 3 5 was statistically significant at the 99 percent confidence level, compared with a 56 percent confidence level for B 5 . Therefore, there exists a good chance profits will be greater if firms fish above Lower Matecumbe Key rather than fish the adjacent area down to Big Pine

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86 Key. Fishing in the region below Big Pine to Key West most probably does not increase a firm's profits compared to fishing the area from Big Pine Key up to Lower Matecumbe Key. The model would have to be respecified to determine if there exist only two significantly different fishing grounds (regions), i.e., above and below Lower Matecumbe Key. Empirical values for the fishing effort and price variables were held at the respective 1973 levels: 618, for X] ; .834, for x 2 ; 33.08, for X3; and 326.88, for x^ . Product price, P , was assumed equal to $1.08 per pound.

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CHAPTER VI THE MANAGEMENT MODEL The purpose of this chapter is to present a framework with which decisionmakers can evaluate management policies. The framework is based on results from the estimated time-series bioeconomic industry on firm harvest models in the study. In the first section the analysis of maximum economic yield (MEY) for the industry is presented. Next, analyses of alternative combinations of traps per firm and number of firms are presented. Finally, the alternative management considerations outlined in the study objectives are analyzed. Maximum Economic Yield for the Industry " 1 " When the quantity of lobster harvested is such that the cost of an additional unit of input (P v ) is equal to the value of the marginal 1 product (VMP ) for that input, then maximum economic yield with respect 1 to the given input (MEY ) is achieved. Maximum economic yield with i respect to inputs Xj and X 2 can be determined by first simultaneously determining the optimal level of both inputs. These input levels are then substituted into the production function (Equation 22) to predict MEY. To determine optimum Levels of Xj and X 2 for the industry simultaneously, the profit function (Equation 47) is differentiated with "^Recall that capital notations for the variables represent industry inputs and lower case type for variable notations represent firm inputs. ? represents ex-vessel product price in the firm and industry models. 87

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88 respect to Xj and X 2 and set equal to zero to determine a maximum (or minimum) level of inputs. n x = TR TC Bl B 2 n, = P (K + — + —)X 2 [1876 + 11.55 X x ] (48) y Xi x 2 where, IIi = industry profit, 1876 + 11.55 Xj = per firm total costs expressed as a function of traps, and other terms are defined as before. B P |f= —2 11.55 X 2 = 0 (49) 3Xi Xj 2 M_ = JL _ 1876 11.55 Xi 0 (50) 9X 2 X 2 2 Solving Equations 48 and 49 simultaneously results in 213 firms in the industry, each fishing 795 traps. Using Equation 22. maximum economic yield was estimated at 5,778,274 pounds. This estimate was 16 percent higher than industry landings in 1973. The number of firms in the industry, at 399 in 1973, was 87 percent higher but each firm fished 429 traps, 87 percent less than the estimated value. Several implications can be drawn from this analysis. First, industry profits have currently not been maximized nor has total industry landings reached a peak. Second, firms could be larger and more efficient, maximizing profits through economics of size. Finally, total industry costs could be reduced due to fewer firms, resulting in a larger total industry profit. Maximum economic yield was less than the estimated maximum sustainable yield (HSY) and resulted from an optimum allocation of factor

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89 resources. However, management author i Lies allocating factor resources could consider factors such as "grandfather clause" and minimum levels of input uses (such as more firms than the optimum 213 firms solved for in this study). Consequently, only one input at a time will most likely be considered for regulation. Alternatively, the management authorities may not strive to reach the most profitable level of utilization, at least initially, since social and political institutions must be considered. For these reasons the remainder of this chapter will consider alternative levels of maximum economic yield with respect to given constraints. That is one input will be analyzed while other inputs are held at current levels . Evaluating MEY Maximum economic yield was estimated in the previous section using the bioeconomic industry harvest model. In the previous chapter it was explained that the traps data used to estimate the parameters for the industry model were not adjusted for influences that make a trap catch "better" for one firm than another. The reason for this was that data such as that used to estimate the parameters for the firm harvest model were not available over time. Trap data in the analysis of the firm harvest function included these influences making estimation of the optimal number of traps a partial effect and probably more accurate. Consequently, MEY was reestimated constraining the number of traps per firm to three levels most likely to be politically acceptable based on analysis in this study. This evaluation involves comparing landings (MEY), total revenues (TR) , total costs (TC) , and profits (0) for the industry and the firm, among the three levels of traps per firm (X]).

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90 The technique used to reestimate MEY was different than the first method which involved a simultaneous solution of the industry profit function. In this case the assumed number cf traps per firm (X^ and the estimated optimal number of firms (X 2 ) required for industry profit maximization was substituted into the original bioeconomic industry harvest function. In the following equation landings are now defined as maximum economic yield (MEY) for a given combination of traps per firm (Xi) and number of firms (X 2 ), assuming a constant mean seasonal water temperature (X 3 ) of 77.591°F: ». a ^1 ^2 MEY a + — + VTF + B 3 (77.591). (51) x l x 2 The optimal number of firms (X 2 *) was defined as that number which maximized industry profit while fishing the number of traps per firm that was specified for the estimation of MEY. Consequently, total cost per firm and resulting total industry cost varies according to the number of traps specified. 1 Optimal number of firms was derived for each level of traps per firm from the following equality between the value X P was previously defined as average total cost per firm ror the X 2 industry. Alternatively, the estimated value of P can be considered to be a function of the number of traps the firm fishes. The estimation of P using OLS regression technique was X2 P v = 1,876 + 11.55 Xj X 2 where, SE = 2.168; SE = 1,540; R 2 = .74; SEE = 3,752; d.f. 23 and Xi a P Y $11.55.

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91 of the marginal product for number of firms (VMP ) and the total cost (52) where, VMP = MP *P , the marginal product of firms multiplied times X2 X2 y the ex-vessel price per pound (P ) , P = 1,876 + 11.55 Xj, the firm total cost function, and X 2 X2* = optimal number of firms estimated. The three levels of traps per firm (X^ selectee to reestimate MEY were (a) the 1973 mean number of traps per firm for the industry (429), (b) the mean number of traps per firm in the survey (513), and (c) the optimal number of traps per firm for profit maximization estimated in the firm analysis from cross-sectional data. The respective optimal number of firms (X^*) estimated from Equation 51 are (a) 271 firms fishing 429 traps each, (b) 236 firms fishing 618 traps each, and (c) 225 firms fishing 700 traps each. The criteria for evaluation are presented in Table 11. Comparable values can be derived for the typical firm by dividing the table values by the appropriate number of firms. In Table 11, landings were estimated at 4.7 million pounds given the optimum number of firms (271) estimated from Equation 51. Each of these firms were assumed fishing 429 traps. If all firms fished 618 traps instead (the cross-sectional sample mean), 236 firms would be the optimum number required for a maximum industry profit which would be $3.8 million.

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92 Table 11. Maximum number of firms (X 2 *) , landings, revenues, and costs for industry profit maximization given desired management levels of traps per firm (X^, economic study of Florida spiny lobster industry Optimum number firms
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93 Estimated earnings and costs for the input levels are also presented in Table 11. These estimates are with respect to 1973-74 season stock levels and environmental conditions. Pol icy Implications The estimated MSY of six to seven million pounds presented in Chapter IV currently has not been attained. Landings are within 20 to 40 percent of this estimate of MSY. It appears unlikely, given the estimated MEY of 5.8 million pounds, that fishing effort will cause landings to surpass MSY, at least in the near future. This is based on the fact that 7 million pounds are not reached until 649 firms enter the industry with 700 traps each. With the 400 firms presently in the industry each would have to fish 1,000 traps to harvest 7.2 million pounds. These levels of inputs are considerably above typical levels found in the industry. Therefore, the current major concern facing the regulatory agency is maintaining a politically acceptable maximum economic yield (MEY) for the industry. From the evaluation of MEY it is obvious the policy maker is faced with numerous choices of combinations of traps per firm and number of firms. The optimum combination of these resources depends on the state's management objectives. For example, objectives based upon a strict profit maximization motive may lead to regulatory legislation that would reduce the current number of firms to less than 300 (based on Table 11) , allowing only the most efficient firms to operate. Conversely, objectives based on a social welfare optimization motive may very well encourage maximum entry of less efficient firms. The number of firms would be limited only by the probability of landings surpassing MSY.

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94 As more biological information concerning MSY becomes available, the relationship between MSY and KEY will become more useful in developing management, guidelines. An analysis of the impacts of a wider range of various combinations of inputs and management objectives is presented in the next section. Discrete Analysis of Alternative Combinations of Firms and Traps Per Firm Extreme variation may occur in the impact of the different management programs, depending on which resource (X^ or X2) is manipulated and to what degree. Thus it is extremely important to know the impact of various combinations of these resources in order to design policy goals and select parameters for management programs. To illustrate this point Tables 12 and 13 were developed to show the impact of various combinations of traps per firm and numbers of firms, measured as landings (Q, q), total revenue (TR) , total cost (TC) , and profit (IT) for the industry and the average firm. Table 12 was developed for various numbers of firms in the industry holding traps per firm at 700 traps. Illustrated in Table 13 are various levels of traps per firm holding number of firms at the 1973-74 season level of 400 firms. Alternative Number of Firm s in the In dustry Seven hundred traps per firm were assumed because this figure was felt to be a realistic estimate given results of the various analyses. In the previous chapter, the average number of traps per firm in the cross-sectional firm analysis was found to be 842 for the size group with the highest profits. The average number of: traps for the group with the second highest profit level was 561. For these, two groups combined

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95 there was an average of 701 traps per firm. Finally, the MEY analysis using the bioeconomic industry harvest function at the beginning of this chapter resulted in 795 traps per firm as optimum. Industry landings (Q) ranged from 3.1 to 7.4 million pounds as the number of firms has varied from 100 to 1,500 in Table 12. This range represents only a 141.7 percent increase in total industry landings as the result of a 1,400 percent increase in effort. Total costs become greater than tctal revenues when the number of firms exceeds 966. If the 1973-74 season level of 400 firms were in effect, landings would be 6.6 million pounds with industry profits of $3.1 million. Thus, if each firm fished 700 traps (selected economic optimum for 1974) 225 firms would maximize industry profits. Approximately 772 firms would likely dissipate all industry profits, while the 400 existing firms could operate at a total industry profit level of $3.1 million. Maximum industry profits would occur with 225 firms, each fishing 700 traps. This would result in landings of 5.6 million pounds. Estimates on a per firm basis presented in Table 12 were derived by dividing total industry estimates by the appropriate number of firms. Estimated landings per firm (q) ranged from 4,938 to 30,646 pounds for the alternative programs. Costs per firm were constant in Table 12. Estimated average profits per firm ranged from $23,137 for 100 firms in the industry to $3.00 per firm for 771 firms in the industry. Total costs per firm were estimated to exceed total revenues per firm when the number of firms exceeded 771. With these estimates maximum profit per firm occurred at 121 firms while maximum industry profit occurred at 225 firms.

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96 H ol TO 01 0) n i ° * TJ O 3 o u r» jo 0J n " Ps— ^ 60 C -3 § 3 3 O 01 cs. m « u oi ^ o -rf 01 >j B p. u "H rH V-i Ql 0) 01 > I x u 1-f CI 1. c c .« u 0 • 01 rH -H ON 0) ir. > • H rd 01 > rH •H CO cs tr c oi E , iJ mlJ riX II ctj ^ ui 3 IM (I 0 »J c 3 *H 01 u Hflli 01 >-< 01 eg u rH 01 o B xi R O O 1 o u o H H a B 01 r> 01 ^ H r^oicomcofOrHO^xiiA cn on no m CN IN CM ON CN On no no rCO o « r-i DO c rH rH NO NO On On ON ON ON nC nD NO OnONOIOnOnOnOnOI NO CTN Cn NO NO nO nO On On On ON CJn On C7> nO Oi ON NO m cn cn ON rH r~ no no est in CO CO vO 4" H rH rH o 00 CO O to o*> ov 00 vD rH m ro rH CM i-i O CO cr% CM 00 (N rcn vo m m CO o> rH r->. CM 00 ON m CO 000* o m CJ rH rt •»£> Ov in o CM -T Ov CO . CJ rH -* CM O in to ON o> vO X' CO Ov r~ CO CN 00 -Jin to r> CTv rH VO ON Ov Tot rH rH rH H CN) CM CM CM CO CO to CO o\ CO o CO vO rH CM ON CO CM • CM rH P»CM o> m CM vO m r*» ON a CO i-H CO r-H CO Ov CM nO r-H C I CO o o rH <1 o CM ON r m r-. 00 r»00 o> CO CO Ov tjv r» o rH m H r> rH CM CO CM CO CM oo vO rH CO CO CO O to 4 m m vO VO iO vO kC lO r> rr*» CM Ov r-J m CM CM sO cn CM p* CO OO in CM m lO c ro rH CO o CO Ov vO Ov VO o tr ro E t! I-' 3 "H rH O m o m o m O o r -4 O o CM in ro CM o o CM ro to to ro rl u O « o. a 01 2 3 CO c I. p. d a a 00 .2

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97 Alternative Levels of Traps Per Firm The effects of varying traps per firm from 2C0 to 1,000, holding the number of firms at the 1973-74 level of 400, is presented in Table 13. Total industry landings (Q) decreased from a maximum of 7.2 million pounds using 1,000 traps per firm to 1.4 million pounds using 200 traps per firm. At levels less than 205 traps per firm total costs were greater than total revenues (Table 13). Maximum profit for the industry and per firm occurred when the average number of traps per firm was 580. At this level total industry landings were 6.1 million pounds. Landings (q) per firm ranged from 3,527 to 17,926 pounds for a variation in traps from 200 to 1,000 traps per firm. Total costs per firm ranged from $4,186 to $13,426 at these input levels. Profits per firm ranged from a maximum $7,970 with 580 traps per firm to $39 with 205 traps per firm. At 618 traps per firm (sample mean) total industry landings (Q) were 6.3 million pounds. This level of landings was greater than the 5.3 million pounds estimated using the mean number of traps per firm in the time-series analysis (429 traps per firm). Evalua tion of Estimar.es Model estimations thus far appear to be reasonable in comparison to actual primary and secondary data. In 1973, 399 firms fishing an average of 429 traps entered the industry and landed 4.99 million pounds. According to the analysis, 400 firms each fishing 429 traps would land approximately 5.3 million pounds. The average full-time firm earned a profit of $8,719 in 1973 fishing 618 traps (Prochaska and Williams [37]). This compares with the estimated profit of $7,943 per

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98 c tJ re D OJ (J B 10 u •rt . 0 6 c o r-H u « a) 3 cr 0' CO o v 10 ID -H 0" M 'j 01 C'2 n re ,< Ot o in II .o § w 9 a 4 a0 OJ >, M ;r ro tn tH X 3 — 13 :> C oi 0J -n H u 01 J 1 CJ s> CO 4J v-l u « a) ,o c. o G B H 01 t< U :>> a n oj a. U IK tw t3 o 3 <0 0) r-( -H •H to u n F. o >> o w t-i to lu re to 1 CJ >M to o u * * tn m tn tn o CN m tn CO CTv to r> m fx. CM tn tn •a CO O Ov Ox CO tn o Ot CO 1 Pt< IA r-h» CN1 i— < V© rH o m o> a •a CO u •H cn o tn >o CO ON CO CO m > rH o\ m cn vO m 0J VO 00 OA m CO r J CO CO o « TR cn co ON m vjr— * m CS CO H o CO P>s vo kO LA ^ CJ *H H to ^ U 0 H 01 3 C a > oj ^ Pi ci H 3 4) ^ o. x a 13 >o u U »H CO * * m CN vO rH m in CS u rH CI H vO m j CO rH rH CO rH rH 00 m CM •H o CO
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99 firm using 618 traps. 1 These estimates are not unrealistic when one considers that the number of firms in the secondary data includes small part-time and recreational firms with low net revenues as well as large commercial firms. Discrete input substitution analysis was limited by the fact that only a limited number of selected combinations of input levels can be evaluated. However, it was possible to evaluate all economically feasible combinations of number of traps per firm and number of firms in the industry by analyzing isoquants developed from the bioeconomic industry harvest model. Isoquant Analysis A production isoquant can be defined to show the various combinations of traps per firm (Xi ) and number of firms (X2) that are capable of harvesting a given level of landings (Q) . The isoquant can then be used by analyzing the marginal rate of technical substitution between inputs to illustrate the broad range of alternative combinations of traps per firm and firms to achieve management objectives and the 2 ultimate limit of the use of a particular resource. The rate at which traps per firm (X^) and number of firms (X2) are substituted for each other is important in determining the results of changes in the combination of inputs. This rate can be defined as the "''Total costs do not include opportunity costs such as captain's salary and returns to investment. Captain's salary was estimated at $5,130 for the typical firm. 2 "Notationally isoquants in Figure 13 can be represented as « « « 02 63 Xi = 3i [Q a — — ] x 2 x 3

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100 marginal rate of technical substitution of traps per firm for firms (MRTS V v ) and is expressed in the following equation: x l x 2 MP dX 1 X, MRTS, = — = — — • ( 53 ^ XiX 2 dX 2 MP X 2 MRTS , v is the reduction in number of traps per firm necessary to x l x 2 maintain the same level of landings after an increase in the number of firms . Using input levels for the 1973-74 season as set forth in the timeseries data, MRTS v was estimated to be 1 x l x 2 01 02 MRTS Y „ = -(— -)(— T ) =-2.69 . (54) X > X 2 Xi 2 X 2 Increasing the number cf firms in the industry (X 2 ) from 400 to 401 would require decreasing the number of traps per firm (X^) by three (.7.69 rounded) to 426 traps to maintain 1973 landings of 5,253,958 pounds. This would result in a total decrease of only 774 traps in the industry. Total cost per firm would decrease by $34.65. Constant landings would result in an identical level of industry total revenue, but the additional firm in the industry would decrease average revenue per firm by $91.23. The reduction of 826 traps would reduce industry total costs by $7,064 and thus increase industry total profit. Assuming 429 Xi, 400 X 2 , $1-08 P , TC equal to $1876 + $11.55 X 2 . 2 MRTS., „ = 2.69 is rounded to 3.0 since inputs are indivisable XiX 2 thus not accurately maintaining the equality of MSY and total revenues. 3 (400 x 429) (401 x 426) 774.

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101 MKTS diminishes as more firms arc substituted for traps per XiX 2 firm and this is illustrated by the concave isoquants in Figure 13. This condition is recognized as satisfying the principle of diminishing marginal rate of technical substitution and Ls caused by two factors. First, the marginal product of firms (MP ) diminishes as the number of X 2 firms increases while the number of traps per firm is held constant. This is defined as a downward movement along the MP„ curve. Second, as X 2 the number of traps per firm decreases, the marginal product function of firms decreases (thus shifting the MP V curve downward). As more firms A 2 (X2) are substituted for fewer traps per firm (Xj) the marginal productivity of the additional firm in the industry will be less. The opposite occurs as the number of traps per firm (Xi) is substituted for the number of firms (X 2 ) . The same two forces act to increase the marginal product of number of traps per firm (X x ) while the marginal product function of number of firms (X 2 ) decreases. Analysis of the marginal rate of technical substitution between inputs can be of importance in providing a priori information to decision makers about the results of suggested changes in the structure of the harvesting sector of the fishery. This analysis includes (a) observing the effect of movements along an isoquant and (b) determining the location of ridge-lines (defined) . Movement Along An Isoquant For firms fishing 700 traps, MRTS „ ranges from -.0632 for 100 x l x 2 firms to -14.2143 for 1,500 (Table 14). MRTS „ for 249 firms (-.3922), x l x 2 . for example, means that if decisionmakers decided to allow the number of finns in the fishery to increase by one to 250, and yet still maintain

PAGE 115

102 J1 to o l*i CU 4-J o (3 Ci< or. 1 — 1 H rc OA H Cti rH in 1-1 M 01 (X 1 U p, O CU CO a r. CU 3 n B o a «J cu •> i 60 a .a CO c •H M v. •H OJ M M M 6 Q, CU a (X 3 00 u J5 O m « co CU CO m I* CO rH O rH * — i rH E rH H CO n e Cfl H o •H V cd 'X -j) m CO 3 n) a cu o CT rH CD CO T3 o CU (X C/j m 0 60 iH p4 ( ! X) o-"IJ •>*! *d»J.t. CXil

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103 the previous level of landings (5,848,203 pounds) where industry profits were maximized, the number of traps per firm would have to be decreased by 2.55. 1 This was illustrated in Figure 13 as moving along the isoquant where landings (Q) equals 5,848,203 pounds. Table 14. Marginal rate of technical substitutions (MRTS x ) of traps rvar" f -J i*Tn ( Yi I Pel i X L 111 V.-**-]./ fnr nnmhpr nf flmm (Xi 1 holdine traps cer 4~ "i T*m r* on efflnf" JL J_L Ul LvlloLuiHat 700, economic study of Florida spiny lobste: "I Tt Al*. C f~ T* V lNLlluUt-J Ul Marginal rate firms of technical (x 2 ) substitution (MRTS ) x l x 2. 100 .0632 150 .1421 200 .2527 250 .3922 300 .5686 350 .7739 400 1.0108 425 1.1411 450 1.2793 500 1.5794 1000 6.3175 1500 -14.2143 Carrying this example one step furtber and assuming a $1.08 product price and previously estimated total costs per firm, the net effect on industry and firm profits can be easily approximated. Since each firm is fishing approximately three (2.55 rounded) fewer traps with the additional firm in the fishery, total costs per firm decreased by $11.55 Notationally this can be expressed as MRiS A J A 9 For Xi 700 and X 2 250, the change in Xi was .3922 = -2.55.

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104 times 2.55, or approximately $35.00, but industry total costs increased by $12.99. This amount is due to increased fixed costs generated by the additional firm. Furthermore, industry total revenue remains unchanged since product price was held constant and landings were unchanged due to substitution of inputs along the isoquant. However, total revenues per firm decrease by approximately $101 because the same level of total industry revenues was divided by one additional firm. The analysis of the marginal rate of technical substitution between inputs can also provide useful information in deciding which inputs should be changed (limited or allowed to increase) to induce desired changes in sustainable yield levels. For example, at 400 firms in the fishery, MRTS., equals approximately unity (1.0108) and substituting X X X 2 either traps per firm (X^) or number of firms (X 2 ) for the other at this point would not significantly change total industry landings. As more than 400 firms enter the industry, the marginal increase in industry landings is greater if increments are made in traps per firm than if additional firms are allowed in the industry. At 425 firms the marginal product of traps per firm (MP V ) is 14.1 percent greater than the marginal product of number of firms (MP.. ); and at 500 firms, MP is 57.9 X 2 -M percent greater than MP . This suggests that once the number of firms X 2 exceeds approximately 425, further efficiency in industry harvesting costs is questionable. This is assuming, of course, that proportionate increases in costs per trap are not unreasonably higher than costs per firm, which is highly unlikely. Therefore, if some reasonable level of profit maximization is part of the overall management goal, no more than 425 firms should be allowed to enter the industry, based on the assumptions of this analysis.

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105 Ridgelines The boundary lines shown in Figure 13 indicate the maximum amount of one input that can be combined with another input without causing profits to be negative. This boundary is calculated as those points 1 where the firm's total revenue equals total cost. The boundary lines were calculated by setting total revenue minus total operating cost equal to zero and then solving for each input in terms of the other. The economically feasible combinations of traps per firm (X^ and number of firms (X2) are shown in Figure 13. The area between the ridge lines defines the region of profits for the firm. Note that any number of firms beyond approximately 950 will result in negative returns at any level of trap use. The minimum number of firms required to yield revenues equal to costs was 16. The left-hand ridge-line asymptotically approached this limit of firms (X 2 ) , but beyond the realistic range of traps per firm (X^). The production function specified that a minimum of 51 traps per firm was required to land a positive yield, but when costs of production are considered, at least 207 traps per firm were ''"The right-hand ridge-line is expressed as the following relationship : Si B 2 y Xi X2 y The left-hand ridge-line can be expressed as $2 Si P K P — 1,876 X 2 = P ~ 11.55 X 2 X 2 y y X 2 z y Xi where, k = a g 3 X 3 9773480.707, X 3 77.591, TC = total operating costs (previously defined) , and P = $1.08 per pound, v

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106 required, as indicated by the zero slope of the lower left-hand ridgeline. The feasible range for traps per firm increased above 250 traps as revenues remained above costs. Summary of Management Tools When combined with reliable input cost information, isoquant analysis can be a very effective tool in evaluating the impact of management strategies. Discrete analysis is useful if one of the input levels has been pre-determined, which may often be the case due to social and institutional constrainst. An unconstrained maximum economic yield can be determined by solving the first order conditions of the industry profit function. If inputs are limited, maximum economic yield can be derived by substituting the particular input constraint and an estimate of the optimal profit maximizing level cf the other input into the bioeconomic industry harvest model. These tools have been developed as a result of this study to aid in the design and evaluation of management strategies. With this goal in mind the remainder of this chapter is devoted to analyzing a few selected traditional management programs and a suggested management strategy designed from the tools presented in this study. Anal y sis of Traditional Ma nag ement Programs Types of traditional management programs considered in this study were (a) regulating inputs through licensing and (b) issuing landings quotas. Specific evaluation criteria included were industry revenues, harvesting costs, and enforcement costs. Revenues to the state to cover •implementation and enforcement costs were analyzed with respect to revenues available from license fees and/or taxes on landings.

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107 For each of the programs analyzed the following assumptions were made, unless otherwise specified: ex-vessel price per pound (P ) equaled $1.08 (1974 mean price); number of firms in the industry (X 2 ) was 400 (1973 level); traps per firm (X]) was 618 (sample survey mean); desired level of landings (Q) equaled 5 million pounds (1973 level); and total cost per firm equaled $1876 plus $11.55 per trap (estimated). Licensing Traps Licensing of traps and the charging of a fee increases costs but appears economically and politically feasible, provided that some form of "grandfather clause" is included which limits the number of firms in the industry to at least those that were previously fishing. 1 As the cost of traps increases, the number of traps per firm must be reduced to obtain higher marginal productivities so that the value of the marginal product can equal the higher trap cost. This would reduce effort in the form of traps as captains attempt to maximize profits. As a way of illustrating the effects of this program, consider the analysis in Table 15. Total landings would be 6.28 million pounds and average firm profits would be $7,325, if 618 traps were employed per firm. Given assumed desired annual landings of 5 million pounds, a reduction in average traps to 400 per firm would be required. Industry profit would be $2.65 million after the reduction, a portion of which may be taxed through a license to finai-ce the management of the program. After deducting opportunity costs in the form of captain's wages and A "grandfather clause" refers to legislation which states that fishermen licensed prior to the enactment of some limited entry regulation must be allowed to remain in the fishery.

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108 bt) o" c a T-i E 3 0) PH m to o 4 — t rH o u 11 >. l1-. VH U C4 VI >< u a a rl a >c a •rl p.rH x r! u 01 Vi VI u 4-1 n .o IM > o 0 i rH X M cj rl 0) c rl i (14 IX 3 o U) C H Cn 4 u UN ci 0 rl IM !>. Vi o 01 H m tn 0) rH > (0 "44 3 o rH o(I rN •a r-N *J 44 t-C a *S V c u u O e >-i o H J. J a a o U u 01 O 1 S n. •r< u to a Ul o o rH H c n r; cj H re (I) o u 4-n o tO i — 14 o H 60 c H r ^ •O O" C ^ <0 rJ u< c\! O X H ti 'J -H O en cD ct CO CN CM m on vO VO to lO >» cn rH o to rH •* CO tC in CO tO » r-l CM 0^ to •* o co oo r» lO m •a 1 rH rH rH rH m rH vO vO o r~l ro m rH LOt rto m u"l tr ft r-i rH H rH rH rH rH rH rH * m in CM CM U3 m rH m H r-i rH on m cc O o"l rH i — to CM o o CI ON o 'i en ON o rH n CI o m m ON m co o% r-. CO rH CM CM CM CM c-J rH o o o o O o o o o o c o >r> sf o CO o o » >a r-) en m CN1 CM CM r-t CD >o o en 00 in to ON n 0O rH ON m o CM UN i O ^> -H 44 o 11 o. U s re C re n u a o p. | c: r". 3 I u CO DO Ol

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109 returns to investment from each firm's profit, the residual could be considered the maximum amount in total fees the? firm could afford to pay. This value divided by the number of traps is the maximum trap fee. If management objectives would insure the maintenance of a minimum $5,000 salary for the captain and average profit of $7,325 for the firm, the maximum trap license fee would be $5.81 1 per trap. Any difference between a lower fee and $5.8.1 would be considered residual returns to ownership. To compute the values in Table 15, the trap fee was treated as an additional variable cost to the firm and added to the estimated $11.55 cost per trap. The optimum number of traps per firm which resulted in maximum profits per firm ($7,970) was 580 (Table 13) when no license fee was imposed. Optimum number of traps decreases to 557 if a $1.00 per trap license fee is charged. This results in maximum profit? per firm decreasing to $7,402 (Table 15). The number of traps per firm required to maintain industry landings at the assumed desirable management level of 5 million pounds would not change, but profit per firm at this level would drop 5.7 percent to $6,623 due to the trap license fee. Profit per firm ranged from near zero to $7,402 with the license fee (Table 15), compared with near zero to $7,970 without the license fee (Table 13). The percentage difference in firm profits ranged from 6 to 17 percent and was greatest at the higher levels of traps per firm (Xj). Beyond 207 traps per firm, the firm does noc return a profit if a $1.00 license must be paid. This source compared with 205 traps per firm without a 1 ($7,325 $5,000) * 400 traps = $5.81 maximum license fee. 2 Considered In the range of a politically feasible fee.

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110 license fee. Notice that beyond 400 traps per firm no regulation of traps is needed to maintain the desired harvest of 5 million pounds if the number of firms is limited to 400. As estimates of enforcement and implementation costs increase the license fee would need to be adjusted accordingly. The estimates presented in this section would change as different management objectives and values are assumed for ex-vessel price (P^) , number of firms (X2) , and the trap license fee. Such a program may be impractical since the number of traps per firm is not easily regulated. It would be extremely difficult and expen sive to regulate the number of traps a firm is fishing. However, the above analysis provides valuable information with respect to the results expected as number of traps per firm varies. Further analysis of implementation and enforcement costs may be warranted before any attempt to manage trap numbers can be a feasible management alternative . Otherwise this management program may be deferred until more cost-effective means of regulating traps are discovered. Licensing Firms This type of management program is similar to licensing traps in that it induces an increased cost per firm through a fee. As firm costs increase only the more efficient fishermen will be able to make a profit and remain in the industry. A program that restricts the number of firm could also require restrictions on number of traps and/or landings but. these restrictions were net assumed in this analysis. For illustrative purposes a license fee of $1000 per firm was assumed feasible (Table 16) ^Refer to Table 12 for some comparable levels of number of firms (X2) assuming no firm license fee.

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Ill r-t -1 £ O tr ci id V E to C V, a' 6 ri Cu M o a o a l|4 to 01 |H II tr u 0 H r-l o X c ct) [1 C ro O ViH Vi 0/ t(0 r-f 0) K p. 3 •J tr H IJ •a M a r: 3 •r-t 0 0 g a. u to o> 13 a. >. 01 u CM o ij X •H to 3 e p. i — 1 •H C 01 — 1 u to II 01 4J > to o 1 X o Hi i-H c D >> (H a g r-l 0, CX> n in Q to io r^. •rt CD r-l to o gi rH r-t > CO lu 3 r-t cr U-t 01 a > * — » >. X 3 4J 3 n P 01 01 u O *J 3 •rl r-l u B «i <3 0 n G U l 01 o O r_ o E 01 V *J o > u o 01 o -j (0 r-l 3 3 C DO O U r-s u rj — i-> o H H 60 C O Si". r-l r-i r-l r-l t-t r-t r-l r-l VO SO VO cr» cri ON On o> a\ o> t> O O o a o O o o r-t iH rH r-t f-l r-l i-H CO tn o i— 1 co m sf r-t CO vO CO vO co o m IN CM CM i-H * . o IT, o> vO CO CO C4 u m CO ©\ CM f i m CM CM 1 J m rH a\ o o VO (0 00 CO o o ro CM o CM rH r» CM u"t ON CO / — « u \D 00 CM ON O VO ro rH H C*t r-H rH CM CO CO O 00 a CO ON ro r>CO
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112 Profits per firm decreased approximately six percent as a result of the $1,000 firm license fee with a range from $23,599 for 121 firms to $4 for 694 firms. Total industry costs increased with the license fee and ranged from $1.3 million for 121 firms to $10.6 million for 966 firms. As a result, the optimum number of firms for maximum industry profit decreased from 225 firms (Table 12) to 211 firms. Total industry landings were reduced by 336,447 pounds due to fewer firms fishing but profit per firm increased by $2,846 because total industry cost was reduced more than total industry revenue. The optimum level of firms for maximum firm profits remained the same at 121 firms as a result of the parallel shift in the industry cost function. Implications of this analysis are that inputs (traps) used in the fishery would be reduced through rational economic behavior of firms when licence fees are charged on a per firm basis. License fees could be set to allow the desired level of firms to maximize profits while harvesting the level of landings desired by management authorities. Licensing firms would appear to be a more manageable and enforceable program for regulating entry of effort into the fishery due to the relatively fewer number of firms than traps in the industry and current crfif t registration requirements. The number of licenses issued would be based on desired levels of traps per firm (X.), landings (Q) and expected prices of inputs and outputs. If traps are not regulated, limiting firm numbers does not guarantee that the desired harvest level selected would not be surpassed if the harve3t level desired is less tban MEY. Depending on the importance of maintaining a desired level or landings, a landings quota could

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113 be attached to the firm license to insure actual landings equal projected desired landings. L anding Quotas Under this management alternative each firm would be allocated a percentage of the desired harvest. This percentage could be based on landing records of individual firms and desired harvest levels. The desired harvest level would be announced prior to the opening of the season. For example if each firm of the 400 in the industry were allotted .25 percent of an estimated 5 million pound harvest level, the landings quota per firm would be 12,500 pounds. Profits per firm would be a function of fixed costs plus the number of traps each firm fished since the number of traps per firm determine total cost. In order that efficiency and technological innovation would not be impeded, firms could be allowed to lease part or all of their quotas at the market price. To prevent monopolistic practices from developing a maximum number of quotas per firm could be established. An alternative to establishing a constant quota per firm would be to vary the quota per firm based on percentages of previous years' landings. For example, percentages could be 60 percent of the first year, 25 percent of the second and 15 percent of the third. This absolute figure is adjusted up or down by a constant percentage per firm depending on the percentage increase or decrease in the estimated sustained yield for the coming season. Other activities such as leasing would not change . The license fee paid for the quota could be based on estimated profits per firm in conjunction with implementation costs as discussed

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114 previously for the firm licensing program. The quota limits per firm could be set forth as a percentage of each firm's expected total revenues from landings. For example, in Table 12, with 400 firms fishing 700 traps each, profit per firm was $7,734 without any license fee. Assuming that total implementation and enforcement costs of the program would be $800,000 or $2,000 per license, firm profits would be 57.6 percent instead of 77.6 percent of total costs. To enhance the acceptability of the fee charge next year's license fee could be set at 11.3 percent of the previous year's total revenue ($2,000 * $16,320) instead of 25*9 percent ($2,000 * $7,734) of the previous year's profit per firm. Quotas could be offered for sale on a first come, first serve basis or more efficiently by some form of auctioning. If firms exceeded their landing quotas a fine per pound could be levied that would be severe enough to discourage such practices. The major advantage of a quota system is the assignment of ownership to the resource. Consequently the quota system allows the free market system to operate more easily than would the normal conditions of a common property resource. Free enterprise is conducive to efficiency and technological innovation. As the marketing system operates more freely, less government intervention is required, leading to lower management costs. The quota system also would have the most direct control over landings and, therefore, could be used for controlling landings with minimum delay in situations where MSY has been reached or surpassed. However, several disadvantages are associated with the quota system. First, the quota system would require accurate information on maximum sustainable yield levels which might necessitate considerable research and management costs. Analytical results in this study show that current

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115 landings are considerably less than MSY thus highly accurate estimates of MSY are not required for reasons of over-fishing from a strictly biological point of view. Therefore, it is questionable whether the additional research expense to accurately determine MSY is justified in the short run for management of the spiny lobster industry. Another possible misconception is that a quota system leads to MEY. This is not necessarily true, particularly with respect to an industry such as the spiny lobster industry where a large percentage of landings are caught in the beginning of the season. With a quota system, effort can just as easily become excessive (meaning, fishing as many traps as without the management program) as fishermen attempt to fill their quotas early before lobsters become scarce. This situation would cause harvesting costs to increase due to the larger number of traps fished. A Suggested Alternative: Harvest Rebate Program The harvest rebate program integrates several features of previously discussed programs. In this program effort measured by the number of firms would be limited and would include a license fee. The harvest rebate program offers the flexibility of allowing each firm to maximize landings. Finally, this program allows the market system to regulate harvest since higher license fees will discourage inefficient fishermen. Landings regulated in this manner could be substantially less costly to regulate due to less government intervention than in the more traditional management programs discussed. These advantages are not to imply that the harvest rebate program is "the approach" for fishery management. Rather, this program was designed to specifically consider problems of the spiny lobster industry,

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116 but in some cases it may be applicable to other fisheries. The following is an illustration of how such a program would operate and the analysis of specific effects on landings, revenues, costs, profits, and optimum input combinations. Configuration of the Harvest Rebate Prog ram Establishing this program would begin with a moratorium on all lobster licenses. Using the "grandfather clause" approach the total number of firms would be initially limited to the 1973 level of 400. Next, an accurate recording of the average number of traps fished per firm (Xi) would be necessary. This parameter would serve as the foundation for the total program in a given season. Once the optimum number of traps (x^ ) is established using the firm harvest model (Equation 31), the maximum number of firms required to harvest the desired level of landings (Q) would be determined. Those firms not allowed to enter the industry would receive rebate payments. Who would receive permits would be a difficult question to answer. One approach is presented here. As an initial program activity, for example, an application deadline could be established for licenses and rebates. At this time a range of probable license fees and rebate payments would be announced. After assessing the ratio of harvesters to rebate receivers a more accurate estimate, of license fees and payments would be announced and a three-week period (arbitrary) would be allowed for an>one wanting to change status. The consequences of too many changing status should be made clear to the participants since it could be detrimental to them. For example, too many rebate receivers could reduce individual payments.

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117 fit 41 3 E u C <** « II X u > 03 od 41 M o C -3 u © u u s < x S«5 w E -S 6 --n <~ p _ oc X O 3 o ex E v. o ft I? e v. •o i. i o • ru C 41 C — -O 3 O J: •< I — — I . u X o u. x sw o c c >> c -v) £ 3 Q g a c e o •3 O o 00 O O O 3 SO o so > so CM St co st rH o C£ Hi l-i 4J J CO C >rl O K 41 a o >> i-l r-< r-l U f= c o r-l U M O 3 z o 00 c .= N~l -J 3 °E I CO DO c C 3 -J 60 4J <« C «~N a • x w u -a c «i 3 e §. ri «-i C O 41 -r< U t-t O i-i 8 «. 4) »-* l/N «r« 3 O or u 41 U !-« est 41 3 o CC G 41 01 41 •O C 41 <9 41 C u 0 r3 41 > U U to a o jz u a. o u >. u u U td C T< ai X 41 •a 4> !C t-* a> h O 3 US o CO vO CO 0^ iC H r-i CM fO rhCO 00 o in IC cn CO O »-l vO in Cl oo O SO a\ 0> O CT. C3 O on cyi o OV O in rT SO o ro o o ro so O LO CO CO m Ci CO in CM r— CM
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118 AJ c r« u o. , U X> CM U u — •o c 3 At C 6 U i i H o . — > i — . /-^ in T •100 a t-x «o <* CN 00 to CM r 00 w"i fNI rj — ii CN :s o CN OK cn csl i cv c o a :i 9 CO r-CO CO* c• 1) r • H kO rO oco \o CO ON in 0 0 JJ JJ \o 1—4 in o vO o (-< . -* vO f ! to coin CO vn CS O CM u u CO CO rn CM CM CM CM 1 to x 1 i-» •< M m >^ u }.« p 3 u ^» s . — o o O O O o o o o o c c o o O CM c o o o o CO n O o in CM o o © o o sj Xi o vD r— t in 00 CO CO o v£> C-J o ,—1 to r*. CM o tr, to r*t <— 4 o*» o 00 CM [3 g CM C J CM i H . ij^ E O P B 0) •.< 3 D* cr c u u r*. rm -J CO o ^o CO o O c a 00 •O O v£> m u j to (O m CM CM .-i r V— ' W •v4 C'j -a 0J CJ X •o 4) I") O R C B O o O o o o O o o m '.J o o o CM o O o o o CO DO M o m in 00 in f-< o o o in o o tM u h. ro -~< r-* o> O m VD H ft. n. r4 »-i • — • E? c P a i< T> •1 AJ a «-• CO o vn o ro
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119 4J 1 01 V-4 3 o 0 ... 4-1 1 1-4 CJ 1 : P0) o i 1 c •O rH'H Cfl 0) < CJ p. 0J d Ih pm w C X U-l 4-1 V-i d XI re a. -H cfl o w ft •H P 0 o •X) rJ cfl H 00 oo >^ to oc a) * d ft S p 4J 0 / — > d C a O X> )J cnn-' !-i o CN tCj 3 •H d CO CJ rl CJ X •rH u X II 0 cfl H rH *o rH TO u 3 ft O -H 4-1 rfl X ^ — ' a; rfl CU to f 1 D' do* w d 0 I cfl d 111 [fl cti CJ CJ cu H )-l J> X £ CO rH c rH to CN Cfl QJ MH inp r* o •H II 0 rH tfl ^-^ QJ X CJ So) to •H 0 re '4 -i 60 t= s •rH 4J rl 00 ft 'd C41 J-i s CI CM 00 rH U X tfl r — < JP Cfl Pi J3 X w rH to CN 0) rQ <11-4 •> co UH •H 0 r•H X CJ cu rH II 0J 0) CO o 0) U-l W cfl d ^ 4J TO d L|_| n s -< > 'J CU ' — . O0 M cu <~» CO d cfl •H H u 4-J MH d 00 > CU Cfl CD bO U V-i • «\ CJ O •H O -H rH 0) -\3 > re p 0 re CO X) 4-J k oox >« C * •H •H tfl W cfl o rH f. M d ft Cfl CN 60 U rH ^ oi 3 o a X ( j Cfl 60 pq TO a) > d rH i-i 0 d to CO ft o U QJ CJ CJ cu rl p. m •H CU d CO :^ M UH 60 O U UH P, U-i r* QJ , i UH > 3 re •rl 4-J CO O O -H ill •i ' Q 0J \ O 3 4J H S Cfl U it H CU CJ UJ S r UH [ t Tj X ft c •H 0 3 3 to cu (0 CJ to T J Cfl 0J •rl d 60 II UH d cc— 1 r* t p > r-H rC •H d d rJ O Cv CO IH J CO ffl ^ o .1' 4 J X h •H CU CN a d CJ CJ o CN -rl U / — X Cfl O 4J X U (-4 J »~J *n ' J to H re ^ rH P, vO 0 pq d UH K H ei j 1 cu o 1 1 >r J cfl rH ^— ' c CO Cfl d C 'rl 1 1 CJ iH 1 ' | CJ . r .-J J-J [r i! rH CU CJ d u LU co to 6 Cfl TJ > •H tfl QJ M cu CJ bO u co *H * h C H 60 cl c3 Fcu > H M to cu m "3 rH 4-i CM !-i cfl 60 p -J •H rt rl •H N 01 cu X! JJ -H cfl ll OJ CJ 4J r* •H II (3 > i-l CO CU •> TS P, re CJi. cfl 4-1 0 •rl U QJ 3 >-< 0 3 CU cfl U H ' -1 •H >-< td rH a, CnI r* Hi rH T3 O Cfl rH to cu cu 4^ 4-J UH rP X W 4-1 4H >-l o li -1 i-j to to to to 2 (3 4-> 4-> t-H CU 60 C 3 rl M •H 3 S4 •rl 0 •H •H 0 1 J2 O H o cu cu cu P TO 01 UH • M to Cti ,H II M ^ a CO o r* •H d 4-1 CO u o 0 0 U 0) CN >< 0 P. d ptl i^j 0 •H re O H Uh rH 0) >< CQ w H 4J 1 C Cfl ft > 3 0 <}• U >4H CU H CU IU O d d 4-1 a) re o w cu cu > Cfl g o U-l 4J 0 3 0) rH rl H ft X> tH 4-1 •rH re d 60 ft H oi > X >«H II 60 O 0 rJ CJ c d e to -u > CJ . — s rH4-l 0 V iH rH 3 rH •rl O to iH M rH X to u X /• — s Cfl c 01 CO CJ p CJ cu ft X • X O -H -K 4J o 4J a 01 4-1 O QJ "> a lT| 60 ft TO CJ MH CN d rH O > 60 CO O QJ 4-> m d d x 3 ^ — ' U QJ p J3 .c O U CO • -H ft rH Cfl rH U O H cfl QJ o UH QJ X. rH 4J cfl X Cfl CU •> 0 II r! >H OJ 4J rH U r4 o U a in cfl — ^ / — •< 60 "u to H CO TO 4-J (/J o 4-1 o o 3 1= QJ d 00 0 X •H a) (0 CO + ft 01 CJ ft T) > •rl -H ^— N CJ d 6C •rl •rl •H •H CP rH <1J •1 H II II t*H U-l 0 tJ CD cfl > UH TO rH to & t-^ re & 00 o rl ^— / •H > cfl 4-1 •rl C Cfl Q) «J oo I 3 CN CN l-l 60 X UH cu 0 d CJ U CJ •rH Q cfl r, re X X ft P cfl 4J O pej OJ CJ G c. O rH r-H re 0 •H M u u QJ UH p. rJ /-S TO ^ — 0) cfl w P U II P UH ft cu rl U < ry c"> 1' CO CU H -H 1! o iJ II QJ c d II 1' > CN Cfl M CO ct) ft to 0 0 •r-i CO •H ^-^ X 0 cu ft 3 4J QJ 0 •rH 4 J O tfl CO O -H rH re 60 LA \ CU 3 O LO 3 t= U V-i t_> TO rH 4-J H xCJ ^— ' t= u d 10 •H a *H OJ M d CJ d > @ cu 3 > U-l 4J ft QJ ^ 3 > •H s C^ ^x Ll (fl .r.^ U > O QJ rH > TO •rl cfl UH rH O 01 Cfl rH cfl U r-KO CJ cu *f t l-l rH 01 d UH l-l u D ^ P, rH B ^ tJJ 00 X ^ ft Pi > P a; rH o O 4-1 P4 01 3 a •rl 4J a 0 CJ I I • H 0J d o H 4J a. B 3 re re < a o •H d CJ G XI (fl H r<

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120 After the three-week deadline licenses and rebate certificates would be issued. Licenses would be paid in installments of 25 percent down; 40 percent by September 15th, since August is usually the best harvesting montb; 25 percent by November 1st; and the final 10 percent by the first of the year. The installment plan would closely parallel the timing of the majority of landings. The balance of the license fee would be paid by the first of the year when the majority of the stock has been landed. Rebate payments would be made at the same time and rate. Alternatively, an auction system could be set up to determine the first round of harvesters and rebate receivers. This has been suggested in the literature in a theoretical framework that essentially equates marginal cost and marginal revenue. This approach could also be used if economic renc is an important consideration of the analysis, a point with which this study has not been concerned. Regulation of the harvest rebate program should not be any more expensive than the cost of current regulatory programs. All craft and gear must be easily identifiable from the air. More thoughtshould be given to legislation and regulation of designated fishing areas prohibiting trespassing of all non-licensed fishermen. Hypot hetical Example and Analysis of Harvest Rebate Program The structure and bioeconomic status of the spiny lobster industry was analyzed under the harvest rebate program assuming various levels of traps per firm. The levels of traps per firm selected were previously used throughout this study and ranged from 200 to 1000 traps per firm. The results of this analysis are presented in Table .17 and include

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121 numbers of harvestors and rebate receivers, profits before and after the program, percentage changes in these profits, revenues and costs to the state, production revenues and costs, and landings with and without the program. The remainder of this section discusses the assumptions of the example and the results of some of the specified levels of traps per firm. Ass umptions License fees were arbitrarily assigned and were assumed politically acceptable as were administrative costs for implementation and enforcement of the program. Lobster fishermen were assumed to be profit maximizers and thus would select the alternative which >7as most profitable to their individual firm. The ratio of harvesters to rebate payment receivers was determined by the minimum number of firms (400 in total) required to land the desired industry harvest level of 5 million pounds for a given level of traps per firm. Rebate receivers were maintained at their previous profit levels. License fees were assigned with several objectives in mind, one of which was to allow harvesters to earn a profit at least five percent higher than their previous level (Column 12) . Another major objective in assigning the level of the license fee was to collect the required revenue to maintain a self-supporting program, assuming administrative costs were not greater than $250,000. In addition, higher license fees were assessed for firms fistiing larger numbers of traps since profit percentages per firm increase as the number of traps per firm increases. License fees ranged from $1,000 for firms fishing 429 traps each to $17,000 for firms fishing 1000 traps each.

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122 Total cost per firm was constant regardless of whether a license fee was assessed because the number of traps was assumed constant among firms. Underlying criteria used to arbitrarily assign program costs and revenues were primarily based on the number of fishing firms (harvesters) to be supervised and relative profit levels of these firms. Number of traps per firm at 700 The maximum number of firms required to harvest the desired industry level of 5 million pounds was estimated to be 171 firms fishing 700 traps each (Table 17) . If only this number of firms choose to participate in a harvest rebate program as harvesters, 229 firms would elect not to fish for lobsters and would collect a rebate payment of $7,733 each for the season (Row 3, Columns 6 and 16). These rebates would cost the state $1.8 million ($7,733 x 229). Revenues for harvesters in the program would increase approximately 179.2 percent to $21,593 per firm before license fee charges (Row 3, Columns 7 and 8). At this rate the state could charge a maximum license fee per firm of $13,860 and the firm would be at least as well off than before the program at $7,773 profit per firm (Row 3, Columns 6 and 10). Approximately $2.4 million (Row 3, Column 9) in revenue to the state for rebate payments and management of the industry would be generated. Assuming the regulatory agency set the license fee at $11,500 to cover rebate payments and program expenses, total profit per firm (harvester), estimated to be $10,093, would be 30.5 percent above profits before the program. Rebate receivers would collect as much as they were making before the program without expending any costs. In addition, these firms could invest their time, skills, and capital elsewhere.

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123 Total industry profits could increase (often including license fees) by 19.4 percent. Incomes to fishermen would be improved, resources would be allocated in an efficient manner and the stock of spiny lobsters would be in no danger of over-exploitation. Number of traps per firm at 618 and 500 Assuming 618 and 500 traps per firm (Rows 4 and 5) profits per firm and total industry profits could also be increased under the harvest rebate program compared with the profit structure prior to the program. However, as the number of traps per firm (X^) would decrease profits for each firm and for the industry would decrease (Columns 8, 12, and 15). This situation would occur because the constant rate of increase in total cost per firm would be greater than the rate at which the MRTS x l x 2 would decrease, thus resulting in a less steep increasing total revenue function within the range of data. For example, if a decrease in traps per firm were induced by regulations that limited trap numbers per firm, total cost per trap would decrease. As the number of traps would decrease, MRTS. r would increase. As MRTS„ „ increases along the iso-M A 2 X 1 X 2 quant (Figure 13) the marginal productivity of a firm decreases, thus requiring more firms in the industry to harvest 5 million pounds. More firms increase total industry costs and thus decrease net returns (profits) to the firms and the industry. With the harvest rebate program, profits per firm (Column 12) increased 24.4 percent to $9,879 and 19.0 percent to $6,490 for firms fishing 618 and 500 traps, respectively."'" License fees were assumed at Profits remaining above the license cost were derived by subtracting Column 11 from Column 7 in Table 17.

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124 $9,500 and $5,000, respectively, to cover rebate payments plus a balance of $136,970 and $25,412, respectively, for administrative costs. At 618 traps per firm (Column 16) 210 firms received a rebate for not fishing (Column 16) . Then the number of firms decreased to 154 as traps per firm decreased to 500 because more firms are needed to harvest the assumed 5 million pounds. As a result of the rebate program, total industry profits increased 15.9 percent with 618 traps per firm and 12.5 percent with 500 traps per firm. When revenues for administrative costs (Column 14) are not adequate to meet the $250,000 budget assumption license fees would have to increase (Column 11, parentheses) to a level that will generate the required revenues. For example, if the harvest rebate program was implemented and each firm was allowed to fish 500 traps, the number of firms choosing to fish would be 246 while the number of rebate receivers would be 154. Maximum revenues to the state (Column 9) would be $1,596,540, while program costs for payments to rebate receivers would be $1,204,588 (154 x $7,822). The $5,000 license fee would pay for rebate payments but would leave only $25,412 to administer the program. To remedy this deficit the license fee would need to be increased to $6,000, resulting in a $271,412 budget for administrative costs, excluding rebate payments. This situation would decrease profit per firm from 19.0 to 6.3 percent (Column 12) . In the case of 429 traps per firm the required revenues could not be raised without decreasing profit per firm to less than 5 percent. In this case the program was not able to totally support itself (Column 14, Row 6).

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125 Nu mber of traps per firm at 42? At 429 traps per firm the program could not support itself and would experience a $201,560 deficit (Column 14). Only $328,000 of the $529,560 (Column 16 x Column 6) rebate payments could be met with a license fee of $1,000. At this level firm profits would increase 17.3 percent compared with profits outside the program. To help make up the deficit in rebate payments, the license fee would have to be increased to $1,535 which would decrease firm profits to 5.0 percent. Still, a $26,080 deficit in payments would remain with no budget for administrative costs. Another alternative would be to reduce rebate payments to non-fishermen to a profit level less than what they were making fishing for lobsters. Assuming idle capital and labor resources were invested elsewhere, this may be a feasible alternative. Number of traps per firm at 350 and 200 If firms were limited to 350 and 200 traps each, all firms would be needed to harvest the 4.5 and 1.4 million pounds, respectively. Since more firms would be required to harvest the desired level of 5 million pounds no management program would be needed since more firms than currently exist are required to harvest MEY (Rows 7 and 8). The average product per firm with 350 traps was 11,241 pounds and with 200 traps was 3,527 pounds. A total of 445 firms with 350 traps each, or a total of 1,416 firms with 200 traps each, could be allowed in the industry to harvest an MEY of 5 million pounds. Ov erall summary of analysis (Ta ble 17) For the range of 200 to 1000 traps per firm selected industry landings wtre maintained at 5 million pounds under the program, whereas

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126 landings without the program would have ranged from 7.1 to 1.4 million pounds, assuming all 400 firms in the industry fished (Columns 3 and 4). No limit on the number of fishermen was required when fishermen were limited to 350 or less traps each. Firms were limited to 328 if each fished 429 traps and to 140 if each fished 1000 traps (Column 2) . Net profits for this group increased in the range from 17.3 to 38.7 percent (Column 12), for 429 and 1000 traps per firm, respectively. Total program cost ranged from $2.3 million (1000 traps per firm) to $0.5 million (429 traps per firm) and was paid for by licesne fees ranging from $17,000 for firms fishing 1000 traps each to $1,535 for firms fishing 429 firms each (Columns 11 and 14). Except for a $26,000 deficit assuming each firm fishing 429 traps the program was totally self supporting and firms receiving rebate payments were maintained at their previous incomes. The increase in total industry profit with the program ranged from 7.3 percent assuming 429 traps per firm to 48.8 percent assuming 1000 traps per firm. Assuming the harvest rebate program would be feasible, individual firms, in many cases, would require a careful evaluation of their operations to determine if a license should be purchased or a rebate payment received. To aid in this decision making process a breakeven criterion was developed as a result of this study. Breakeve n Criterion Using the time-series data and primary data obtained from the crosssectional survey, an estimate was developed to provide an indication of which firms might elect to receive payments for not fishing, given the structure of the industry for a particular season. The breakeven

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127 criterion (BEC in Column 17, Tabic 17) was based on the total cost or total investment of the firm. This information was transformed into average product per trap required to cover operating costs and license fee. Thus a given firm may decide to fish a particular season if the owner feels he is capable of harvesting an amount equal to or greater than the BEC per trap. To obtain the values for BEC, total cost per firm (Column 5 plus Column 11, Table 17) was divided by the number of traps fished per firm (Xi, Column 1, Table 17) which was multiplied times the ex-vessel price (P ). Total firm cost includes the new license fees. The result was y the average product per trap (Q/X^) required to cover costs. To evaluate this criterion, landings per trap derived from the various data used in this study were compared with estimates of BEC for comparable input levels. Landings per trap (Q/Xj) for the industry from 1963-73 ranged from a low of 29 pounds in 1973 to a high of 49 pounds in 1966. Landings per trap in the cross-sectional sample ranged from a minimum of 10.68 pounds to a maximum of 54.86 pounds for firms fishing 665 and 401 traps, respectively. The median for the sample was 21.43 pounds for firms fishing 560 traps. The data in Table 18 illustrate the median and mean landings per trap for the given range of number of traps fished (X^) in the sample. The relatively low values of average landings per trap in the timeseries and cross-sectional data may be due to over-capitalization in traps since no limits exist on traps. Estimated average landings per trap (Q/X|) with the harvest rebate program are higher than comparable

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128 Table 18. Median and mean spiny lobster landings per trap for sample of firms classified According to number of traps per firm (Xj); economic study of Florida spiny lobster industry Landings Number of traps fished per firm per trap <200 200-399 400-499 500-599 600-699 700-899 >900 Total Median 21.80 22.67 17.07 24.10 26.28 19.33 16.32 21.43 Mean 26.02 22.92 27.45 24.10 22.54 19.26 16.93 21.37 Observations 3 4 3 2 r 5 3 25 breakeven estimates (BEC) as illustrated in Table 19. 1 Estimated landings per trap (Q/X^) were derived by dividing the total number of firms in the industry after the harvest rebate program into estimated landings after the program. Since the breakeven criterion of landings per trap was below the estimated actual landings per trap the firm would have some flexibility in its decision on whether to fish or not. BEC ranged from 16.09 pounds per trap for 429 traps per firm to 28.17 pounds per trap for 1,000 traps per firm. The figures in parentheses (Table 19) represent BEC after adjustments in the license fee were made to compensate for deficit program costs illustrated in Table 17 (parentheses in Column 11) . Estimated landings per trap ranged from 35.02 to 42.54 pounds per trap, thus resulting in a range of 54 to 21 1 . Q/Xj can. be represented notationally as Q/Xl = (X 2 *)(X!) where, Q/Xj estimated average landings per trap, Q estimated landings with harvest rebate program (Column 4, Table 17), X2* = maximum number of firms required to harvest Q , given Xj (Column 2, Table 17), Xj assumed number of traps per firm (Column 1, Table 17).

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129 Table 19. Analysis of landings per trap required to break-even under the harvest rebate program for alternative levels of traps per firm (Xj), economic study of Florida spiny lobster industry Number of traps per firm 1,000 800 700 618 500 429 Q/Xj 35.79 40.00 41.74 42.54 40.67 35.02 EEC 28.17 28.49 28.39 27.74 23.43 16.90 (32.25) (28.64) (25.28) (18.06) % A 21.29 28.78 31.98 34.79 42.39 54.05 Max . No . 140 156 171 190 246 328 Firms Note : Q/Xi is estimated landings per trap under harvest rebate program. BEC is landings per trap required to break-even under price and cost assumptions of harvest rebate program (break-even criterion) . % A is the percentage difference in Q/Xj and BEC. Max. No. Firms is the maximum number of firms allowable in the industry for given levels of traps per firm under the harvest rebate program. percent above 3EC, respectively. For example, at 700 traps per firm BEC was 31.98 percent below the estimated average landings per trap. At 500 traps BEC was 42.39 percent below (Q/Xj) and at 425 traps BEC was 54.05 percent below Q/Xi . As traps per firm decrease, the difference between estimated landings per trap and the breakeven level became larger. This is due to the law of diminishing marginal rate of returns resulting in an increasing marginal product for a trap as the number of traps per firm decreases. Thus the program does appear realistic when compared with expected changes in the industry structure and performance as a result of the harvest rebate program. One question that may be of concern about the harvest rebate program is, "What happens if firms do not select the appropriate plan designed for them?" Several problems could cause the estimated number of rebate receivers snd harvesters to change.

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130 First, the estimation of traps per firm could be reevaluated. As previously mentioned, considerable effort and funds could be spent to accurately estimate average traps fished per firm. Second, the license fee could be too high if too many firms have applied for a rebate. On the other hand, the license fee could be too low if too many firms have applied for a license. In the short-run, the rebate could be increased before the suggested three-week deadline if too many license applications were received. If too many applications were received for rebates the license fee could be lowered during this period. Finally, another problem might be that estimates of input and output prices could be different from various sectors of the industry. The state should be prepared to absorb the inaccuracies of the program should the ratio still be out of proportion after short-run remedies have failed. Program adjustments could be made the following year based on experiences in the previous year(s). In summary, the harvest rebate program is offered as a non-tradition al alternative. Its features include increased profits to the industry and firm, depending on estimated levels of traps per firm. Since inputs would be reduced, current over-capitalization would be reduced, allowing more efficient harvesting through such activities as economies of scale. More importantly the rebate program would allow the fishermen to make the decision of whether or not to fish. It could also lead to improved stock and fishing grounds since fewer traps and craft would be employed in the harvesting process of the industry.

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CHAPTER VII SUMMARY AND CONCLUSIONS Florida's spiny lobster ( Panulirus argus ) industry achieved tremendous growth during the past two decades and is presently the second most important fishery in the state in terms of dockside value of landings. Spiny lobster landings in Florida exceeded 11 million pounds in 1973 with an estimated retail value of over $40 million. Florida landings represent approximately 98 percent of total U.S. landings. The tremendous growth in landings is a result of a disproportionate increase in inputs into the fishery. Number of spiny lobster firms, number of traps, and size of firms (gross tonnage) have increased throughout the past two decades. The rate of increase has been greatest since 1965. The increase in number of firms and total traps fished was 80 percent and 242 percent, respectively, between 1965 and 1972. During this same period total industry landings increased only 16 percent, while landings per firm actually decreased by approximately 60 percent. An increase in the retail price of lobster tails from $1.50 per pound in 1960 to over $9.00 per pound in 1975 has induced the growth in inputs employed in the spiny lobster harvesting process. Thus the immediate problem addressed in this dissertation was that of answering economic questions relative to industry growth. "Over investment" in capital (gear and craft) and labor (fishermen) has occurred in an effort to harvest a relatively fixed supply. The increased fishing effort in 131

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132 the fishery also raises concern about the possibility of "overexploitation" of the fishery stock. The primary objectives of this study v?ere to (a) evaluate the extent of fishing effort in the industry and determine both the maximum sustainable yield and the maximum economic yield, and (b) analyze alternative management programs which would allow for a more efficient utilization of the fishery stock. To achieve these objectives, two analytical models were developed for the Florida Keys spiny lobster fishery. A bioeconomic model was estimated for a time period in which the biological stock was allowed to vary. The second model (firm harvest function) was estimated for a given stock of lobster resources. With these two models the impacts of selected management programs were analyzed by simulating the industry with respect to estimated optimum levels of input s . The scope of the study was defined to include only the Florida spiny lobster fishery. The data for the empirical analysis represented Monroe County, Florida, since approximately 80 percent of Florida domestic landings are landed in Monroe County. Theoretical considerations and industry data availability required that the bioeconomic model be estimated as a function of traps per firm, number of firms employed in the industry, and mean seasonal water temperature. The mathematical form of the model was a reciprocal equation which represented behavior consistent with suggested theory and the curtent status of the industry with respect to sustainable yield and present management policies. Annual time-series data from 1963 to 1973 were used for estimation. The overall explanatory power was high. and each coefficient was statistically significant in the model.

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133 The firm harvest function was estimated from a cross-sectional sample of lobster firms. Spiny lobster fishermen selected by a statistically designed sample were interviewed in 1974 concerning specific aspects of the spiny lobster harvesting process. This data was used to analyze the lobster harvest function for a given stock level on a per firm basis. A Cobb-Douglas functional form model was used to relate firm landings to the number of traps fished and fishing intensity. Fishing intensity was measured as percentage of traps pulled per week, number of weeks fished, and size of the craft. Location of fishing grounds was entered in the model to adjust for area differences in fishing conditions. All variables with the exception of one location variable were highly statistically significant. The cross-sectional harvest model was used to estimate the profit maximizing level of traps per firm. This value was then substituted into the bioeconoinic industry function for traps per firm to complete the industry analysis. Maximum sustainable yield for the industry was approximated by observing the range of estimated maximum industry landings as traps per firm and then firms were increased to practical feasible limits. While one input was varied the other was held constant at actual mean, minimum, and maximum levels employed in the industry. The estimated range in maximum sustained yield was between 5.9 to 8.9 million pounds. For the purposes of ths study, 8 million pounds was defined as an extreme estimate of maximum sustainable yield while 6 million pounds was defined as a conservative estimate. Maximum economic yield was estimated for the industry allowing both traps per firm and number of firms to be simultaneously determined such that maximum economic profit would be attained. Maximum economic yield

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134 was estimated to be 5.8 million pounds. The optimum level of firms was determined to be 213, each fishing 795 traps. Estimates were based on 1973-74 ex-vessel prices ($1.08 per pound) and 1973-74 total costs per firm and per trap. These optimum levels would require a reduction of 47 percent in number of firms and a slight reduction of 1,836 traps in the total industry from 1973 levels. Total industry landings would be increased approximately 16 percent over 1973-74 season harvest. Estimates will change depending on relative changes in the cost of production and product prices. As usual, maximum economic yield was less than the predicted maximum sustained yield. Recognizing that maximum economic yield may not be the immediate goal for management because of the political and social consequences of extreme adjustments in the short-run, further analyses were completed. The analyses considered (a) parameters from the firm harvest function which represented current stock levels and thus would be relevant for current management programs and (b) alternative levels of one input while holding the other input at politically realistic levels. These analyses provide information to regulatory agencies which could be used in assessing benefits and costs of alternative management programs. Fewer than the optimum number of firms would be allowed to enter the industry if the major objective of the regulatory agency was to maximize average net return per firm. This objective was evaluated using value marginal product analysis with respect to the industry harvest function. The results showed only 121 firms could be allowed to eater the industry assuming 700 traps per firm and 1973-74 factor costs and product price. Total industry profits would be maximized with 225 firms using value marginal product analysis, thus defining the range of

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135 number of firms that could enter the industry based on rational profit maximizing objectives of the regulatory agency. As a result, total industry landings would range from 3.87 million pounds with 121 firms to 5.65 million pounds with 225 firms. Considerable substitution between number of traps per firm and number of firms can be made without changing the level of landings thus providing numerous policy alternatives. Rates of substitution between numbers of traps per firm and number of firms were determined. Beyond 400 firms substantial increases in number of firms would be required to maintain landings due to a reduction in traps per firm. An analysis of the possible range of combinations of traps per firm and number of firms where profits are positive was presented with the use of isoquant map. The conclusion was that profits would not be possible if more than 900 firms would enter the industry, nor would it be feasible for a firm to fish with less than 75 traps. For purposes of this study "management" was defined to include maintaining current levels of inputs, as well as increasing or decreasing their levels. Traditional programs were analyzed by simulating the behavior of the spiny lobster fishery under programs which would license traps, license firms and issue landing quotas. Finally, an alternative management scheme, entitled "harvest rebate program," was suggested. This program would incorporate aspects of the traditional system. Programs were analyzed under the previously stated factor costs and product price assumptions. The desired value for landings was assumed to be 5 million pounds. Seven hundred traps were determined as optimum for 197.5-74 stock levels for profit maximization.

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.136 Licensing of traps appear.'; feasible iii a theoretical framework if performed in conjunction with some form of "grandfather clause" legislation. The objective would be to increase costs per trap to a level where the level of traps fished would be such that the value of the marginal product would be equal to the marginal factor cost of a trap. Data for this analysis was obtained from the survey of spiny lobster firms and results showed that typical firms in the industry would be required to reduce number of traps fished. Assuming 400 firms in the industry, firm and industry profits are maximized at 557 traps per firm. No profits are returned if a firm fishes less than 207 traps. Furthermore, if less than 400 traps per firm are fished, no regulation of traps would be needed to maintain the desired 5 million pound level for landings. Licensing of traps from a pragmatic standpoint, however, may not be feasible since policing the number of traps per firm would be difficult and expensive to regulate. The firm licensing program was essentially based on the theoretical motive of increasing marginal factor costs of the firm to a level where the value of the marginal product of an additional firm added to the industry is equal to the marginal factor cost of the firm. Such a program may or may not limit the number of traps fished and/or landings. Seven-hundred traps fished and a $1000 license fee were assumed per firm for the simulated example. The analysis showed profit per firm was maximized with 121 firms, while total industry profit was maximized with 211 firms in the industry. Total landings were 3.87 million pounds for 121 firms compared with 5.51 million pounds for 211 firms in the industry. If more than 694 firms entered the industry no profits were earned. If each firm

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137 fished 700 traps, no more than 175 firms could be allowed in the industr in order to maintain a desired harvest level of 5 million pounds. Licensing firms appeared to he a more manageable program for regulating entry of effort into the fishery than licensing traps since a much smaller number of units (number of firms) would have to be regulated. The number of licenses issued would be based on the regulatory agency's objectives and selected parameters for traps per firm, landings and expected prices of inputs and outputs. Furthermore, if traps were not regulated, limiting the number of firms would not guarantee that the desired level of landings would be achieved. Landing quotas could be useful as a management tool for expedient adjustments to precisely control industry landings. Since current landings were less than the estimated range of maximum economic yield levels precise control of landings was not viewed as an immediate concern in the Florida spiny lobster fishery. Consequently, an example of the industry structure and behavior regulated through landing quotas was not simulated. However, a quota fee could be assessed in a similar manner to the firm licensing program. The major advantage of the quota system would be that it would allow the harvesting process to operate freely to optimally combine inputs. Free enterprise is conducive to efficiency and technological innovation, which could lead to reduced total industry costs in the long run. Conversely, disadvantages of the quota system are: (a) that an accurate estimation of maximum sustainable yield would be needed which could generate high research costs; (b) maximum economic yield would not necessarily be attained since the incentives of over capitalization still remain; and (c) the fisherman's motivation due to dreams of "the

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138 big catch" would be destroyed if he were limited to a predetermined har vest level. An alternative approach to management, the "harvest rebate program was offered for further consideration. This program integrated several features of the previously discussed traditional management programs. Effort in the form of firms would be limited and license fee would be required. The harvest rebate program offers the flexibility of allowing each firm to maximize landings. Finally, this program would allow the market system to regulate harvest since higher license fees should discourage inefficient fishermen. Landings regulated in this manner could be substantially less costly to regulate due to less government intervention than would be the case in the more traditional management programs discussed. The harvest rebate program was analyzed simulating the industry behavior under various levels of traps per firm. License fees were ranged from $17,000 to $1,000 per firm, with the optimal number of firm ranging from 140, each fishing 1,000 traps, to 328, each fishing 429 traps. Those fishermen choosing not to fish would receive a rebate pay ment equivalent to the average firm profit without the program for a specified level of inputs. The increase in profit per firm for those fishermen electing to pay the license fee ranged from 38.7 percent with 140 firms in the industry to 17.3 percent with 328 firms in the industry. Profits for each of the 400 firms before the management program ranged from $5,935 for firms fishing 1,000 traps to $7,943 for firms fishing 618 traps. Maximum revenue to the state, given the assumptions of the analysis, ranged from $745,544 for 328 firms to $2,701,160 for 140 firms.

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139 Finally, a breakeven criterion was developed to help the fisherman decide whether he should fish under the harvest rebate program, or elect not to fish and receive a rebate payment. The criterion was in terms of the minimum pounds per trap necessary to maintain a profit level equal to or greater than the profit level without the program. The conclusion was that a firm must harvest an average of 16.90 pounds per trap (assuming 328 firms, each fishing 429 traps) to 28.49 pounds per trap (assuming 156 firms, each fishing 800 traps) before it would be economically feasible to purchase a license to fish. Thus, fishermen participating in the program would operate with considerable flexibility, firm and industry profits would be equal to or greater than would be the case without the program, and the program would be totally self-supporting.

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APPENDICES

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APPENDIX A Table Al. Spiny lobster landing-j ar.l dollar value, Florida and U.S., 1952-73, economic study of Florida spiny lobster industry U.S. Florida 1,000 Cents Cent 6 Percent of U.S. 1,000 per per Tear Pounds Dollars Pound Pounds rollars Pound Pound s Do! lars 1952 2,419 740 30. 6 1,612,400 403, 100 25 .0 67 55 195.3 2.745 752 27.1 1,995,000 399 COO 20 .0 i 3 5 3 1954 2,849 837 29.4 1 ,947,300 428 4J5 22 0 68 31 1955 3,154 962 30.1 2,295,400 527, >?-' 2 23 . 0 73 55 1956 3,849 1,210 31.4 3,113,000 825,056 26 .5 81 66 1957 4,687 1,500 32.0 4,039,800 1,123,545 27 8 86 75 3958 3,583 1,226 34.2 2,954,307 836,631 28 3 82 '..8 1959 3,698 1,268 34.3 3,130,733 954,605 30 0 ! 6 75 1900 3,210 1,344 41.9 2,S;8,540 I, i 00, 2=4 33 6 89 B2 1S&1 3,235 1,263 39.0 2,603,439 969,303 34 6 67 77 1962 3,664 1,561 42.6 3,107,000 1. 187, 177 38 2 35 76 1963 4,130 1,798 43.0 3,535,194 1,407,746 39 3 86 78 3 964 4,083 1,830 46.0 3,631,130 1,562,163 43 0 89 83 1?65 6,237 3,626 58.1 5,714,093 3,219,241 56 3 92 89 1966 5,844 2,882 49.3 5,33fi,:i»6 2,<.68,969 46 1 92 86 1967 4,868 3, 125 64.2 4,413,5'.7 2,732,724 61 9 91 88 19 Co 7,476 5,367 71.8 6.155,036 -,i08,.' n9 71 6 82 82 1969 8,731 6,310 71.9 7, isl, J 3 3 5,257 , 5. .2 69 4 B6 a 3 J970 10,34 5 6,33.! 61.2 9, .359,.,,;? 5.91S.479 60 0 9 i 1971 5,439 7 Cfi y 93.7 o t 'n r . »>.•> 7,056, ^38 8'. 0 9/ 89 \ 97? * 1 . 0? j i i tee '03. 3 10,f 3?,!W 10, 986, 1C3 .3 95 96 1972* il,S07 103. 1 1J ,416,782, •J, 771 , 425 ;o'' } )i 97 1973 9,872 10,567 io: o 10,221,242 105 7 98 97 19/3" 11,376 12,007 105.5 1' , ! 7 J , '(:£.'' 11,661 ,141 1C'4 4 93 97 Sourc e; National Marine rishe-ies Serv.r.-. T, »':.ery Statistics cf the. !.-.ited Stales (forvarly Bureau of Cinserciol Fisheries), U.S. Government Print ipg Office, Washington, D.C. Annual Issues, 1952-71. h2tlcral Marine Fisheries Service, Florida Uindinps (f.-r.:erly Euresu of Cossevcial Fisheries), U.S. Governxeat Prir.:iag Oft ice, Washington, D.C. Monthly and annual issues, 1971-73. Note: Prom personal lntervt»vs with staff i-f the Statistics and Market Nevs Division, HHFS, mKDC, It was indicated that approt-livitBiy 80-92 perrcflt oi actual :ardi.:is ate documented . For exar.plc, in H73 it is ^.cimted that two million p-njisda of -rrocorii?d spiny lobster landings frua FljriJa vert aarkeLed in Georgia, r-.en.. are bas-.d on personal ctlnlons of statistical analysts -.ol'. acting and aiialy'i,^ the data iz.£ jrc not t'oturipnted facts. *Out of season landinf.: Included tor 1972 snd 1 973 w*re 782,974 *i:4 1.5C4 .480, respectively. Those arc landings in Florida pcua .'roa foreign vit»r5 djrlng the closed ^caaon In Florida allowed due to new 1972 legislation. The following data for out of season landings were obtained froo fisheries Statistics, Southeastern Fisheries Center, U.S. D.C, SuAA, KMfS, Miami, Florida. Te*r i East Coast Vo1 Coasr Qorida Total C_-nts Pounds Dollar* Pounds Do! 1.1T3 Pounds Dollars per Pound 1972 530.734 532.907 252,240 252,224 73.-, 974 785.131 100.3 3 97) 1,250,351 1.) 90, 551 245,129 249, 3th ] ,504,489 1 ,4 !' ,S89 95.7 F.at lifted hy 11,807 x $1,031 12,173.017 141

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APPENDIX B u p. o o o z o oin !-»<"*"> CO o> CM •4 rH cm - cn rm CO r^. CM CM m o m 30 rH O m O CM 0> C J CM ON O vO co rH CM CM CM CM CM cn CM m m CM •a Ps| cn m co •4 m m i — 1 CO m CO o rH CO vD CO Q> CM 00 r-. r^. co m >o r* O o o CC rH <£ ON r-. *£ rO m On H t-t rH iH r-4 CM CM CM CM CM CM m cn . CM «£> no CM O to r* m CO m ON o O <3 CM vO rH rH CO vO O r^-^r H H rH CM CM co in co m i — 00 ON On m O O N M r>j Ch r>. rrccn 1 ^ ^ n n rH H H f ) N o o c; o go o CN rH rH rH n o o vo O co vc £> ON ON CT> C~* ON o o •H •J I** | 0 a j> > 6 u .c C «H H u r-l rH O c O u «H u 1 1« K <0 U P :j O CO .142

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APPENDIX C Table CI. Input/Output relationships, Florida west coast, 1952-72, economic study of Florida spiny lobster industry Year Pounds Per Trap Dollars Per Trap Pounds Per Firm Dollars Per Firm 1952 213 53 17,717 4,429 1953 134 27 15,887 3,177 1954 62 14 9,896 2,177 1955 93 21 18,802 4,324 1956 137 35 32,408 8,363 1957 154 42 30,957 8,437 1958 100 28 22,205 6,218 1959 78 23 14,987 4,421 1960 39 15 12,674 4,879 1961 54 18 15,010 5,148 1962 42 16 14,238 5,436 1963 46 18 14,896 5,808 1964 39 16 11,473 4,885 1965 49 28 20,301 11,423 1966 49 22 13,672 6,191 1967 30 18 9,154 5,601 1968 40 29 14,415 10,398 1969 48 34 17,360 12,406 1970 46 27 20,332 12,131 3971 32 28 14,068 12,145 1972 20 21 13,069 14,003 143

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APPENDIX D CROSS-SECTIONAL DATA COMPUTATIONS Definitions : xi = (TR) , average number of traps fished for the season. X2 = (PWK) , average number of rounds per week for the season. X3 = (WK) , number of weeks fished during season (36 maximum). xij = (LOWD) , size of hull in square feet; computed as hull length (LO) times hull width (WD) . X5 = (DU) . dummy variable for upper Keys; DU = e if included and 1 if excluded. Xg = (DL) , dummy variable for lower Keys ; DL e if included and 1 if excluded. i months, 1, 2, ... 8 (August March). PULL = pulling a trap out of the water once (also termed hauling) . TOTAL PULLS = total number of times a trap was pulled (P) out of the water (could be same or different trap(s)). ROUND = pulling all traps fished, once. R. = total rounds per month i. 1 TOTAL ROUNDS = total number of times all traps fished were pulled (R). SET PERIOD = length of time a trap sets between pulls (SP) . SP^ = set period for month i. D^ = days per month i. LO = hull length. WD = hull width. T^ = traps fished in month i. DATA COLLECTED (or known): T , SP., D , x 3> LO, WD, x 5 , and x 6 . 144

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145 DERIVATIONS : 8 P = I (T.) (R.) i=l 1 1 R . = Di i SP. R = E R. i=l 3 x 2 = R_ *3 (1) (2) (3) (4) (5) xit = (LO) (WD) (6)

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APPENDIX E .J " S 2 S 5 5 < < < <• *: • \c z ;= j ro >c . cn c*" rv »7 <7 <— , vD r-~ ro vtJ i/> CT 1 »— < H (1 >A c-j n n ^ m e» o o * *s ri cr ro 3^ C r-s n vO i O ri N N (M n o to ifl CI -7 O CO -7 W ri tO -7 t-« -7 O C"> CT> O cn r-. rv xn : n .-n n : (n to rl ^ N N -( cr> — > o m m cn cn i.i rv k O c j C 'N t-J O ^ n MA N o fin i-l CS lTi J^ N 2 N H -J n h 3 'C -j cn >r rv cn .-M o Cn: rc. cn O *-* H n n «j -J CO ri CN VO fv m ri ri lA a* *a m \C r -j >f n ^ ^ H ov r in ts m sT C ITi vT n f> cc * rv L-i cj* cr> 33 rN C C O C irt •n rs cm CN CN iv in m o -7 cn D >C O cn cn fM acc O .'O iA 0> CN CJa M < CC N *C (N -O -.7 CN H fN CN CN CN O C O O O o o o o rv cn *7 '-O O rv O >— I O in eg ir» u"i O cn cn cn tv co O *7 CO CO CO C O iH m O On r-. O 0> CO JH H ri .< N .-t o CN un rv CN O fv o o o o »-n •-H N CI OCJ i-i r ; O \0 *T' -1 CO tv r-* f — m (N —i r-i •£. CN O O »n O J" CN CN CJ vj r vj »r a) o o o o o o e o o o ^7 C cn O m c -i C On m 'n C ri CC O -• O^t O r-. n O O O C cn -7 cn CC " N »A ^ iv c-i a.C -7 O .-n vO j r> ,n j> x IN O -J f» c— l N iA iA vj iT, cn cn »v CO m o m ^-j o rv .7 r-j o cn *7 *n un iv rv o en e4 m o m m j-j o i' 1 O w & < O co <**' r-» co •» O O J*— t CO CO I ^ « *3 O JO fN CN <-"> vj -sO *n «n -7 n cn CN CN r-. ,T O ^-i C" »? t7> C7> cn cn cn n w .» id >r ^ o >o ^7 rv tO JT OO — « J> sT rUN iT* »7» in m i-i— O vC co cn -7 O rv ri O CN IN CN CO 00 O rv rv ci
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APPENDIX F Table Fl. Spiny lobster landings in Florida ports caught in foreign waters, 1964-73, economic study of Florida spiny lobster industry Total Florida Landings Florida Landings Florida From Domestic From Foreign Landings Waters Waters Quantity Quantity Quantity Percent of (Pounds) (Pounds) (Pounds) Florida 1964 3,631,100 2,632,547 998,553 27. 6 1965 5,714,100 4,719,847 994,253 17. 4 1966 5,350,000 3,151,150 2,198,850 41. 1 .1967 4,414,000 1,915,676 2,498,324 56. 6 1968 6,155,000 2,880,540 3,274,460 53. 2 1969 7,582,000 4,036,698 3,495,302 46. i 1970 9,862,462 6,745,924 3,116,538 31. 6 1971 8,205,803 4,669,102 3,536,701 43. 1 1972 l.l,986,22l a 5,488,338 6,497,883 a 54. 2 1973 12,676,188 a 6,621,122 6,055,066 a 47. 8 Source; Foreign water landings obtained from unpublished data collected by the Statistical Reporting Service of the National Marine Fisheries Service, Miami, Florida. Out of season landings included for 1972 and 1973 were 782,974 pounds and 1,504,480 pounds, respectively. These are landed in Florida from foreign waters during the Florida closed season. 147

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APPENDIX G TOTAL PRODUCT AND MARGINAL PRODUCT EQUATIONS FOR FIRM HARVEST FUNCTION MODEL (xj) — TRAPS In q = 4.41843 + .7577 In xi In MP = 4.07715 .2423 In xi (x 2 ) -PWK In q = 9.367628 + .4399 In x 2 In MP = 8.5787272 .5601 In x, (x 3 ) — WEEKS In q = 7.985825 + .3721 In x 3 In MP = 7.101433 .6279 In x, (xi,) — LOWD In q = 7.4999502 + .3083 In x 4 In MP = 6.526395 .6912 In Xu XI, (z) -DAYS IN SET PERIODS X2 = 7/z |J4.23501 x^x/V"^ 2 + 15 = 12116 ."1.M991 In MP 9.40232 1.43991 In z 148

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APPENDIX H Table HI. Comparison of spiny lobster production practices by craft length for firms sampled, Florida Keys, 1973-74 season, economic study of Florida spiny lobster industry Item Unit 16-22 Craft length 24-28 (feet) 31-36 40-55 Traps fished no. 341 561 842 809 Traps lost: Number no. 98 193 318 371 Percent % 29 34 38 46 Traps fished per day no . 139 190 202 272 Hours fished per day hrs . 7 S 8 9 Pulls per season no. 27 27 25 27 Weeks fished wks . 35 36 33 25 Trips per season no. 66 103 89 48 Boat and vessel size: Length ft. 20 26 34 46 Width ft. 7 9 12 15 Volume of Lobsters: Per trap lbs. 18 22 22 20 Per week lbs. 175 339 549 636 Per trip lbs. 93 118 204 331 Note : Data reflect averages for classes of craft size. 149

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APPENDIX I (Table 18 Computations) 1. X l assumed equal to 1000, 800, 700, 618, 500, 429, 350, and 200. x * m 465,173,997.25 2 2 (4,773,480.707) 1,439,976,169 3. Q n = 8,610,545.714 = 1*429 ^976 , 169 4. Q, = 9,773,480.707 ^39,976, 169 _ 465,173,997^252 A Xi X 2 5. TG/X 2 = 1,876 + 11.55XJ Q (1.08) 6 ' 1x7X2 = "Too TC/X 2 ft Q B (1-08) 7. ff /x 2 = TC /x 2 X 2 8. % A Column 7 ir/X : * Column 6 1 ^ 2 A 9. Maximum State Revenue = (Column 10) x (Column 2) 10. Maximum License Fee = (Column 7) (Column 6) 11. License Fee assumed: $20,000 for 1000 traps per firm 18,000 for 800 traps per firm 15,000 for 700 traps per firm 13,000 for 618 traps per firm 10,000 for 500 traps per firm 5,000 for 429 traps per firm 4,000 for 350 traps per firm 3,000 for 200 traps per firm 12 % A r „ , ft* = [Column (7) Column (11)] : [Column (6)1 1 */x 2a 13. State Revenue (Column 11) x (Column 2) 150

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151 14. Administrative Revenue = (Column 13) [(Column 6) x (Column 16)] 15. % A Tot. Ind. = [(Column 7) x (Column 2)] * [(Column 6) x 400] 1 7T ** 16. X 2 400 Column (2) 17. B.E.C. = [(Column 5) + (Column 11)] f [(Column 1) x (1.08)]

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APPENDIX J Spaces provided for answers have been omitted from the original thirteen page questionnaire for inclusion in this text. The questions and multiple choice answers are the same. A map of the study area used to identify the actual fishing grounds for each fisherman has also been excluded . (CONFIDENTIAL: Please do not give name) SPINY LOBSTER FIRM SURVEY QUESTIONNAIRE Please answer all questions based on 1973-74 season. Answer all questions as accurately as possible. If the exact answer cannot be recalled, please give your best approximation. If additional space is needed to answer (or simply comment on) a question use the back of that page and properly indicate additional comments. I . DESCRIPTION OF LOBSTER PRODUCTION UNIT A. Operation Unit: ( ) Vessel, Boat 1. Fabrication (i.e., wood, fiberglass, steel, etc.) 2. Length (feet), Breadth (width) (feet) 3. Depth (feet), Draft feet (loaded) (feet) 4. Gross Tons, Net Tons 5. Engine Make, Horsepower 6. Age of Vessel, Age of Engine 7. Top speed: Empty, Loaded, Average Speed E. Method and Crew: 1. Type ( ): Trap, Diving, Bull Net, Other 2. If trap: Single, Trot Line 3. Number of men in crew excluding captain 4. Approximate age of regular crew members (4 blanks) 5. Does a single trip involve more than one day away from port? Yes, No. If yes, what is the average length of time away from port per trip? (Days) C . Gear : 1. Traps: a. Average number of traps fished in each month. b. Maximum number of traps fished at any one time: 2. Electronic equipment on board. Give make and model number. 3. Method used to haul traps. If hydraulic, please give capacity, size, and make if known. 4. Preservation techniques used? Live, Ice, Freeze, Other 5. Please list other gear used but not listed above. 152

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153 II . FISHERMAN'S LOBSTER PRODUCTION TECHNIQUE A. Materials and Style of gear. 1. Trap Design a. Briefly describe trap style b. What type of throat structure is used? c. Hoi many entrances do you have and where are they located? d. Is a bait cup used? Yes, No e. Type of material used? Is it readily available? 2. a. What type of bait do you use? b. Wiry do you prefer this type? c. On the average, how often do you have to replace the bait in a trap? d. Is it easy to acquire the bait you are using? B. Description of fishing ground and fishing intensity. 1. Please draw areas on the map on the next page as shown in the example. Then number each area consecutively (beginning with #1) based on the amount of fishing you do in that area. (i.e., area I is fished most by you) 2. For the areas you have indicated on the map please give your best answer to the following questions describing each area. Area # (see map) (1 . . 2 . . 3 . . 4 . . 5 . . 6 . . 7 . 8) (1) Approximate distance from home port (miles) (2) Average traveling time from home port to each area (minutes) (3) Botton conditions (enter letter): a. rocky/coral; b. sandy; c. grass; d. other (4) Average depth (feet) 3. Please indicate your best estimate of the following information for the three major areas you fished for the following months: (a) average depth, (b) average water temperature, (c) average number of traps. (See map attached to back of questionnaire). 19 73-74 season (Aug . Sept . Oct . Nov . Dec . Jan . Feb . Mar) Area it (get from map) (a) Average # traps (Dotted lines used to separate mere than one (b) Average water temperature , . , , , . N ; ' ° , area fished for a month.) (c) Average number traps made 4. List all ports at which you landed during season. (8 blanks) 5. Daily Activity: a. What is the average hours per day worked? (From departure of port to return) (Hours) b. Of the above hours, approximately how many are spent actually hauling traps? (Excluding traveling between fishing grounds) (Hours) c. How many traps can your operation pull and shoot per hour? d. On the average, approximately how many trips did you make per week for each month? (1973-74 season) (Aug. Mar.) e. What is the average length of time traps set between hauls for each month? (Days) f. Approximate number of days of bad weather which prevented you from fishing for each month? (If unknown, give best estimate for total season. (Season total) (Aug. Mar.)

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154 III. COSTS OF PRODUCTI ON A. Initial Costs (fixed costs) : 1. Value of vessel (boat) (Excluding gear, electronic, and hydraulic equipment)? ($ ) 2. Type (make) and value of electronic equipment on board? Value $ , Describe 3. Replacement value of engine? $ 4. Value of Hydraulic and other equipment on board? Value $ Describe. 5. Cost of insurance? a. Protection and indemnity (P & I)? ($ ) b. Hull ($ ) 6. Interest on Loan? ($ ) 7. Fishing and vessel (boat) licenses and permits? ($ ) 8. Trap construction: a. Number of traps built for 1973-74 season? b. Cost of line? ($) Type used c. Cost of wood? ($) Type used d. Cost of buoy? ($) Type used e. Cost of labor used in building traps? ($) f. Other costs (i.e.. cement, oil, nails, wire)? (Specify amount) 9. Please describe and give value of other miscellaneous initial expenses? B. Operating Costs (Variable Costs). 1973-74 season. Please leave blank if the item does not pertain to your operation. Item .... Amount Used .... Total Cost ($) 1. Fuel (gals.) 2. Oil (gals.) 3. Bait (lbs.) 4. Ice (lbs.) 5. Groceries 6. Other miscellaneous trip expenses 7. Labor costs a. Captain share (%) b. Crew share (%) c. Boat share (%) d. Wages (hours) e. Bonuses f. Labor taxes g. Other (specify) 8. Maintenance and repair costs a. Hull b . Engine c. Electronic equipment d. Other machinery e. Gear (traps) f. Other (specify) 9. Cost of trap losses No. of traps lost 10. Other expenses (Specify)

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155 IV. PRODUCTION AND EARNINGS 1. What percent of your total income is earned from lobster fishing? 2. Please complete the following table on monthly landings and values to the best of your knowledge: (1973-74 season) 1 973-74 Season: Landings & Value (August March) Total Lobster (lbs.) Lobster ($) Finfish (lbs.) Finfish ($) Other (lbs.) Other ($) 3. Please answer the following questions to the best of your knowledge. Space for answers is provided in the table. A. What is the average size of legal lobsters landed for each month? B. How many pounds of "shorts" do you see in your traps per trip, on the average, for each month? C. What is the average number of traps lost each month? D. How many pounds of lobsters do you believe were stolen from your traps, on the average, each month? 1973-74 (August March ) Tota l Quest. A Quest. B Quest. C Quest. D 4. Please check the range of your total earnings from lobster fishing only for the 1973-74 season. (Below $2,000 to above $30,000) 5. If you fished and if you recall, what was your approximate total season landings and total number of traps fished each season as shown in the table. (72-73) (71-72) (70-71) (69-70) (68-69) Total Landings Total Traps Fished 6. What do you feel would be the most efficient combination of the following if you could design the ideal operation unit? A. Vessel: Make, Length, Width, Gross Tonnage, Fabrication B. Engine: Make, Horsepower C. Size of crew D. Electric Equipment E. Hydraulic Equipment F. Total Number of Traps G. Approximate Cost of Complete Operation Excluding Crew and Traps ($) H. Given this "Dream" Operation Unit Approximately How Many Pounds Do You Believe You Could Have Landed in 1973-74 Season?

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156 V. ABOU T THE CAPTAIN AND HIS VIEWS ON MANA GEMENT AND REGULATION 1. The Captain A. Age (years) B. Years lobster fishing (years) C. Father's occupation D. What generation lobster fisherman are you E. Education (grade school, high school, college) 2. Is your lobster operation considered single firm, partnership, or Corporation? 3. Is there any cooperative activity with other fishermen (i.e. sharing of labor)? Explain. 4. Do you find that the size of lobsters has decreased over the years? Yes. No. If so, by how much or in what manner? 5. What are the major factors used by you to determine when and where to fish certain areas? (i.e. with respect to such things as tides, month, wind, moon, temperature, barometer readings, etc.) 6. If the landing of shorts was legal, how many pounds of shorts could you have landed in the 1973-74 season in addition to the legal lobsters you landed? (lbs.) 7. How many pounds of shorts do you feel were landed in your area in the 1973-74 season? (lbs.) 8. If you were not a lobster fisherman what other occupation would you have chosen based on your qualifications. A. Other fishing (specify) Estimated income ($) B. Non-Fishing (specify) Estimated income ($) 9. What kind of regulation or management would you recommend with respect to the following: A. How long should the season be? Why? B. What months should the season include? Why? C. Should the number of licenses be limited? If so, how and to whom? D. What is the maximum amount you are willing to pay for a license? E. What should a lobster's legal carapace length be set at? (inches) F. Other comments.

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APPENDIX K o «t> o -»«-"•> *^ on u-\ <»"y o H ro r-j */3 m cO v£, -J (sjei^onr-sosOt/sm r-i -J (O M 'O CO OJ CO J f-i rH O vr m cn is , , r~i N IS o o\ r-J fSj CC CO rs. « CO m o c**i o ic n vo -J tN t— < ci O N TO * O H »j (*) H CO f-J o -o *o co mO m CO *3 N ^ o od rn — i r-« r^l o co --r J iN 3 » » »-j O O i -J - co -J co O I h rJ n cm r-> CTv. CT> O vT> O ^ .J tN i-i ci o h O r. 1 H i-i rs, co m iri m tri n n m n ao cr> as c r, cr» co csi cc co o tj-, N CO O m *j m o 11 1^ } fj 1^ (N Jv >D n CN C C> H ^ Is J « O is Cn -J sO (O w-i on C t~* O rs in tN D CO ^ ^ " H t^^isr\ONNn i-s to os sr co co r-. cs» «n nriN fs, t-l OS O* CO OS CCsO r^j CO CO n iA <*> r-fl n (N 7v CO C N r k vf i.n os >/i i*H CO ^ ri i o n n S O -< OS O -* vO cc 'Sj ^ n ri -i C to n. w s^ *J d 0 iys ts CO N CO fi r-»o>rov.orovOfs O C-J r» o iT is fs csi rsi co m c co m r"i Os o to is ."si k y*> O -J o O no O* — • »is O" C in n m ft ho I /I " * c -* s. w O U) tf* V* (g ~> sw «w TJ li U -H 1 Cm C. O 0 M « V, r-4 a 4» > U £1 CO ii O CD .ty o •i a J A O. H w O. •o M II u CJ r. a U fC -«-* *j o. P. V k* ^ M a c c 'o. »« o «? u u : i It f c vT e > H M c VI o a -J « M XI *, C O. 01 e> o CQ U -/. U V 1 u< U. O o 1 a. t< > U 4> rs O OS X OS O i . sT C U-t |s t) CN o < o I *J : o w o ^ b o o ^ CJ M 3 -a c k 41 > O P 3 3 iH 15 o K -I S-8 q « a > x: > u c ts o o u ^ u u J3 4J 9 e " o J> u cy •8 B u -1 157

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APPENDIX L rH U CO 3 o c a) CO *rl co B •rl -O 0 •H «W 4-J O OT ai o 3 •P 4-1 CO a; u 3 1 o id c CD • Q) > O D u • o 3 H O CO CO CO WJ t-i C •H t-H 13 rH C O J ^ 4-1 •H 4J C CD •a ^ CCJ CD lO a) ^ X i-i to • <| v! io 4-1 X CO N J O CO ^ CD CO co ai XS CD c ,? 3 O >-i « 0) Pu CO p. ^ cd <-* U X H ^ CO <-s M CO C -a a T3 rt a. u^00OtHrHa\^cn^vor^cNcovfv0csiins0^f^00O 00tHr _l OOC) OOOOOOOOOOOOOOOOOrH voc»0O-J4CMOMC0H00NOMOC0O rH co vC r-n X) co o o CTi CJ> CO r- co vO VD r-^ c r» vC vO in r> m o CO O CT> in 00 m o rH tH m o o O vO 00 CO CO in i-H o C0O ro co .o 1 — O o o C5 o CO CN o o CN CO vD cn vO c rH o o m i — i o o\ o o o m co ro m rON ro
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REFERENCES [1] Allen, Bennet M. "Notes on the Spiny Lobster ( Panulirus interruptu s) of the California Coast," University of California publication in Zoology, Vol. 16, No. 12, 1916. [2] Barnhart, P. S. "Notes on the Artificial Propagation of the Spiny Lobster," California Fish and Game , Vol. 5, No. 2, 1919. [3] Bell, Frederick W. "Estimation of the Economic Benefits to Fishermen, Vessels and Society from Limited Entry to the Inshore U.S. Northern Lobster Fishery," BCF, DER, W.P. No. 36, March, 1970. [4] _. The Economics of the New England Fishing Industry: The Role of Technological Change and Government Aid, Federal Reserve Bank of Boston, Research Report No. 31, .1966, 215 pp. [5] • "The Relation of the Production Function to the Yield on Capital for the Fishing Industry," R ecent Developm en t and Research in Fish er ies Economics , Frederick W. Bell and Jared E. Hazleton (eds.), published for the New England Economic Research Foundation, Dobbs Ferry, New York: Oceana Publications, Inc., 1967. [6] . "The Pope and the Price of Fish," The Amer ican KccT ^r.dc R eview, Vol. LVIII, December, 1968. [7] Bell, Frederick W. and Richard F. Fullenbaurn. "Economic Impact of Alternative Management Strategies for the Northern Lobster Fishery," NMFS , ERD, File Manuscript No. 108, August, 1972, [8] Bromley, D. W. "Economic Efficiency in Common Property Natural Resource Use: A Case Study of the Ocean Fishery," BCF, DER, W.P. No. 28, July, 1969. [9] Butler, J. A. and N. L. Pease. "Spiny Lobster Explorations in the Facific and Caribbean Waters of the Republic of Panama," U.S. Department of Interior, Fish and Wildlife Service, BCF, Fisheries Report No. 505, 1965. [10] Carlson, Ernest W. "Bio-Economic Model of a Fishery," BCF, DER, W.P. No. 12, March, 19o9. 159

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160 [11] . "An Economic Theory of Common Property Fishery Resources," NMFS, ERD, File Manuscript No. 66, July, 1970. [12] . "The Biological and Economic Objectives of Fishery Management." NMFS, ERD, File Manuscript No. 140, September, 1971. [13] Carlson. Sune. A Study of Price Theory of Production , New York: Kelly and Millman, Inc., 1956. [14] Cheung, Steven N. S. "Contractual Arrangements and Resource Allocation In Marine Fisheries," Economics of Fisheries Management: A Symposium. Edited by A. D. Scott, 1960. [15] Chislett, G. R. and M. Yesaki. "Spiny Lobster Fishery Explorations in the Caribbean," UNDP /F AO Caribbean Fishery Development Project, Bridgetown, Barbados, 1971. [16] Christy, Francis T., Jr. and Anthony Scott. T he Common Wealth i n Ocean Fisheries , Baltimore: The John Hopkins Press, 1965. [17] Cope, C. E. "Spiny Lobster Gear and Fishing Methods," U.S. Department of Interior, Fish and Wildlife Service, BCF, FL Wo. 487, 1959. [ 1 8 J Council of Economic Advisors, Eeo-.u 'inic Rep ort : to the Pieficien' , Annual Report of the Council of Economic Advisors, Washington, D.C.: U.S. Government Printing Office, 1975. [19] Crawford, D . R. and W. J. J. DeSmidt. "The Spiny Lobster, F anulir us argus, of Southern Florida: Its Natural History and Utilization," Bulletin of the U.S. Bureau of Fisheries, Vol. 38, 1923. [20*1 Crutchfield, J. A. "Economic Objectives of Fishery Management," The Fisheries: Pro blems In Resource Ma nag ement , ed. J. A. Crutchfield, Seactle, Washington: University of Washington Press, 1965. [21 j Crutchfield, James and Arnold Zellner. "Economic Aspects of the Pacific Halibut Fishery," Fi shery In dustrial Review , U.S. Fish and Wildlife Service, Vol. 1, No. 1, April, 19~62. (22] Dees, L. T. "Spiny Lobsters," U.S. Department of Interior, Fish and Wildlife Service, BCF, FL No. 523, 1968. [23] DeWolf, A. Gordon, The Lo bster Fishery of the Mari time Provinces: Economic Effects of Regulations , Bulletin of the Fisheries Research Beard of Canada, Bulletin 187, Ottawa, 1974. 1>41 Dow, Robert L. , Frederick W. Bell and Donald M. Harrimqn. "BioEccnomic Relationships for the Maine American Lot:. tor Fishery, with Consideration of Alternative Management Schemes," NMFS, ERD, File Manuscript No. 149, April, 1973.

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161 [25] Ferguson, C. E. The Neoclassical Theor y of Production and Dis tribution , Homewoods, Illinois: Cambridge University Press, 1969. [26] Fullenbaum, R. F. "A General Equilibrium Demand Model for Living Marine Resources: An Application of General Equilibrium and Common Property Resource Theory to the U.S. Seafood Sector," NMFS, ERD, FL No. 116, August, 1971. [27] Gates, J. M. and V. J. Norton. "The Benefits of Fisheries Regulation: A Case Study of the New England Yellowtail Flounder Fishery." Sea Grant Resource Economics, University oi Rhode Island, Marine Technical Report No. 21, Kingston, R.I., 1974. [28] Gordon, H. Scott. "The Economic Theory of a Common Properr v Resource: The Fishery," Journal of Political Economy , Vol. 62, April, 1954, pp. 124-142. [29] Herrington, William C. "Some Methods of Fishery Management and Their Usefulness in a Management Program," U.S. Fish and Wildlife Service, Special Scientific Report No. 18, 1943. [30] Huq, A. M. and H. I. Hasey. "Socio-Economic Impact of Changes In the Harvesting Labor Force in the Maine Lobster Fishery," NMFS, ERD, File Manuscript No. 142, January, 1973. [31] Idyll, C. P. "Spiny Lobster of the Caribbean (Abstract)," F.A.O. Fish Report No. 71.1, 1969. [32] Lampe, Haxlan C. "The Interaction Between Two Fish Populations and Their Markets," Frederick W. Bell and Jared E. Hazleton (eds . ) , Recent Development and Res earch in Fisheries Economies . Published for the New England Economic Research Foundation. Dobbs Ferry, New York: Oceana Publications, Inc., 1967, pp. 179-195. [33] Mendeehall, W., et al. Elem entary Su rvey Samplin g, Belmont, California: Dunberry Press, Wads^orth Publishing Co., 1971, p. 40. [34] Nesbitt 5 Robert A. "Biological and Economic Problems of Fishery Management," U.S. Fish and Wildlife Service, Special Scientific Report No. 13, 194 3. [35] Pontecorvo, Giulio. "On the Utility of Bio-Economic Models for Fisheries Management," Ocean Fisher y Management : Discussion s and Re sea rch, U.S. Department of Commerce, inOAA and NMFS , NOAA Technical Report NMFS CIRC-371, April, 1973. [36] Prochaska, F. J. and J. R. Eaarda. "Florida's Fishery hanagement Progrums: Their Development, Administration and Current Status," Florida Agriculture Experiment Station Bulletin No. 768, University of Florida, Gainesville, 1975.

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162 [37] Prochaska, F. J. and J. S. Williams. "Economic Analysis of Cost and Returns in the Spiny Lobster Fishery by Boat and Vessel Size 5 " A Florida Sea Grant Publication No. SUSF-SG-76-004 , University of Florida, Gainesville., July, 1976. [38] Rich, Jack. "Natural Resources and External Economics: Regulation of the Pacific Halibut Fishery," Ocean Fishery Management: Discussions and Resear ch, U.S. Department of Commerce, NOAA and NMFS , NOAA Technical Report NMFS CIRC-371, April, 1973. [39] Robinon, M. K. "Atlas of Monthly Mean Surface and Subsurface Temperature and Depth of the Top of the Thermoclinc: Gulf of Mexico and Caribbean Sea," Scripps Institute of Oceanography, University of California, San Diego, S10 No. 73-8, March, 1973. [40] Russell, E . S. "Some Theoretical Considerations on the 'Overfishing' Problem," Journal of Conservation and International Exploration , March 6, 1931. [41] Schaefer, Milner B . "Some Considerations of Population Dynamics and Economics in Relation to the Management of the Commercial Marine Fisheries," Journal of Fi shery Research Board of Ca nada , Vol. 14, No. 5, 1957, pp. 669-681. [4?] Smith, F. G. W. "The Spiny Lobster Industry of the Caribbean." Caribbean Research Council, Fisheries Series, No. 3, 1948. [43] _ _. "The Spiny Lobster Industry of Florida," Florida State Board or Conservation, Educational Series No. 11, Marine Laboratory, University of Miami, 1958. [44] Smith, V. L. "On Models of Commercial Fishing," Journa l of Politi cal Economy , Vol. 77, No. 6, March/ April, 1969. [45] Sokoloski, Adam A. "The Status of Fisheries Management Research: An Overview," Ocean F ishery Manage ment: Discus sions a nd Research, U.S. Department of Commerce, NOAA and NMFS, NOAA Technical Report NMFS CIRC-371, April, 1973. [46] Tint;, R, Y. "Cultural Potential of Spiny Lobster (Panu lirus argus Larreille)," Ecosystems Department, Battelle Northwest Laboratories, Richland, Washington, 1.973. [47] Turvey, Ralph. "Optimization and Suboptimization in Fishery Regulation, 11 The American Econ omic Revie w. Vol. LIV, No. 2, Part L, March, 1964, pp. 64-76. [48] U.S. Department of Commerce (Formerly Bureau of Commercial Fisheries), NOAA, NMFS. "Basic Economic Indicators: American and Spiny Lobsters," U.S. Government Printing Office, Current Fisheries Statistics No. 627, Washington, D.C.: August, 1974.

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163 [49] • Fishery S tatistics of the United States , Washington, D.C.: U.S. Government Printing Office, Annual Issues, 1952-72. [50] . Florida Landings , Washington, D.C.: U.S. Government Printing Office, Monthly and Annual Issues, 1971-73. [51] . Unpublished data from a survey of spiny lobster captains (Bruno Noetzel, Principle Investigator), Washington, D.C., 1974. [52] U.S. Department of Commerce (Formerly Eureau of Commercial Fisheries), NOAA, Ocean Survey Branch. Unpublished surface water temperature data obtained from a monthly national ocean survey. Rockville, Maryland, 1952-72. [5 3] Van Meir, L. N. "An Economic Analysis of Policy Alternatives for Managing the Georges Bank Haddock Fishery," BCF, DER, WF No. 21, May, 1969. [54] Williams, Joel S. and F. J. Prochaska. "The Florida Spiny Lobster Fishery: Landings, Prices, and Resource Productivity," Florida Sea Grant Program, Report No. 12, Gainesville, Florida, February. 1976.

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BIOGRAPHICAL SKETCH Joel Sylvan Williams, the son of Joe and Ann Williams, was born July 29, 1947 in Houston, Texas. The major portion of his life was spent in a small rural community located in the southern portion of Louisiana, commonly referred to as "cajun country." After graduating from Hessmer High School, Hessmer, Louisiana, in May 1965, he entered Louisiana State University located in Baton Rouge, Louisiana. There he received a Bachelor of Science degree in Agricultural Business in August, 1969. He then entered the Graduate School of Purdue University as a graduate research assistant and received his Master of Science degree in Agricultural Economics in January 1972. In September 1971 he enrolled in the Graduate School of the University of Florida, Gainesville, Florida. As a graduate research assistant, in the Food and Resource Economics Department he pursued the degree of Doctor of Philosophy. In March, 1975 he was employed by Virginia Polytechnic Institute and State University as an assistant professor in the Department of Agricultural Economics. Joel Sylvan Williams is married to the former Susan Emily Tate, a cajun queen from Big Mamou, Louisiana. He is a member of Omicron Delt. Kappa, Gamma Sigma Delta, Omicron Delta Epsilon, and the American and Southern Agricultural Economics Associations. 164

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. >ka, Chairman Associate Professor of Food and Resource Economics 1 certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ) / /!/ ././, i/u^^'l^ W. W. McPherson Professor of Food and Resource Economies 1 certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. (mes Heaney ' / 'Associate Professor oJl Environmental Engineer ing

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ^Wmes C. Cato Assistant Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. if '7tu/ fi Gary D. IJynne / Assistant Professor* of Food and Resource Economics This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 1976 D&ixj, College of Agriculture Dean, Graduate School


39
Table 1. Industry harvest function variables in theoretical model
and reduced form, economic study of Florida spiny lobster
Industry
Variable Variable
In Theoretical Model In Reduced Form
Notation
Definition
Notation
Definition
Y
BE
bioeconomic yield
Q
total industry
landings
El
land (area of fishing)

e2
labor
Xi
traps per firm
e3
capital
x2
number of firms
e4
management
Xi
traps per firm
Si
population of mature
progeny

S2
parent population

S3
environmental attributes
X3
surface water
temperature
to decline with additional fishing effort. In addition, the reciprocal
function exhibits diminishing marginal returns which is consistent with
the stage, of production in which firms are expected to operate. The
industry harvest yield function can be expressed in reciprocal form as
A A
~ .. 3\ 32
Q = a 3 3X3 (14)
1 *2
The industry harvest function is used to determine an estimate of
maximum sustainable yield (MSY) to serve as a guideline in developing
management programs. Since the reciprocal function only approaches a
maximum, the MSY analysis considers "approximate" or "practical" maxima.
These maxima are estimated using various combinations of explanatory


47
and the solution of Q was equal to MEY with respect to X2 for a given
level of Xj, X2, and X3, expressed as follows:
62
MEY = Q = a + H ~ + B3X3 (18)
xi X2
Thus, traps per firm, estimated from the firm analysis was used as the
constant exogenous variable to characterize firms in the industry har
vest function model. Ordinarily least squares regression techniques
were used to estimate the parameters.
Study Area and Data Acquisition
The Florida spiny lobster fishery primarily consists of the area
known as the Florida Keys region. This region is made up of two coun
ties (Dade and Monroe) and is located in the southernmost portion of
the state. Spiny lobsters are landed in small amounts in other coun
ties, mostly Pinellas, but these are usually caught in foreign waters.
Monroe Count}7 was selected for the study area for several reasons.
A trend analysis of the Florida spiny lobster fishery was conducted us
ing secondary data for 1952-71 (Williams and Prochaska [54]). From this
analysis the Florida landings were estimated to be approximately 95 per
cent of total .S. landings in recent years. Approximately 50-60 percent
in the last five years of Florida landings were caught in foreign waters
(Appendix E). The majority (over 90 percent of these foreign lobsters)
were landed in Dade County. Of tbe remaining 40-50 percent of total
Florida landings (which came from domestic, waters) approximately 80-90
percent were landed in Monroe County (Appendix F). Monroe County is
geographically located in tbe middle of the domestic spiny lobster
fishery (Figure 6). A final consideration is that the impact of confining


139
Finally, a breakeven criterion was developed to help the fisherman
decide whether he should fish under the harvest rebate program, or elect
not to fish and receive a rebate payment. The criterion was in terms of
the minimum pounds per trap necessary to maintain a profit level equal
to or greater than the profit level without the program. The conclusion
was that a firm must harvest an average of 16.90 pounds per trap (assum
ing 328 firms, each fishing 429 traps) to 28.49 pounds per trap (assum
ing 156 firms, each fishing 800 traps) before it would be economically
feasible to purchase a license to fish. Thus, fishermen participating
in the program would operate with considerable flexibility, firm and
industry profits would be equal to or greater than would be the case
without the program, and the program would be totally self-supporting.


128
Table 18. Median and mean spiny lobster landings per trap for sample
of firms classified according to number of traps per firm
(Xj). economic study of Florida spiny lobster industry
Landings
Number of
traps fished per
firm
per trap
<200
200-399
400-499
500-599
600-699
700-899
>900
Total
Median
21.80
22.67
17.07
24.10
26.28
19.33
16.32
21.43
Mean
26.02
22.92
27.45
24.10
22.54
19.26
16.93
21.37
Observations 3
4
3
2
C
.)
5
3
25
breakeven estimates (BEC) as illustrated in Table 19. Estimated land
ings per trap (Q/Xj) were derived by dividing the total number of firms
in the industry after the harvest rebate program into estimated landings
after the program. Since the breakeven criterion of landings per trap
was below the estimated actual landings per trap the firm would have
some flexibility in its decision on whether to fish or not.
BEC ranged from 16.09 pounds per trap for 429 traps per firm to
28.17 pounds per trap for 1,000 traps per firm. The figures in paren
theses (Table 19) represent BEC after adjustments in the license fee
were made to compensate for deficit program costs illustrated in Table
17 (parentheses in Column 11). Estimated landings per trap ranged from
35.02 to 42.54 pounds per trap, thus resulting in a range of 54 to 21
Q/Xj can be represented notationally as
o/x Qa
Q/Xl 0S*KXi7
where,
Q/Xi = estimated average landings per trap,
Q = estimated landings with harvest rebate program
(Column 4, Table 17),
X2 = maximum number of firms required to harvest Q ,
given Xi (Column 2, Table 17), A
Xj assumed number of traps per firm (Column 1, Table 17).


TABLE OF CONTENTS (continued)
CHAPTER
VI Discrete Analysis of Alternative Combinations
of Firms and Traps Per Firm 94
Alternative Number of Firms in the Industry .... 94
Alternative Levels of Traps Per Firm 97
Evaluation of Estimates ..... 97
Isoquant Analysis 99
Movement Along An Isoquant 101
Ridgelines 105
Summary of Management Tools 106
Analysis of Traditional Management Programs 106
Licensing Traps 107
Licensing Firms ............ 110
Landing Quotas 113
A Suggested Alternative: Harvest Rebate Program . 115
Configuration of the Harvest Rebate Program .... 116
Hypothetical Example and Analysis of
Harvest Rebate Program 120
Assumptions 121
Number of traps per firm at 700 ........ 122
Number of traps per firm at 618 and 500 .... 123
Number of traps per firm ar. 429 125
Number of traps per firm at 350 and 200 .... 125
Overall summary of analysis (Table 17) 125
Breakeven Criterion 126
VII SUMMARY AND CONCLUSIONS 131
vi


LIST OF TABLES
Table
1
2
3
4
5
6
Industry harvest function variables in theoretical
model and reduced form, economic study of Florida
spiny lobster industry
Stratified population of boats and vessels, defined
as firms, economic study of Florida spiny lobster
industry
Stratified sample of boats and vessels, defined as
firms, economic study of Florida spiny lobster
industry
Estimated levels of maximum landings (Q) for given
levels of traps per firm (X^), number of firms (X),
and seasonal water temperature (X3), economic study
of Florida spiny lobster industry
Regression statistics for the cross-sectional firm
harvest function model, economic study of Florida
spiny lobster industry
Page
39
51
51
60
70
Marginal products for various lengths of set periods,
economic study of Florida spiny lobster fishery
7
8
9
10
Weekly landings expected for given dates within the
spiny lobster season, economic study of Florida spiny
lobster industry
Marginal products of craft size (X4) for sample sizes
observed, economic study of Florida spiny lobster
industry
Optimum levels of trap usage per firm and resulting
levels of profits, total revenue, total cost, and
landings given trap cost, economic study of Florida
spiny lobster industry
Optimum levels of adjustment factors (X2, X3, and X4)
resulting levels of profits, total revenue, total cost,
and landings per firm, economic study cf Florida spiny
lobster industry
vi i i


AN ECONOMIC ANALYSIS OF ALTERNATIVE
MANAGEMENT STRATEGIES FOR THE SPINY LOBSTER INDUSTRY
JOEL
SYLVAN WILLIAMS
A DISSERTATION PRESENTED TO THE GRADUATE
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
DEGREE OF DOCTOR OF PHILOSOPHY
COUNCIL
FOP THE
UNIVERSITY OF FLORIDA
1976

ACKNOWLEDGMENTS
My debt of gratitude for assistance during my graduate career
exceeds my ability to provide acknowledgment. I trust that my many
unrecognized benefactors will assume my great appreciation and thanks.
The greatest debt should be acknowledged first. Mine is to my
wifas Susan, for her moral support, understanding, and patience.
Fred Prochaska served as Chairman of my Supervisory Committee,
academic and professional advisor, and friend. Joe Havlicek provided
substantial guidance during stages of the final draft. W. W. McPherson
provided a wellspring of experience from which I have freely drawn as a
student and as author of this dissertation. Jim Cato provided compre
hensive critique that greatly improved the overall quality of the final
draft. Jim Heaney and Gary Lynne also provided constructive criticism
of the study. For tnese contributions, as well as many left unmentioned,
I am grateful and wish to thank the members of my Supervisory Committee.
I wish to thank Leo Polopolus, Chairman of the Food and Resource
Economics Department of the University of Florida, for providing finan
cial assistance during my graduate career. In addition, I wish to
extend my appreciation tc Lloyd Johnson and Pete Maley of NMFS and to
members of the Summerland Key Chapter of O.F.F. for their contributions
during the survey of spiny lobster captains.
I am else Indebted to Ms. Sandy Waters end Ms. Carolyn Aloeter for
their indispensablehelp in the voluminous typing task and numerous

clerical activities performed during this study. Ms. Jennie Lou Carroll
arduously accomplished the transformation of this dissertation from a
longhand manuscript into its present form. For this feat she has earned
my gratitude and admiration for her considerable ability and perseverance.
Jii

TABLE OF CONTENTS
ACKNOWLEDGMENTS H
LIST OF TABLES viii
LIST OF FIGURES xi
ABSTRACT xii
CHAPTER
I INTRODUCTION
Objectives
Scope
II LITERATURE REVIEW
Introduction .
Spiny Lobster Research ....
General Bioeconomic Management Research
Bioeconomic Lobster Research
Regulatory Management Programs for Florida
Spiny Lobster
Ill THEORETICAL MODEL
Biological Theory of a Fishery
Traditional Economic Production Model .
Bioeconomic Model
Summary ......
6
7
9
9
9
14
18
20
24
30
32
35
iv

TABLE OF CONTENTS (continued)
CHAPTER
IVEMPIRICAL MODEL AND DATA 36
Definitions 36
Bioeconomic Analysis 37
Firm Analysis 41
Maximum Economic Analysis (MEY) 45
Study Area and Data Acquisition 47
Sample Selection and Size 49
Survey Technique 33
VANALYSIS OF RESULTS 54
Bioeconomic Model 54
Maximum Sustainable Yield (MSY) Estimate 59
Value Marginal Product Analysis 62
Analysis of Firm Harvest Function Model 67
Firm Harvest Model 67
Estimated Parameters 71
Traps per firm? (x^) 72
Rounds per week (X2) 73
Weeks fished per season (X3) 75
Craft size (xt,) 78
Optimum Resource Allocation of the Firm ...... 80
VITHE MANAGEMENT MODEL 87
Maximum Economic Yield for the Industry 87
Evaluating MEY 89
Policy implications ?3
V

TABLE OF CONTENTS (continued)
CHAPTER
VI Discrete Analysis of Alternative Combinations
of Firms and Traps Per Firm 94
Alternative Number of Firms in the Industry .... 94
Alternative Levels of Traps Per Firm 97
Evaluation of Estimates ..... 97
Isoquant Analysis 99
Movement Along An Isoquant 101
Ridgelines 105
Summary of Management Tools 106
Analysis of Traditional Management Programs 106
Licensing Traps 107
Licensing Firms ............ 110
Landing Quotas 113
A Suggested Alternative: Harvest Rebate Program . 115
Configuration of the Harvest Rebate Program .... 116
Hypothetical Example and Analysis of
Harvest Rebate Program 120
Assumptions 121
Number of traps per firm at 700 ........ 122
Number of traps per firm at 618 and 500 .... 123
Number of traps per firm ar. 429 125
Number of traps per firm at 350 and 200 .... 125
Overall summary of analysis (Table 17) 125
Breakeven Criterion 126
VII SUMMARY AND CONCLUSIONS 131
vi

TABLE 0? CONTENTS (continued)
APPENDIX
A Spiny lobster landings and dollar value, Florida and
U.S., 1952-73, economic study of Florida spiny lobster
Industry 141
B Spiny lobster capital and labor inputs, Florida west
coast, 1952-72, economic study of Florida spiny lobster
industry 142
C Input/Output. relationships, Florida west coast., 1952-72,
economic study of Florida spiny lobster industry 143
D Cross-sectional Data Computations 144
E Spiny lobster landings and dollar values, Florida east
and west coasts, and Monroe County, 1952-73, economic
study of Florida spiny lobster industry 146
F Spiny lobster landings in Florida ports caught in
foreign waters, 1964-73, economic study of Florida
spiny lobster industry 147
G Total product and marginal product equations for firm
harvest function model ^ . 148
II Comparison of spiny lobster production practices by
craft length for firms sampled, Florida Keys, 1963-74
season, economic study of Florida spiny lobster
industry 149
I Table 18 computations 150
J Spiny Lobster Firm Survey Questionnaire 152
K Spiny lobster inputs, outputs, and values, Monroe
County, Florida, .1963-73, economic study of Florida
spiny lobster industry 157
L Data used to estimate firm harvest function, 1973-74
survey of spiny lobster captains, economic study of
Florida spiny lobster industry 158
REFERENCES 3 59
BIOGRAPHICAL SKETCH
164

LIST OF TABLES
Table
1
2
3
4
5
6
Industry harvest function variables in theoretical
model and reduced form, economic study of Florida
spiny lobster industry
Stratified population of boats and vessels, defined
as firms, economic study of Florida spiny lobster
industry
Stratified sample of boats and vessels, defined as
firms, economic study of Florida spiny lobster
industry
Estimated levels of maximum landings (Q) for given
levels of traps per firm (X^), number of firms (X),
and seasonal water temperature (X3), economic study
of Florida spiny lobster industry
Regression statistics for the cross-sectional firm
harvest function model, economic study of Florida
spiny lobster industry
Page
39
51
51
60
70
Marginal products for various lengths of set periods,
economic study of Florida spiny lobster fishery
7
8
9
10
Weekly landings expected for given dates within the
spiny lobster season, economic study of Florida spiny
lobster industry
Marginal products of craft size (X4) for sample sizes
observed, economic study of Florida spiny lobster
industry
Optimum levels of trap usage per firm and resulting
levels of profits, total revenue, total cost, and
landings given trap cost, economic study of Florida
spiny lobster industry
Optimum levels of adjustment factors (X2, X3, and X4)
resulting levels of profits, total revenue, total cost,
and landings per firm, economic study cf Florida spiny
lobster industry
vi i i

LIST OF TABLES (continued)
Table
11
12
13
14
15
16
17
13
Maximum number of firms (X2*), landings, revenues,
and costs for industry profit maximization given
desired management levels of traps per firm (Xj),
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of firms
(X2) assuming traps per firm (X^) equals 700, mean
seasonal water temperature (X3) equals 77.591F,
and ex-vessel price per pound (Py) equals $1.08,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of traps
per firm (Xq) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals
77.591F, and ex-vessel price per pound (Py) equals
$1.08, economic study of Florida spiny lobster
industry
Marginal rate of technical substitutions (MRTS^ ^ )
of traps per firm (X^) for number of firms 1 2
(Xi) holding traps per firm constant at 700,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of traps
per firm (X][) assuming number of firms (X2) equals
400, mean seasonal water temperature (X3) equals
77.591F, ex-vessel price per pound (Py) equals
$1.08, and trap license fee equals $1.00 per trap,
economic study of Florida spiny lobster industry
Analysis of alternative levels for number of firms
(X2) assuming traps per firm (X]) equals 700, mean
seasonal water temperature (X3) equals 77.591F, ex
vessel price per pound equals $1.08, and license fee
per firm equals $1,000, economic study of Florida
spiny lobster industry
Page
92
96
98
103
108
111
Median and mean spiny lobster landings per trap for
sample of firms classified according to number of
traps per firm (Xj), economic study of Florida
spiny lobster industry 117
Median and mean spiny lobster landings per trap for
sample of firms classified according to number of
traps per firm (X¡), economic study of Florida spiny
lobster industry 128
ix

LIST OF TABLES (continued)
Table
19
Page
Analysis of landings per trap required to breakeven
under the harvest rebate program for alternative
levels of traps per firm (X^), economic study of
Florida spiny lobster industry 129
x

1
2
3
4
5
6
7
8
9
10
11
12
13
LIST OF FIGURES
Growth curve for a fishery stock
Page
26
Number of mature progeny as a function of parent
population levels
Equilibrium harvest as a function of parent population
Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to landings
Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between industry
total revenue (TR) and industry total cost (TC) with
respect to number of firms
The Florida spiny lobster fishery
Observed and predicted volume of spiny lobster
landings, 1963-73 for Monroe County, Florida 56
Spiny lobster bioeconomic industry harvest function 61
Value marginal product of traps per firm (Xj) divided
by the maximum number of firms observed (399) in the
industry in 1973 64
Value marginal product of firms (X2) 66
Firm harvest functions with respect to effort measured
as gear (X3), fishing intensity (X?, X3), firm size (X4),
and adjusted for fishing grounds (X5, Xg) 69
Marginal product curve for spiny lobster craft size
(HP ) 80
x4
Spiny lobster harvest isoquants and ridge lines defining
expansion paths where returns equal total costs, (assum
ing ex-vessel price per pound (P) equals $1.08, industry
total cost equals $1,876 plus $11.55 per trap per firm '
(X¡), and mean seasonal water temperature (X3) equals
77.591F)
xi
102

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
AN ECONOMIC ANALYSIS OF ALTERNATIVE MANAGEMENT STRATEGIES FOR
THE SPINY LOBSTER INDUSTRY
by
Joel Sylvan Williams
December, 1976
Chairman: Fred J. Prochaska
Major Department: Food and Resource Economics
Florida's spiny lobster fishery has achieved tremendous growth in
landings during the past two decades. However, the growth of inputs
into the fishery has lately increased at a considerably higher rate,
resulting in declining catch rates, over investment and a potential
for over exploitation of the spiny lobster stock.
This dissertation was designed to evaluate the current level of
resource use, determine the maximum sustainable and economic yield
levels, and analyse alternative lobster management programs. Bio-
economic and firm harvest analytical models were developed and esti
mated. Maximum sustainable yield was estimated to be approximately
seven million pounds while maximum economic yield was estimated to be
5.8 million pounds annually, slightly above current levels. Optimum
levels cf input use are 215 lobster firms each fishing 795 traps.
Ihese levels require a 47 percent reduction in the number of firms
in the industry with no redaction in number of traps fished.

Political and social considerations often make the maximum economic
yield not a feasible management alternative. In this case an analysis
of input (firm and trap) substitution was completed and presented for
alternative input and output levels. Resulting cost, revenue and pro
fit levels were determined for alternative program levels.
Specific management programs considered in the analysis include
licensing, quotas and a harvest rebate program. For each program,
maximum yield levels, costs, revenues and profits were determined. For
the harvest rebate program alternative levels of administrative costs
and related sources of revenue were analyzed.
xiii

CHAPTER I
INTRODUCTION
The Florida spiny lobster (Panulirus argus) is produced in the
warmer ocean waters and is easily distinguished from its northern, cold-
water cousin, the American lobster (Homarus americanusl by its lack of
claws and relatively smaller size. Over the past forty years the
Florida spiny lobster has developed from a casual food source of the
habitants of the Florida Keys to an important commercial food resource.
Second only to shrimp as a seafood, spiny lobster landings in Florida
exceeded 11 million pounds in 1973 with an estimated retail value of
ever AC million dollars. Over 1,100 licensed fishermen landed lobsters
in 1971. Florida represents approximately 98 percent of U.S. spiny
lobster landings (Appendix A). The Florida spiny lobster fishery is
experiencing an ever increasing number of problems that require imme
diate attention by the legislature, regulatory agencies, and researchers
One of the basic underlying forces creating problems within this
fishery is consumer demand given the relatively fixed supply of stock.
Spiny lobster is now a preferred item in seafood markets and restaurants
An increasing tendency for U.S. consumers to eat in restaurants has
created upward shifts in demand. The demand for spiny lobster is highly
income elastic but inelastic with respect to its own-price elasticity
of demand (Allen [1]). U.S. consumption currently accounts for approxi
mately SO percent of the world spiny lobster production. Canada and
1

2
Europe account for approximately 10 to 15 percent while the small amount
remaining is domestically consumed in the producing countries.
Between 50 to 60 countries produce and export spiny lobster tails
to the U.S. The top four spiny lobster producing countries are
Australia, Cuba, South Africa, and New Zealand. These countries produce
approximately 65 percent of world landings while fifth ranked U.S. pro
duces about 7 percent of the world total (U.S. Department of Commerce [43]).
Retail prices have increased substantially in recent years. In
1960 the retail price of spiny lobster tails was $1.50 per pound arid the
U.S. consumed 53 percent of the world production. By the 1970s U.S.
consumption increased to over 80 percent of the world production of
spiny lobsters. The 1970 retail price for spiny lobster tails was $3.43
per pound and reached $5.40 per pound in 1972. Currently, spiny lobster
tails are retailed for as high as $9.27 per pound.^ In roughly ten
years retail price doubled and has almost tripled in the. last five
years.
Rising retail prices have encouraged increased exploitation of
spiny lobster stocks. This has resulted in an increasing number of
biological and economic problems in the Florida spiny lobster fishery.
Soma of these problems could also be credited to the nature of this
industry or fishery. Unlike most economic enterprises the spiny lobster
fishery is a common property natural resource which is characterized by
unlimited entry. As such, the fishery generates excess use of inputs
to maximize catch without any economic incentive to conserve or replen
ish the resource for future use,
January 24, 1975, average retail price for three seafood retailers
in Gainesville, Florida.

3
The spiny lobster fishery is currently subject to some limited form
of fishing regulation. Conservation directed regulations presently pro
hibit stripping eggs from females, specify trap dimensions so small
undersized lobsters are released, close areas believed to be nursery
areas, and specify a season which protects recruitment.
An investigation of the possible excessive use of resources in the
industry gives reason for concern.'*' In the last 20 years the number of
firms, defined as the sum of vessels and boats, increased from 54 in
1952 to 394 in 1972 (Council of Economic Advisors [18], Bell [3]). Num
ber of vessels began increasing at an increasing rate around 1965.
Simultaneously capital and labor inputs began to increase. From 1965
to 1972 firm members increased over 80 percent. Use of other inputs
since 1965 also increased substantially: Number of traps by 242 percent
number of traps per firm by 60 percent; and number of fishermen by 101
percent (Appendix B, U.S. Department of Commerce [49], [50]).
Landings increased from 956,000 pounds in 1952 to over 5 million
pounds in 1972. However, since 1965 landings have increased only 4.4
million pounds or 16 percent. Pounds landed per trap averaged 213
pounds in 1952, 49 pounds in 1965, and 20 pounds in 1972. From 1965
to 1972 dollars generated per trap decreased from $28 to $21; annual
landings per firm decreased from 20,301 pounds to 13,069 pounds; and
Until 1975 approximately 50 percent of spiny lobster landings in
Florida were harvested from the Florida domestic fishery. The remaining
50 percent were harvested in foreign water fisheries, primarily the
Bahamian fishery. Approximately 10.0 percent of these landings were
reported as Florida "east coast" statistics.
In 1975 the Bahamian government closed its fishery to U.S. fisher
men. Due to this U.S. landings were down approximately 25 percent in
1975 compared to 1974 landings.

4
annual total revenue per firm increased 23 percent from $11,423 to
$14,003 (Appendix C).
During the 1952-72 period when total revenue increased at a de
creased rate, costs of inputs used in the fishery steadily increased
due to upward shifts in the demand for inputs. But, in recent years,
input costs skyrocketed primarily due to rapidly increasing inflation
which has been shown by changes in the consumer price index (CPI) for
major inputs used in this fishery (Barnhart [2]). The CPI (1967 base)
for petroleum products was 108.9 in 1972 and increased 109.5 points
between 1973 and 1974. For wood products, the CPI was 144.3 in 1972
and increased 11.8 points between 1973 and 1974. CPI representing
engines used in the fishery was 117.9 in 1972 and increased 31.0 points
from 1973 to 1974.
Information on costs of inputs and returns for the 1973-74. spiny
lobster season was acquired in a survey of captains of spiny lobster
boats and vessels/- In 1959 the average spiny lobster craft ranged from
fourteen-foot wooden skiffs that were either rowed or powered by an out
board motor, to larger wooden-hulled craft ranging in length from 26 to
36 feet and powered by 125 to 150 horsepower gasoline and diesel engines.
Average cost of the skiff began at $150 while average cost of the engine
and hull of larger craft ranged from $3,000 to $10,000. From the 1974
survey, average cost of only the engine was $8,257. This was based on a
range from $500 for a 40 h.p. outboard motor to an excess of $60,000 for
AThe survey of 25 captains was completed in October, 1974. The
random sample was stratified according to length of boat and area of
fishery with confidence levels of 90 percent. Individual strata were
weighted according to landings from these areas and size of boats in
these areas.

5
diesel engines approaching 500 h.p. Average cost of the hull for this
sample was $8,748. The range was from $400 for a sixteen-fooc fiber
glass skiff to over $20,000 for wooden and fiberglass vessels with a
maximum length of 55 feet.
In 1959 a wooden lath trap complete with buoy and line cost an
average of $6.00 each. In 1974 average cost of materials alone for a
wooden lath trap was $11.00. The cost was a few dollars more if the
trap was used for deep-water fishing. Average cost of fishheads used
for bait was 5 cents per pound in 1959 compared with 11 cents per pound
in 1973. The prime interest rate increased from approximately 6 percent
in 1959 to 9.5 percent in 1973 signaling a substantial increase in the
cost of capital.
Spiny lobster captains surveyed in 1974 claimed the costs of petro
leum based products, such as polyethlene rope, styrofoam buoys and fuel,
were triple 1973 prices. Engine costs were increasing at the rate of
15 to 25 percent per year. Fiberglass boats were increasing in cost at
similar rates. Because of the shortage of cypress lumber the cost of
cypress lath for trap construction was also increasing. In addition,
the introduction of sonar and other fish locating devices, hydraulic
pullers, and ot.her harvesting improvements, has substantially increased
the capital investment which the commercial lobster fisherman must make
to remain competitive. The increase in number of traps used per fisher
man represents a substantial increase in investment.
One problem that appears to exist in the fishery is a resource al
location problem . "over-investment" in capital (gear and craft) and
labor (fishermen). Too many inputs are employed to produce a relatively
fixed supply of spiny lobsters. This is reflected in the substantial


increases in inputs (traps, vessels, and gross tonnage) compared with
the increase in landings. The broad over-investment problem of the
fishery begins with the fishermen. Capital and labor investments in
crease at the fishermen's level due to (1) a struggle to overcome a
severe price-cost squeeze; and (2) interdependencies in the production
function creating negative externalities to the fishing firm or producer.
As a consequence of this increaseing level of effort, a second
problem of the fishery that may be occurring is one of "over-exploita
tion" of the fishery stock. Decreasing stock levels can cause serious
long-term damage to the fishery and welfare of fishermen.
Objectives
The overall problem is defined as one of resource allocation. The
general objective is focused upon the determination of an optimal allo
cation of resources for selected price, cost, and fishery management
alternatives. Optimal allocation may entail protecting the stock from
reaching a level beyond recovery as well as regulating economic factors
of the fishery.
The specific objectives are
(1) To identify the major factors affecting the quantity of
spiny lobster harvested, and to estimate the harvest
function of the Florida spiny lobster fishery;
(2) To evaluate the potential substitution between specific
resources used to harvest spiny lobster in Florida;
(3) To determine an optimal combination of inputs for the
Florida spiny lobster fishery; and

7
(4) To evaluate the impact of selected management programs
on resource allocation in the fishery and on the optimum
combination of inputs used by firms. Specific programs
considered are limiting licensing of firms and traps,
establishing landings quotas, and a harvest rebate program.
The results of this study will provide a basis for establishing
guidelines for managing the Florida spiny lobster fishery. The focus
is on the analysis of management strategies which might help reduce the
cost and difficulties of regulating effort. In addition, study results
can be conceivably viewed as a case study applicable, at least in ap
proach, to other marine resource allocation problems. Finally, individ
ual fishermen may use the results of the production analysis as a basis
for both long and short-run decision making.
Scope
Spiny lobsters landed in Florida are harvested from the domestic
Florida spiny lobster fishery and foreign water spiny lobster fisheries
More than 95 percent of spiny lobster landings harvested from the domes
tic fishery are landed in Monroe County. These landings comprise ap
proximately 50 percent or more in past years of all spiny lobster
landed in Florida. Without the Bahamian fishery, landings from Monroe
County make up over 90 percent of U.S. spiny lobster landings. Conse
quently, although the scope of this study is defined as the Florida
spiny lobster fishery, the data for the empirical analysis are delin
eated as that of the Florida Keys or Monroe County, Florida.
The majority (approximately 90%) of foreign water landings were
lost as a result of the 1975 closing of the Bahamian fishery.

8
A literature review of theoretical and/or applied bioeconomic re
search is presented in the next chapter. The theoretical model is
presented in Chapter III while the data and empirical model are presented
in Chapter IV. Results of the analyses and their practical interpreta
tion are given in Chapter V. Four management alternatives and resulting
policy implications are reviewed in Chapter VI. Chapter VII, the final
chapter, includes a summary, conclusions, and suggestions for further
research.

CHAPTER II
LITERATURE REVIEW
Introduction
Previous empirical spiny lobster (Panulirus argus) research is
summarized and some major theoretical and empirical bioeconoxnic manage
ment studies are capsuled in this chapter. This information is the
minimum necessary to understand biological and psychological relation
ships considered in the design of management programs. Furthermore,
existing laws must be understood before alternative programs can be
considered and thus they are reviewed in this chapter. None of the
empirical bioeconomic studies consider the spiny lobster fishery, but
they do include analyses of management strategies which may be appli
cable to the spiny lobster fishery. Severa] recent bioeconomic studies
such as Eromley [8], Fullenbaum [26], and Van Meir [53] contain extensive
and thorough reviews of past theoretical and empirical studies. This
chapter contains a review of selected theoretical concepts and empirical
studies directly applicable to this study. The reader is referred to
the more extensive reviews where appropriate.
Spiny Lobster Research
There is a lack of economic analysis concerned with management of
the spiny lobster (Panulirus argus). Several empirical studies deal
primarily with biological characteristics, environmental conditions
and physical production analysis of fishing craft, gear, and techniques.
9

10
Scientific research in the U.S. on spiny lobster began as early as 1916
(Allen [1] Barnhart [2], and Crawford [19]), but it was not until 1944
that an investigation of the Florida spiny lobster fishery was conducted
by the Marine Laboratory at the University of Miami (Smith [42, 43]).
A review of studies since 1948 provides considerable information that
may be useful in explaining the behavior of landings (Smith [42, 43],
Cope [17], 3utler and Pease [9], Dees [22], Cnislett and Yesaki [15],
and Ting [46]).
Smith's publication in 1958 [43] provides a most complete discus
sion of the Florida spiny lobster fishery including taxonomy, biological
cultivation, fishing gear and methods, dollar value and importance of
the fishery, and state regulations of the fishery. Several other stud
ies published since 1958, including Butler and Pease [9], Chislett and
Yesaki [15], Cope [17], and Ting [46], updated some of Smith's findings.
Butler and Pease [9], and Chislett and Yesaki [15] determined the
feasibility of developing spiny lobster fisheries off coasts of Panama
and Jamaica, respectively. Although they primarily compared types of
gear and fishing techniques, some biological and environmental observa
tions were documented. Cope [17] analyzed alternative gear and fishing
techniques in the Florida fishery. Finally, a recent study by Ting [46]
analyzed the potential for spiny lobster cultivation from a physical
production standpoint but alluded to economic implications. The infor
mation obtained from these studies is briefly summarized.
The Florida spiny lobster (Panulirus arqus) is one of 30 species
distributed nearly world wide in tropical and sub-tropical waters.
They differ from the Northern cold-water lobster (Homardie family) in
that they lack claws and have long antennae for sensing food and danger.

11
They are smaller and have numerous spines covering their back (cape) for
protection against many natural enemies. The average legal size landed
in Florida weighs approximately one and a quarter pounds and is 10
inches long, although in 1968 maximum lengths of 17 inches and weights
in excess of 10 pounds were not infrequent (Dees [22]).
Spiny lobsters generally feed at night on a wide variety of foods,
primarily small crustaceans. They also forage. During the day they
hide in rocks, coral, and other marine, growth but are known to resort to
cannibalism when crowded. Growth is primarily dependent upon the en
vironment. As body weight of the spiny lobster increases the hard outer
shell is shedded. This shedding of the shell is called molting and
occurs several times throughout the life cycle. The body weight in
creases approximately 5 percent during each molting stage. Although
younger lobsters molt more frequently, it takes approximately five
years for them to reach legal size.
Female spiny lobsters do not begin reproducing until they reach a
length of eight to nine inches. An eight-inch spiny lobster can produce
approximately 50,000 eggs compared with 500,000 eggs produced by a 14-
inch lobster. In Florida, mating occurs February through June in shal
low waters. The eggs are hatched in deeper W3ter three weeks later. It
takes the young larvae three to six months to conform to the shape of
the adult lobster. At this stage the young lobster drops to the ocean
floor and is approximately 7/8 inch long. The mortality rate from
hatching to this stage is hypothesized to he over 99 percent.
Water temperature, food supply, reproduction and weather influence
the migration of spiny lobsters. Usually migration occurs between deep
and shallow water but sometimes migration is north in the summer and

12
south in the winter. Extremely cold weather, extended periods of un
seasonable weather, or still, calm weather can cause lobsters to migrate
to deeper water (Smith [43]). This is contrary to the findings of
Butler and Pease [9] that spiny lobsters prefer placid waters. Smith
[43] also reported that spiny lobsters are believed to have migrated
over 1,000 miles but generally do not migrate over five miles.
No evidence is available to indicate whether they migrate over deep
straits, but it is believed that long movements lead to a gradual mixing
which, over time, results in an equalization of the stock. Consequently,
the biological stock of a geographical area, characterized by a deep
water perimeter, should be treated as a single unit. As such, changes in
any part of che fishery will eventually affect the whole fishery. Con
versely, as part of the fishery becomes "fished out" it will replenish
Itself if left alone for a period of time. Some evidence suggest that
maximum exploitation of most spiny lobster stocks in the Caribbean have
been reached, with the possible exception of the southern edge of the
Caribbean Sea (Idyll [31]).
The major portion of commercial lobster landings in Florida are
harvested at depths of less than 50 feet using wooden traps. At least
80 percent of annual landings are harvested in the first half of the
season which lasts from August 1 through March 31. Generally, one to
three fishermen per craft fish 200 to 1,000 traps. Length of the craft
range from 16 to 55 feet. They usually travel less than 25 miles and
return the same day. Based on the theory that a trap offers protection
it can be fished without bait. However, freshly baited traps are pre
ferred- There appears to be no difference in landings between traps
baited with cowhide, which lasts longer, and traps baited with fish.

13
New traps catch better after being in the water at least five days.
Landings are higher if traps are lifted every two to three days rather
than over four days. Traps settling on the bottom collect silt and
foreign matter, which past experiences indicate reduce landings if the
exterior of the trap is not brushed every few days. Landings are higher
for traps set next to reefs or forage areas than for traps set on reefs
and in flat clean areas.
Butler and Pease [9] found that bottom temperature and salinity
were correlated with the presence of lobsters. In a range of 68-85F
more lobsters were landed than in higher bottom temperatures of the
83-85F range. Also in a total salinity range of 28-34/00 landings
were higher than at the 31-32/00 salinity level. Lobsters will not
feed when water temperatures are near freezing and will migrate from
locations with colder water temperatures to warmer water locations. A
study on surface and subsurface water temperature shows that the major
ity of the fishing area in the Florida spiny lobster fishery is iso
thermal year round (Robinson [39]). This means that in depths of less
than 50 feet the difference in the bottom temperature and surface
temperature is insignificant.
Aquaculture of spiny lobster is possible but currently not economi
cally feasible because they require very exacting care and specialized
conditions (Ting [46]). Spiny lobsters require clean, oxygenated water
with a balanced temperature and the individual lobsters kept separated.
To accomplish this requires a large volume of space and labor and thus
a large capital investment. The growth period from juvenile to market
able size is approximately three years in an artifically created envi
ronment, compared with five to seven years in the natural environment.

14
General Biceconomic Management Research
Researchers have been contemplating bioeconomic management of the
fisheries at least as far back as the 1920's as evidenced by Rich's [38]
work on the Gulf of Maine fishing grounds in 1929 and Russell's [40]
work in 1931 titled "Some Theoretical Considerations on the 'Over
fishing' Problem." In 1943, Herrington [29] considered alternative
methods of fishing management and Nesbitt [34] investigated the biologi
cal and economic problems in management of fisheries.
Major theoretical contributions emerged in the early 1950's in the
writings of Schaefer [41], Gordon [28], Christy and Scott [16], Crutch
field and Zellner [21], and Turvey [47]. These antecedents of the past
twenty years are generally credited with developing the fundamental bio-
economic theory. Their differences can be briefly analyzed on the basis
of four management objectives. Schaefer's biological approach was con
cerned with maximizing production from the sea in a strictly physical
production framework. The others were oriented toward the maximum eco
nomic yield concept but differed to a slight degree. Gordon, and
Scott and Christy actually defined a monopoly situation as optimum with
an objective of maximum economic yield above costs. Crutchfield and
Zellner's approach was the same but excluded returns due to monopolistic
practices in order to maintain consistency with federal regulations on
monopolies. Turvey also maximized economic yield excluding returns to
monopolistic practices but, in addition, attempted to maximize consumer
surplus,
More recent research deals with the empirical application of the
above concepts and with some refinements to the theory. Lampe [32]
used a dynamic model of the Cobweb form to investigate the interrela-

lb
tionships between biological arid economic aspects of commercial fisher
ies. Carlson [11, 12] developed a theoretical yield function by inte
grating an economic production function with a biological growth model
and distinguished between firm and industry or aggregate production
functions. Van Mair [53] demonstrated that landings will exceed maximum
sustainable yield (MSY) as a result of excess effort generated in a
competitive economic system such as the George's bank haddock fishery.
To curtail effort at MSY he suggested free entry with landings quotas,
monopolistic exploitation implying the maximization of net revenue above
labor and capital cost, or quotas placed on fishing effort. A problem
inherent in all of these alternatives is defining a unit of effort.
Smith [44] developed a dynamic competitive model of the interaction
between the number of firms (investment) in a fishery and the population
of ar; exploited fish species, which included crowding externalities.
Bell's [3, 4, 5, 6] empirical research dealt primarily with
firm analysis and illustrates the use of econometric techniques in
marine research. He attempted to determine what factors influence the
rate of return and what impact their variability has on the industry.
A major criticism of his findings is that the estimates will not with
stand rigorous statistical tests primarily because of model misspecifi-
cation and lack of a randomly selected sample.
After an extensive review of literature the major revelation can
best be explained by a quote from the concluding statement of the ab
stract of a dissertation written in 1965 (Bromley [8, p. 36]) "The
presence of considerable uncertainty In a fishery, and the lack of per
fect knowledge on the part of biologists and economists, renders in sweep
ing conclusions of traditional writers in fishery, and their subsequent

16
policy recommendations, particulary vulnerable to incrudelity." Since
the time of this statement considerable documentation of theoretical and
empirical marine research has accumulated, yet one has to agree that the
quoted statement can still carry conviction today. This is not to imply
that the research is not useful, but rather that a need still exists for
data, authenticated tools, and methodologies for research applicable to
the bioeconomic management of today's marine resources. Many of the
works to date develop interesting statistical investigations while
others hinge on highly abstract optimization criteria.
The major reason that the success achieved in traditional agricul
tural research, particularly in estimating production functions, has not
been achieved in marine economics research is partly due to basic under
lying problems that have yet to be solved in analyzing marine resources.
These problems relate to the techniques, assumptions, and empirical
limitations (i.e., lack of biological, environmental and economic data)
and are characteristic of the common property nature of bioeconomic re
sources. The very few exceptions to this lack of success have occurred
with species existing in what may be termed "closed systems," in which
the researcher had considerable control over the individual variables.
Very often the problems are related to inadequate specification of the
theoretical bioeconomic structure of the fishery, lack of appropriate
biological and economic data, lack of multidisciplinary research
cooperation in designing models oriented towards a systems approach,
misunderstanding the needs of counterparts in a multidisciplinary team,
and often defining objectives dissonant to the researchers or policy
makers.

17
This is evidenced in a recent publication edited by Sokolosk.i [A5J
in which several researchers addressed the issues and problems encoun
tered when dealing with research directed toward managing marine re
sources. Sokoloski defined a critical area of marine resources research
to be the measurement of the gap between the "optimum" management solu
tion for a given fishery and current management arrangements. To empha
size the relative lack of success with this objective, he listed several
critical issues that have been complicating current research efforts.
They were characterized as empirical and conceptual in nature and multi
disciplinary in scope. One conclusion drawn after reviewing this publi
cation is the fact that substantial uncertainty exists with respect to
the reliability of results in marine economics research and accordingly
the proposed management programs. Many of these problems need to be
solved before sound management programs can be developed for many of the
species. Determination of optimal solutions will require considerable
time, effort, and financial resources.
Pontecorvo [35] pointed out in his work with Pacific red salmon
that the costs of improving information may exceed the benefits. This
should be taken into account when deciding the value of increasing the
sophistication of models designed for direct applicability in managing
a particular fishery. Consequently, when a researcher is given the task
of developing management alternatives for a currently existing real
problem as in the case of the Florida spiny lobster fishery, he is often
not allowed the luxury of exhausting all methodological possibilities in
his investigation due to the reasons previously discussed. Because of
this he uses what resources are available, such as traditionally accept
able or validated theories in economics and marine biology. For

18
example, such resources include production functions exhibiting diminish
ing marginal rates of return, downward sloping demand for a commodity,
and the bio-mass or population of a fish species which is in part depend
ent upon its environment and thus exhibiting a semi-sphere-shaped yield
curve.
Given lack of data, particularly biological data, and lack of pre
cise models which lend themselves to rigorous statistical testing, it
would appear that a reasonable criterion for model building would be
"Occum's razor," the simpler the better. This may not be too unrea
sonable since statistical testing may be more efficient, the results are
timely, completion of the project remains within the limits of the
budget, and it is questionable whether more sophisticated models requir
ing more resources would improve the results. In light of these obser
vations, the approach for this project presented in the next chapter
does not attempt to improve the theory or apply overly-sophisticated
empirical models or models requiring inapplicable assumptions or data
which are not available.
Bloeconomic Lobster Research
Bioeconomic research related to the Northern American Lobster
fishery, Bell, 1970 [3]; Bell and Fullenbaum, 1972 [7]; Dow, Bell
and Harriman, 1973 [24]; Huq, 1973 [30]; and DeWolf, 1974 [23] were
considered in the development of the present models. The latter two
publications by Bell are extensions of his early work on the American
lobster industry. All three of Bell's publications analyze impacts
of different types of management programs through changes in a general
equilibrium model. In Bell's first publication [3], a linearly

19
additive structural production function is specified as an average pro
duct function. From the estimation a simple parabolic yield function
was derived. Number of traps was the measure of a unit of effort.
Bell and Fulienbaum [7] developed a production function which was de
rived from an integration of a logistic growth function, an industry
production function and an industry revenue relationship. The model
includes a biomass variable over time, environmental constraints, total
industry cost, a technology variable and other parameters to be esti
mated, such as catching power of a unit of effort. Variables for which
data are lacking are either assumed away or are assumed to be represented
by some proxy and ultimately the whole model collapses into a simple
second degree polynomial equation presented in Bell's earlier publica
tions, The model appears to be considering all the necessary components
of a total bioeconomic system when, in fact, Bell does not have direct
measures of all independent variables in his first model. Dow, Bell,
and Harriman [24] utilized this model and incorporated undated data for
the bioeconomic model and some biological information on the Northern
American lobster such as history, migration, disease, etc.
Huq [30] analyzed labor mobility and social transfer costs of three
representative lobster fishing communities in Maine. Huq concluded that
substantial immobility and limited employment opportunities exist in the
fishery and thus the human element must be seriously considered in de
signing ary management program.
Finally, DeWolf [23] investigated Canada's lobster fishery. Bio
logical and economic bases of fishery regulations were examined. Also
examined were the economic effects of regulations on the fishery, such
as total industry value, total landings, and net return per fisherman.

20
No quantitative statistical model was used and efficiency (net returns)
was the criterion for evaluation. The conclusions were that previous
regulations of limiting effort have led to economic inefficiencies but
that economic conditions outside the fishery have had an even greater
impact on its present structure.
Regulatory Management Programs
For Florida Spiny Lobster:
Florida laws are designed to regulate the spiny lobster fishing
industry for the purposes of insuring and maintaining the highest pos
sible production of lobster, or in other words, the maximum sustainable
yield. These laws have basically represented biological goals and atti
tudes, but in recent years the need for economic considerations in man
agement schemes has been recognized by .all concerned. During the nearly
4C years prior to 1965, Florida management was mainly concerned with the
conservation of the spiny lobster population through controls on minimum
size and fishing seasons. These regulations are still of importance in
the total management program. Although most of the earlier regulations
have been revised and new regulations added since 1965, gear regulations
were first emphasized in the 1965 legislation. Perhaps more important
in the 1965 legislation was the emphasis on the need for effective
policing policies through the use of marketing by permit number, and
gear and boat identification for surveillance.
The regulations discussed here are as of March 31, 1976. A more
detailed discussion of the present laws and historical pattern of
Florida spiny lobster regulations can be found in a review by
Prochaska and Baarda [36].

21
A $50 permit is required for all persons intending to catch more
than 24 lobsters per day. The permit must be carried on the person at
all times and can be suspended or permanently revoked upon the arrest
and conviction of a permit holder for violation of any of the lobster
fishing laws.
Florida's management program includes two regulations pertaining to
the gear and craft. The first is that all gear (traps and buoys) and
the craft must be permanently identified by the permit number and/or
color code assigned to the fisherman upon receipt of his permit. The
figures on the craft must be at least three inches high to permit easy
identification from the air. The second regulation pertains to the
specific gear requirements. Wooden traps, ice cans, drums, and other
similar devices may be used provided that they are not equipped with
grains, spears, grabs, hooks, or similar devices. The traps must be
designed out of wooden slats not to exceed 3x2x2 feet or the cubic
equivalent. Only the sides of the traps may be reinforced with 16
gauge, one inch poultry wire.
Any gear used to capture lobsters must be marked by a buoy. Up to
twenty traps can be attached to a trot-line, and the line is marked at
each end by the attachment of a flag buoy. Buoys used must be of suffi
cient strength and buoyancy to remain continuously afloat. Any device
not conforming to the specifications listed, or not carrying a valid
permit number, may be seized and destroyed by enforcement officials. It
is unlawful to interfere with anyone's traps or markers without the
owner's permission.
In 1S53 the closed season was set between April 15 and August 15,
and in 1955 it was placed at its present interval of March 31 to

22
August 1. The 1965 act provided that traps may be placed in the water
and baited ten days prior to the open season and must be removed within
five days after the closing of the season, though no lobsters can be
taken during the closed season.
Three types of restrictions on the condition of lobster caught in
Florida exist at present. These deal with minimum size, separation of
head and tail, and egg-bearing females. The minimum size allowed is a
three-inch carapace of a 5 1/2 inch tail, though the tail measurement is
inapplicable if the tail is separated from the body. If head and tail
are separated under required legal permit, the tail must have a minimum
length of six inches. The 1965 act prohibited the catching of egg
bearing female lobsters, and those found in traps are to be returned
alive to the ocean. Stripping eggs from them is also prohibited. That
same act required a special permit if the separation of head and tail
was to be done before landing the lobster. A permit for such separation
may be granted if the operation is so far from land that it is not prac
tical to keep the lobsters alive until landing them.
Historically, in 1929 the first size restriction was enacted, the
minimum being one pound avoirdupois. In 1953 the minimum was redefined
to be a lobster with a tail measuring six inches. The 1953 act rede
fined the minimum size by tail and carapace measurement, with a minimum
carapace measurement of three inches and tail measurement of 5 1/2
inches. Methods of measurement were also given. Finally, a 1969 act
allowed a six-inch minimum on tails separated under special permit.
Presently, no legislation has provided for limited traps per firm,
limited licenses, landings quotas or taxes on landings to restrict the
over employment of labor and capital in the fishery. Groups with common

23
interests in and recent concern for the welfare of the fishery have
expressed a need for information describing the benefits and conse
quences of such regulation.

CHAPTER III
THEORETICAL MODEL
This study dealt with the management of a living marine resource
and the consequences of management strategies on the resources and its
uses. The production of living marine resources differs from tradi
tional production processes in that it requires the capture of a wild
animal without the more traditional production, cultivation and/or
manufacturing of the products involved. Biological behavior of the
animal, changes in its environment and economic factors of production
(labor, capital, management, and land) influence the success of capture
or amount of product entering the market.^ This relationship between
the product, defined as landings, and the above factors or variables
that influence landings, was defined as a harvest function. The
analyses presented in this study were based on the estimated harvest
function for the Florida spiny lobster resource. The theoretical frame
work of a fishery harvest function is presented in this chapter, A
biological growth model of a fishery was combined with the influence of
man in the form of fishing effort and termed a bioeconomic model.
Finally the procedure in which the bioeconomic model was used to
satisfy the remaining objectives of the study is presented.
^Assuming all that is captured enters the market.
2 4

25
Biological Theory of a Fishery
The harvest function, or yield function, (Equation 1) form a biolog
ical point of view represents the level of biomass (or stock of fish)
that can be harvested. The equilibrium level of biomass is that which
can be harvested without changing or damaging the parent stock. The
yield function may be expressed as
Y f(Stock) (1)
D
where,
\' ~ the amount of biomass available for harvest, and
Stock = the t.ocal biomass of fish.
This system is exclusive of the influence of man. Biological theory
states that the change in the stock of a fishery will follow an S-shaped
curve as shown in Figure 1. This theory has been supported by findings
from population studies of deer and insects. Additional support is pre
sented in a recent study by Gates and Norton [27] who estimated an S~
shaped curve for the yellowtail flounder fishery of New England. An
S-sbaped curve suggests that the population increases (a) slowly at
lower levels, limited by the reproductive capabilities of smaller num
bers and the smaller number of fish that are actually growing; (b)
rapidly in the intermediate range, as larger numbers of fish produce
more eggs than can survive and food supplies are adequate; and finally,
(e) slowly at higher levels where pressure from limited food supplies
impedes the population growth in an equilibrium manner and deaths just
offset births. Therefore, stock is a function of the biological
^The material in this section was primarily developed from the
following references: Bromley [8], Carlson [10], Christy and Scott [16],
Cheung [14], and Prochaska and Bsarda [36].

26
Figure 1. Growth curve for a fishery
stock
relationship between the parent population, the mature progeny, and the
influence of the environment on this biological process. The following
implicit relationship is suggested:
S g(Sj, S2, S3) (2)
where
S ~ stock
£j = population of mature progeny,
So = parent population, and
S3 = environmental attributes affecting the biological
behavior of the stock.
The population of mature progeny (S¡) is a function of the parent popu
lation (S2) and the environment (S3). Also determining the level of
mature progeny is the number of young or recruitment; the rate of growth

27
of the progeny; and the natural mortality rate due to diseases or due to
changes in the biological process. Parent population is a function of
the environment, growth rates, and mortality rates. The response of
the parent population to the variables may differ for various levels of
parent stock.
Numerous environmental factors significantly affect the biological
process. Significant factors are the food supply, predators other than
man and hydrographic characteristics including water temperature,
salinity, bottom conditions, currents and atmospheric conditions.
The relation between the number of mature offspring and the parent
population may be derived from these basic biological relationships
The recruitment of mature progeny is of particular interest since that
is an important policy variable used in developing management schemes
that will maintain seme equilibrium level of catch. The relationship
between mature progeny and parent population is a function of the same
variable affecting growth. At very low parent population levels re
cruitment is low because the number of spawners is small. As the parent
population increases, the level of recruitment increases. After some
population level is reached, recruitment levels decline for reasons due
to the environment and biology of the species, such as unhealthy fish
stocks, an inadequate ecological niche, declining growth rates, increas
ing mortality rates, severe competition for food, and adverse hydro-
graphic conditions. Thus, at some intermediate population level, the
ability cf spawners to recruit progeny into the standing population is
a maximum. At low population levels, growth rates are relatively low,
but beyond some population level, the growth rates decline and natural
mortality rates are relatively high.

Relationships between the size of the parent population in one
time period and the number of mature progeny in the. following time
period may be summarized as in Figure ? (Prochaska [36]). The 45 line
OA, represents the level of mature progeny necessary tc maintain the
parent population at its present level. That is, OA traces out the
number of mature progeny, measured on the vertical axis, necessary to
replace the parent population measured on the horizontal axis. The
curve, OM, represents the actual number of mature progeny that will be
produced by each parent population level. For example, a mature progen
of Mi, will maintain a parent population of PjS but parent population P
will produce and the total fish stock will increase. This process
will continue in nature until the actual production of mature progeny
Parent population
Figure 2. Number of mature progeny as a
function of parent population
levels

29
just equals that necessary to maintain a stable parent population, at
P3 where the lines intersect. At population P?., total production of
mature progeny is a maximum, and at P the excess of mature progeny
over that necessary to maintain the parent population is greatest.
The introduction of successful fishing effort while the parent
stock is P3, vill reduce the parent population since there is no net
recruitment with parent stock P3. The reduction of parent stock in the
initial time period results in an increase in the production of mature
progeny in the following time periods. Increased fishing effort may
continue to reduce the parent stock until parent stock, Pi, is reached.
Parent stock, P¡, will produce the largest marketable surplus defined
as equilibrium harvest and represented as M2 Mj in Figure 2. Maximum
marketable surplus is not at the parent population level which produces
the maximum mature progeny (M3). If in any time period more than the
equilibrium harvest is taken, the parent population will move Pq and
again the equilibrium in following periods will be reduced. If the
level of fishing is that which exactly takes the excess over the needed
replacement each season, parent population, Pj will be maintained. This
is defined as maximum sustainable yield (MSY).
The equilibrium harvest shown as the area between the mature prog
eny curve, OM, and the replacement line, OA, in Figure 2, may be ex
pressed in Figure 3. Points Pq, Pi, and P3 correspond with popula
tion levels in Figure 2. The maximum sustained yield, Y is produced
B1
from population Pj which corresponds to P\ in Figure 2. Except at the
maximum sustained yield the same equilibrium harvest may be taken at
different levels of parent population. For example, equilibrium .

30
Parent Population
Figure 3. Equilibrium harvest as a
function of parent population
harvest, Y may be taken with either parent population Pa or Po. MSY
occurs at that point of equilibrium harvest curve where its slope is
zero.
Traditional Economic Productlon Model
A production function normally used in economic analysis is defined
as the relationship between physical inputs and a resulting level of
physical output, similar to the biological yield process. The difference
occurs in the type of relationship between the inputs and the resulting
output. Similarly, theory exists that explains the economic stages of
a production process in an economic system.
Production inputs or factors of production can be defined as units
of effort and consist of land, labor, capital, and management. The

31
production process can be defined as
Ye f(E)
E ~ g(Ej, E2, E3, E4)
(3)
(4)
such that,
Ye = f(Ei, E2, E3, E4)
(3)
where,
Y = output as a result of effort,
1j
E = effort = combined unit of inputs, . E4,
Ej = land,
E2 = labor,
E3 = capital, and
E4 = management.
The assumed objective for firms in the industry is profit maximiza
tion. All firms are assumed to operate in a rational economic manner
with production occurring under conditions of decreasing returns. The
industry is assumed to have an atomistic structure with constant factor
prices and independent production processes.'*'
The biological yield function (Equation 1) is actually a physical
relationship between the various exogenous biological and environmental
attributes and the available fish stock for harvesting. The production
function (Equation 3) is a physical relationship between output and
exogenous variables representing effort. Biological models of fishery
populations without economic considerations are of little value as a
tool for developing useful policy for fisheries management. Likewise,
an economic model devoid of biological considerations is also of little
*The reader is referred to Ferguson [25] or Carlson [13] for a
complete presentation of production economics.

32
value. Thus, the integration of biological and economic considerations
is needed to accurately estimate the relationship between that level of
product which reaches the market (i.e., pounds landed) and those vari
ables that determine that level of product. This process is necessary
to insure that the equilibrium harvest level is both biologically and
economically sufficient.
Bioeconomlc Model
Variables of the yield function (Equation 1) and the production
function (Equation 3) were integrated to form the bioeconoroic model or
the harvest function:
YgE MS, E).
Substituting equations
ybe h(Sj . s
(2) and (4) into (6) gives
3 Ei . E4),
where,
(6)
(7)
Yt, is defined as the bioecoaomic equilibrium yield.
D£j
The biological yield model and the production model provide the
basic foundation from which proper management policies are designed.
Management policies consider equilibrium harvest (Y ) that does not
i)
endanger the parent population (So) while allowing maximization of har
vest ('/ ) for a given level cf inputs. This approach to managing a
fishery is known as maintaining maximum sustainable yield (MSY). MSY
was previously defined as the greatest equilibrium yield possible
without damaging the parent stock and varies in the long-run as a result
of effort, biological changes in the stock, and environmental induce
ments. MSY is an important variable in designing accurate management
policies.

33
MSY expresses a physical relationship and has provided the basis
for conservation programs of U.S. fisheries with little concern about
the economic consequences on the fishermen or society (SoLoloski [45]).
In recent years this philosophy of management practices lias changed and
economics has entered the arena of fishery resource management. Such
things as factor prices, product prices, costs, and other pecuniary at
tributes of the "bioeconomic system" must be considered for proper
management of a fishery. To many policy makers maximum economic yield
(MEY) is now considered the objective of "proper" management as is
assumed throughout this dissertation. MEY occurs at a level of landings
which are less than those suggested by the MSY criterion and thus
requires less fishing pressure.
MEY is defined as that yield where net revenue (NR) is maximized
for the fishery. Net revenue for the industry is at a maximum whe^e the
greatest positive difference occurs between total revenue (TR) and total
cost (TC), as illustrated in Figure 4. MEY occurs where the slopes of
the TR curve and TC curve are equal and can be expressed as follows:
BE
EE
0
(8)
where
represents additional or marginal revenue to the industry
tor additional landings, and
9TC
represents additional or marginal cost to the industry for
BE
additional landings.
Industry total revenue (TR) is derived by multiplying the harvest
function (YRt;) by ex-vessel price per pound (P). As ex-vessel price

34
Figure 4. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to landings
increases the TR curve shifts up and conversely TR shifts down s ex
vessel price decreases. Industry total cost (TC) is defined to be a
function of the exogeneous variables of the harvest function (Y^) and
their related prices. TR and TC may be expressed as
TR = Ybe x P (9)
TC = h(S,E) (10)
One fishermans harvest function is theoretically interdependent
with all other fishermen's harvest functions. Landings for one fisher
man are affected by what other fishermen catch from a given stock.
Consequently, as the number of firms in the industry increase, each
firm's production function constantly shifts downward while the asso
ciated cost functions shift upward. Per unit costs increase for the
same amount of effort expended because of fewer landings per unit of

35
effort. Costs per unit of output eventually rise to a level where
entry into the industry ceases.
Crutchfield [20, p. 12] identified the consequence of such a situa
tion when he said, "... such a market, unregulated, will destroy itself
either economically or biologically." Or in Carlson's [11, p. 7] words,
"In common property resource, the 'invisible hand' guarantees that the
market will arrive at a solution that is suboptimal."
Summary
Biological and economic theory suggests the following bioeconomic
harvest model:
Ybe = f(Si, S2, S3, Elf E2, E3, E4). (11)
Major focus of this analysis entailed determining the appropriate input
Level and subsequent landings where the greatest net revenue is gener
ated to the fishery. Net revenues for various levels of effort such as
number of firms in the industry and number of traps were compared. The
feasibility of alternatives for limiting effort were assessed by con
sidering the impacts these have on net revenues per firm, number of
displaced firms, total revenues to the state from user fees, cost and
time of implementation and enforcement of regulations, and expected
public acceptability.
Development of the theoretical model for this study has resulted
in an examination of the biological theory of a fishery resource and a
brief discussion of production theory. Models of these two theoretical
frameworks were integrated into a bioeconomic model used to explain the
theoretical constructs of management goals, namely MSY and MEY. The
empirical model and data analysis are presented in the next chapter.

CHAPTER IV
EMPIRICAL MODEL AND DATA
The empirical model and estimation procedure are presented in this
chapter in three parts. Types of data used are included in the presen
tation of each structural equation. Delineation of the study area and
the method of data acquisition is presented in the final section.
Estimation and theoretical analysis of the industry harvest func
tion are presented in the first part of the chapter. The second part
of the analysis is concerned with estimation of a firm harvest function
and associated optimum resource allocations for the firm at estimated
fishery stock levels. Implicit industry factor prices and costs were
derived in the firm analysis. The final part of the analysis involved
integrating the results from the industry and firm analyses to estimate
maximum economic yield (MEY) for the industry.
Definitions
A few definitions at this point may help clarify relationships
within the model. The industry hardest function was estimated using
secondary time-series d3t.a for 20 years from 1952-71. The firm harvest
function was estimated using primary cross-sectional data obtained from
a survey conducted in 1974 of 25 full-rime spiny lobster fishermen.
Capital letters are used to represent variables relating to the industry
harvest function, while lower case letters are used to represent vari
ables related to the firm harvest function. The only exception to this
36

37
is P which is always used as the ex-vessel product price per pound for
y
the industry and for the firm. Industry landings are represented by Q
and firm landings are represented by q. Variables representing inputs
into the industry harvest function are Xi, X?, and X3. Firm harvest
function input variables are xj, X2, X3, X4, X5, and x6. In only one
case does a variable from the industry harvest function and the firm
harvest function represent a similar measure of inputs, number of traps.
Xi, from time-series data, represents average number of traps per firm
in the industry for a given year, while xj, from cross-sectional data,
represents the number of traps fished by a given firm. An asterick (*)
superimposed on a variable, for example xj denotes the variable as an
op*-ir.;um solution and facilitates its identification when substituted in
different equations.
Bloeconomic Analysis
Time-series analysis is necessary to determine the direct and in
direct effects of increased effort on catch. Resulting effects of the
traditional economic production relationships are defined as direct.
Indirect effects are the influences on landings from variations in the
fish stock due to variations in effort. Time-series analysis is neces
sary because an analysis for only one point in time will only consider
the effect of effort on landings for the given fishery stock in exist
ence at that time. Evaluating effort over time also allows for the
consideration of expanding effort on the extensive marginmore firms
in the industry.
The bioeconomic model set forth earlier can be restated as
YBE h(El E2 E3, E4 Sl* S2 S3)
(12)

33
In the lobster fishery Ej (land) is not a factor, therefore, Ej drops
out of the theoretical equation. (labor) and E4 (management) are
transformed into output in the production process through the fishing
traps (the primary type of gear used in Florida). Therefore, Xj, traps
per firm, is substituted for E and E4. The remaining production factor
E3 (capital) is represented by both number of traps per firm and number
of firms (measured by number of boats and vessels) X2. Thus X2 is sub
stituted for E3. The biological factors population of mature progeny
(Sj) and parent population (S2) are not available from secondary data.
However both have been shown to be a function of environmental factors,
(S3), in the previous chapter. Water temperature is one of the many
variables which can be used to represent the environment. Water tem
perature however has been shown as a significant factor affecting lob
ster landings (Bell [3]) and thus was used in this study as a proxy for
S3 and is denoted as X3. Thus with these assumptions and substitutions
Equation 12 can be rewritten as
Q = f(Xl9 X2, X3) (13)
Variables in the reduced form equation for the industry harvest function
(Equation 13) are compared to variables in the theoretical harvest func
tion (Equation 7) in Table 1.
The reciprocal form of the yield function was selected because it
is consistent with current conditions and regulations in the industry.
Management regulations such as minimum size limits, gear restrictions,
prohibition of egg stripping and a fishing season set after spawning,
insures some maximum level of stock. The reciprocal function allows
landings to reach a maximum level but does not allow total production

39
Table 1. Industry harvest function variables in theoretical model
and reduced form, economic study of Florida spiny lobster
Industry
Variable Variable
In Theoretical Model In Reduced Form
Notation
Definition
Notation
Definition
Y
BE
bioeconomic yield
Q
total industry
landings
El
land (area of fishing)

e2
labor
Xi
traps per firm
e3
capital
x2
number of firms
e4
management
Xi
traps per firm
Si
population of mature
progeny

S2
parent population

S3
environmental attributes
X3
surface water
temperature
to decline with additional fishing effort. In addition, the reciprocal
function exhibits diminishing marginal returns which is consistent with
the stage, of production in which firms are expected to operate. The
industry harvest yield function can be expressed in reciprocal form as
A A
~ .. 3\ 32
Q = a 3 3X3 (14)
1 *2
The industry harvest function is used to determine an estimate of
maximum sustainable yield (MSY) to serve as a guideline in developing
management programs. Since the reciprocal function only approaches a
maximum, the MSY analysis considers "approximate" or "practical" maxima.
These maxima are estimated using various combinations of explanatory

AO
variables at reasonable maximum levels within the range of the data to
determine a range for MSY.
Maximum economic yield (MEY) for the industry was also determined
from the industry harvest function (Equation 1A). Total revenue (TR)
was computed by multiplying the estimated harvest function (Equation 1A)
by product price (P^). Py is assumed constant and representative of
current prices. was computed as the current average ex-vessel price
per pound.'*' Time-series cost data were unavailable. To determine MEY
it was necessary1 to develop an industry cost function from primary data.
A cross-sectional survey of spiny lobster firms was used to obtain the
necessary data and is presented in a later section. From these data an
industry total cost function was developed. Total industry cost (TC)
was derived by computing the average total cost per firm (ATC) for the
firms in the sample and then multiplying ATC per firm by the total num
ber of firms (N) in the industry. Together, these functions were used
to determine MEY as shown in Figure 5.
Derivation of MEY begins with the determination of the level of
2
firms at which the slopes of the TR and TC curves (Figure 5) are equal.
This is determined by equating industry marginal revenue (partial
derivative, of TR with respect to X2) with industry marginal cost (deriv
ative of TC with respect to X) and then solving for the number of
P was computed by dividing annual total industry value of land
ings bv'annual total industry landings.
2
Any input that serves as a policy variable for management pur
poses is applicable in place of firms. Number of firms is preferred
for reasons to be later discussed in this section.

41
TC
Firms (X2)
Figure 5. Maximum economic yield (MEY) for the industry is
illustrated as the greatest distance between
industry total revenue (TR) and industry total
cost (TC) with respect to number of firms
firms in the industry which is necessary for industry profit maximiza-
j. 2. k ,
tion, X2 The optimum number of firms, X2 is substituted into the
k
industry harvest function to determine Q defined as MEY.
Firm Analysis
The primary purposes of the cross-sectional survey and subsequent
firm analyses were to (a) provide cost estimates required to determine
MEY, (b) determine an optimum allocation of specified inputs for profit
^Notationally the derivation of X2 is a solution of the following
equalities:
(a) industry marginal revenue - industry marginal cost,
% 3TR 3TC
(b) TxT axj and
(c)
p
y
3Y
3X2
P is price of Xo.
X2

maximization for the firm, and (c.) incorporate the analysis of optimum
firm input levels into the MEY analysis and related analysis of manage
ment alternatives.
The firm harvest function is defined as the physical relationship
between landings and various units of effort. Effort may be generally
categorized as related to labor, capital, management, and fishing area
or location (geographical locations). From Equation 11, the general
theoretical harvest function, the typical firm harvest function can be
defined as
q f (ei, e.2, 63* > 1> 2> 3) (^-5)
where,
q = quantity harvested by the typical firm,
e¡ = attributes of the fishing process related to fishing
area (somewhat similar to land factor input),^
02 ~ labor,
63 = capital,
64 = management,
si = mature progeny,
52 parent population, and
53 = environmental attributes.
Enviroraiental and biological influences within a given area were assumed
constant for this analysis, since the data represent the lobster harvest
ing process at a given period in time. Thus, sj, S2>and S3 were deleted
Strictly speaking returns to land are to "ownership" of the
resource and has little relevance to geographical .location in most
instances. Returns to area in fishing is similar to saying a type of
soil is better than another in reference to agricultural production,
which has no relationship with "ownership" of tne various soil types.

43
from Equation 15, except that environmental, and biological differences
among fishing areas were represented by the coefficient for ej. The
objective of this analysis was to determine differences in ej . e4
among firms that influence individual firm landings and thus, production
responses to different levels of input use. A detailed summary of defi
nitions and derivations of variables that significantly influence the
typical firm harvesting process are presented in Appendix D.
A trap is defined as before to represent the unit of effort through
which the traditional factors of production are employed in the produc
tion process. Thus traps, xi, was substituted for e3, and et, in
Equation 15. In addition, the intensity at which the trap is fished
was included in the model through the inclusion of X2 (number of times
a fisherman pulls his total number of traps in one week) and X3 (the
number of weeks fished). These intensity variables adjusted trap use
between firms in a cross-sectional survey and in addition represented
additional use of traditional production variables such as labor and
capital. Variation in firm size and capital investment were included
by a proxy variable, X4, defined to be the square footage of the boat
or vessel.
Quality of fishing grounds with respect to stock and other environ
mental attributes is expected to raise or lower firm harvest and there
fore, were entered into the model using dummy variables. Fishing
grounds were broadly segregated into three different areas defined by
the sample stratification. The upper Keys region (X5) was defined as
the 44-mi.les from Key Largo to Lower Matecumbe Key. The lower Keys
region (xg) was defined as that 31-miles from Big Pine Key to Key West.
The middle Keys region, the base region, was defined as the 37-mile

44
stretch between the above two areas. If a one is entered for X5 and a
zero for xg the firm was fishing in the upper Keys region and vice-
versa for a firm fishing in the lower Keys region. If both X5 and X6
are zeros, the firm was fishing in the middle Keys region. These dummy
variables allow the intercept or position of the harvest function to
vary for different fishing areas.
Underlying bioeconomic theory for the firm does not specify curvi-
linearity in the firm harvest function since the stock of lobsters, or
sustainable yield, is assumed constant for a given period in time. Thus
the Cobb-Douglas functional form was selected which allows for either
increasing, constant, or decreasing returns.*' An additional reason for
the selection of the Cobb-Douglas form was that it requires fewer de
grees of freedom to derive the interactive effect among the independent
variables. The summary of these considerations and the final model for
estimation is represented by Equation 16.
A A A A A A
- 3i 62 33 34 35 36
q = axj x2 x3 x(( x5 x6 (16)
where,
A.
q = estimated landings (harvest) for the typical firm,
X-, number of traps,
x2 average number of times a fisherman pulls his total
number of traps in one week,
X3 = number of weeks fished,
= measure of craft size,
i
"A detailed discussion of the Cobb-Douglas function is presented
in Carlson [13].

45
X5 = dummy variable representing upper Keys region (one
represents upper Keys and zero represents middle Keys),
X0 = dummy variable representing lower Keys region (one
represents lower Keys and zero represents middle Keys),
and
A A A
a, 0i, . .36 are parameters to be estimated.
Optimum levels of inputs were determine at the point of profit maximi
zation for the typical firm. The same computational procedure used in
the time-series analysis was used to derive TR and TC for the firm and
optimal level of input use.
Maximum Economic Analysis (MEY)
The final part of the estimation procedure involved integrating
information obtained in the cross-sectional analysis into the time-
series model which estimated the industry harvest function. This was
then used to estimate maximum economic yield (MEY).
A recognized short-coming of the industry harvest function model
is that the assumption of homogeneity among fishing firms or "fishing
effort" does not prevail in the real world. Firms differ in fishing
power due to such factors as size of craft, fishing intensity, and
amount of gear. However, note that Equation 16 representing the firm
harvest function and based on cross-sectional data adjusted for these
differences. Size of craft was accounted for by xu, fishing intensity
by X£ and X3, and amount of gear by xj. With these adjustments it was
assumed that the firms were homogeneous. The dummy variables, X5 and
X0, further influenced this conclusion.

Estimation of the effect or traps on landings for the typical firm
using the firm harvest function took into consideration influences of
craft size, (X4), fishing intensity (x2 and X3) and differences in fish
ing grounds (X5 and x$). With this estimate an analysis of optimum num-
A
her of traps (xi ) was made. Then holding trap levels at this economic
optimum an estimate of the optimum number of firms was possible. Thus,
xi from the cross-sectional firm analysis was substituted for in the
time-series industry harvest function model to estimate industry land
ings assuming firms are employing the optimum number of traps. Equiva
lent notational form for the industry harvest function now became
A A
$1 62
Q = a + * + + 33X3
xi
X2
(17)
where,
Q = estimated industry landings,
J.
xi = optimal number of traps per firm estimated from firm
analysis,
X2 = number of firms in the industry,
X3 = mean seasonal surface water temperature,
ex, B2> 63 are parameters to be estimated.
HEY with respect to number of firms occurs at that point less than
MSY where the difference between total industry revenue and total indus
try cost are maximized. After deriving industry total revenue and total
cost curves, their slopes were equated and the solution for the optimal
A A
number of firms (X2 ) was determined. X2 occurred when industry margi-
A
nal revenue equals industry marginal cost of an additional firm. X2
was then substituted into the industry harvest function (Equation 17)

47
and the solution of Q was equal to MEY with respect to X2 for a given
level of Xj, X2, and X3, expressed as follows:
62
MEY = Q = a + H ~ + B3X3 (18)
xi X2
Thus, traps per firm, estimated from the firm analysis was used as the
constant exogenous variable to characterize firms in the industry har
vest function model. Ordinarily least squares regression techniques
were used to estimate the parameters.
Study Area and Data Acquisition
The Florida spiny lobster fishery primarily consists of the area
known as the Florida Keys region. This region is made up of two coun
ties (Dade and Monroe) and is located in the southernmost portion of
the state. Spiny lobsters are landed in small amounts in other coun
ties, mostly Pinellas, but these are usually caught in foreign waters.
Monroe Count}7 was selected for the study area for several reasons.
A trend analysis of the Florida spiny lobster fishery was conducted us
ing secondary data for 1952-71 (Williams and Prochaska [54]). From this
analysis the Florida landings were estimated to be approximately 95 per
cent of total .S. landings in recent years. Approximately 50-60 percent
in the last five years of Florida landings were caught in foreign waters
(Appendix E). The majority (over 90 percent of these foreign lobsters)
were landed in Dade County. Of tbe remaining 40-50 percent of total
Florida landings (which came from domestic, waters) approximately 80-90
percent were landed in Monroe County (Appendix F). Monroe County is
geographically located in tbe middle of the domestic spiny lobster
fishery (Figure 6). A final consideration is that the impact of confining

48
Figure 6. The Florida spiny lobster fishery
all domestic spiny lobster fishermen to the Keys region can be ad
dressed,^- For these reasons the study area was delineated to include
only Monroe County. In addition, it is realistic to include only that
area of the fishery over which the state of Florida has jurisdiction
since one of the ultimate objectives is to consider management alterna
tives .
At the time of this final writing the Bahamian government was
proposing to limit its fishing grounds to only its citizens. This will
moan that future Florida landings will be made up almost exclusively
of domestic stock.

49
Department of Commerce secondary data on landings, total value of
landings, and effort for 1963-73 were used for the time-series analysis
[18],[49]. Measures of effort for the industry during this period were
total number of traps; total number of vessels; total number of boats;
total number of fishermen classified as, on vessels or casual; and total
gross tonnage of vessels in the industry. Gross tonnage was measured
only for vessels greater than 5 gross tons and was loosely defined as a
measure relating to the net capacity of the craft. Water surface tem
perature data was acquired from Ocean Survey Branch of NOAA [52]. It
was assumed that surface water temperature and bottom water temperature
vary in proportion in this study. This assumption was based on findings
from a study by Robinson [39] that concluded no thermoclines exist, or
the water is isothermal in the delineated study area. Temperature data
for the study period was in the form of mean, minimum, and maximum
monthly temperatures for three stations located at South Miami, Marathon,
and Key West.
Sample Selection and Size
A sample of the population was drawn since surveying the total
population was impractical from a cost and time standpoint. Sample size
was determined using the following formula:"*'
n
2
(N 1) D + S
where,
n = sample size,
(19)
This formula was obtained from Mendenhall [33j.

50
N = population size,
2
S = estimate of the population variance,
D = B2/4, and
B = bound on the error of estimation (i.e., 10 percent on
each side)
Data from a sample of 15 observations on 1973-74 landings by individual
boats (S) and vessels (6) for sizes ranging from 26 feet to 40 feet in
2
length were obtained for estimating the population variance (S ) [51].
2
The sample was classified into six vessels and nine boats. S a pooled
variance (within craft class) was estimated from the actual survey data
to be 30,129,877.77. B was selected at 10 percent on each side of the
population mean to be estimated. N was equal to 226 and was calculated
from a list of commercial craft registrations provided by the Florida
State Department of Natural Resources. Criteria used to include a firm
in the population was (a) that the address of the craft owner be Monroe
County; and (b) that lobster fishing was listed as the primary (dollar
value) species harvested. A major limitation of this sampling technique
was that fishermen may live out of the county and fish in the study area
and vice-versa. Sample size, N, was calculated to be 21.
Stratification of the sample was based on length of craft and loca
tion of home port. Proportions in each sample strata were equal to
proportions of the population in each strata. Boat length strata were
less than 21 feet, 21-30 feet, 31-40 feet, and greater than 40 feet.
In the stratification of the study area upper Keys was defined as that
area from Key Largo to Lower Matecumbe Key. Middle. Keys was defined as
that area from Craig Key to Bahia Honda Key and lower Keys was the.area
from Big Pine Key to Key West. Based on the population as stratified

51
in Table 2, the following stratified sample illustrated in Table 3 was
drawn. Total number of samples drawn was 25 rather than the required
21 in order to round the desired number of samples to whole numbers
after stratification.
Table 2. Stratified population of boats and vessels, defined as
firms, economic study of Florida spiny lobster industry
Length (feet)
Area
<21
21-30
31-40
>40
Total
Upper Keys
8
28
6
2
44
Middle Keys
33
33
14
10
90
Lower Keys
37
25
18
9
89
TOTAL
78
86
38
21
223
(35%)
(39%)
(17%)
(9%)
(100%)
Table 3. Stratified sample of boats and vessels, defined as firms,
economic study of Florida spiny lobster industry
Length (feet)
Area
<21
21-30
31-40
>40
Total
Upper Keys
2
2
2
0
6
Middle Keys
3
3
2
1
9
Lower Keys
3
3
3
1
10
TOTAL
8
8
7
2
25
The following
formula was
used to
determine the
number of
observa-
tions to be sampled in each strata:
C, c,,
i ij
ij N N
n
(20)

52
where,
N = sample size of strata ij,
Ch = number of craft of length class i,
= number of craft of length class i in area j,
n = total sample size to be drawn, and
N = total populatioii of craft.
Survey Technique
Observational units within each strata were not drawn randomly in
the usual sense. The data were collected in a very precarious environ
ment, at a very difficult time. Florida spiny lobster fishermen, like
most fishermen, are very independent and generally do not divulge infor
mation. So, there was first a problem of locating a fisherman that
would cooperate. A second problem frequently encountered was that many
cooperative fishermen lacked adequate records, particularly costs, so
much of the information was "best estimates." To complicate the matter,
at the time of the survey the Internal Revenue Service was investigating
Florida fishermen because a recent court ruling had changed the tax
regulation, retroactively, and thus information was highly guarded.
Also it was felt by many that a substantial amount of undersized lob
ster were "blackmarketed" from this area. In addition, any list of
fishermen was usually out of date because of the highly mobile nature
of fishermen. Given these circumstances, it was impossible to collect
data on a strictly random basis. Thus, the samples represent fishermen
who would cooperate. Personal interviews were conducted until the re
quired number of observations within each strata was accomplished.

53
Initial fishermen contacts were acquired through the Southeastern
Fisheries Center in Miami and a local chapter of Organized Fishermen of
Florida (O.F.F.).1 In July 1974 the research project was presented and
a questionnaire pretested at a local O.F.F. Chapter meeting in the area.
Possible benefits to the fishermen were explained as well as soliciting
their cooperation for interviews to be conducted in the fall. Also,
names of fishhouse managers that would cooperate in encouraging their
local lobster fishermen to be interviewed were obtained.
In October 1974 the interviewing began using a thirteen page ques-
2
tionnaire with those fishermen that agreed to cooperate the past July.
Once this source of interviews was exhausted, various cooperating fish-
houses were then contacted. Managers were asked to recommend fishermen
that they felt would cooperate and that were needed to complete the
various strata as specified by the sample design. Interviewing con
tinued for three weeks until all observations required in the sample as
stratified were collected. Twenty-eight questionnaires were completed
and after editing for inconsistencies and incompleteness, twenty-five
were used in the analysis. Additional observations were collected for
those strata that were weighted heavier to assure completeness. Data
comparisons of study projections with industry output characteristics
suggest the sample was representative.
The author is indebted to Mr. Lloyd Johnson and Mr. Pete Maley,
agents of the Southeastern Fisheries Center, NOAA, NMFS; and the of
ficers of the Lower Keys Chapter of O.F.F. located in the Summerland
Key area.
2
Appendix J includes the survey questionnaire.

CHAPTER V
ANALYSIS OF RESULTS
Estimated coefficients and tiieir interpretation for the industry
and firms' harvest functions are presented in this chapter. Information
from the industry harvest model was used to derive estimates of MSY and
MEY. Optimum input levels and related costs at current stock levels for
the "typical" firm were derived from the firm harvest model. Informa
tion obtained from both analyses was then integrated to analyze alterna
tive fishing practices.
Bioeconomic Model
As previously mentioned, the reciprocal function was selected for
the time-series estimation because of its theoretical characteristics
and its simplicity. Recall that current management programs such as
size limits and protection of berried females suggested the model to be
realistic. The management program protects the young until they reach
minimum size. Thus, assuming continuous fishing pressure it is possible
that (a) there is a lvel of pounds landed which is a function of the
weight of minimum-sized lobsters and (b) increased effort alone will
not cause total landing to decrease because of present size and sex
regulations.
The reciprocal function allows landings to reach a maximum limit
but does not allow total landings to decrease with increased effort.
54

55
It also allows decreasing marginal returns to fishing effort.
The following spiny lobster harvest function is the statistical
model estimated using time-series data:
q = ¡ + 3i^-+32^- + 33x3 e. (21)
Al X2
The estimated coefficients and standard errors are presented in
Equation (22):
Q = 28,379,136 1,439,976,169 465,173,997 J-
*1 X2
(365,878,684) (216,457,337)
- 239,791 X3.
(170,321) (22)
Overall the model was statistically significant at the .01 level
(F3j7 = 9.16). The coefficient of determination, R2 and R2 (which was
R2 corrected for degrees of freedom) indicated that the model explained
80 and 75 percent of the variation in annual landings, respectively. A
Durbin-Watson value of 2.38 indicated the model hinges on the border
2
between no autocorrelation and inconclusiveness range of the test.
The coefficients for traps per firm, 6i> and number of firms traps in
the industry, g2, were found to be statistically different from zero
at the .01 and .07 levels of significance, respectively.
As a check on the logic of using the reciprocal form of the
function other functions were considered, but none of these yielded
"better" results. For the second degree polynomial function, negative
signs were estimated for the parameters but the coefficients estimated
were not significantly different from zero.
2
Durbin-Watson statistic is not calculated for less than 15
observations. Therefore DW was not used to test in this case. However,
there was no apparent pattern of the residuals.

Million pounds
56
Observed and predicted values of landings for 1963-73 are shown in
Figure 7. Since 1969, landings have varied between 4 and 5 million
pounds, with a slight exception in 1970. Maximum landings observed
within the data range occurred in 1970 at 5.24 million pounds. In 1973
landings decreased to 4.99 million pounds. Assuming current management
regulations are adequate and new technology does not occur, there is
little reason to expect landings to increase substantially above five
or six million pounds annually. This assumes that biological and
environmental factors will remain substantially unchanged.
Figure 7. Observed and predicted volume of spiny lobster landings,
1963-73 for Monroe County, Florida

57
The marginal effect of changes in effort on landings was determined
I/by the partial derivatives of the bioeconomic industry harvest function
(Equation 22) with respect to the specific explanatory variable measur
ing effort. The following marginal products (MP ) of the harvest func-
i
tion are partial derivatives with respect to a given explanatory
variable, x^:
1,439,976,169
2
Xi
(23)
= SL =
8X2
465,173,997
x22
(24)
>ffx3 - -235,791 (25)
The additional pounds of lobsters landed in the industry when each firm
intensifies production by adding one trap is shown by MP As each
X1
firm adds a trap total landings increase at a decreasing rate. The
MP
Xj
additional catch per firm can be calculated by for each MP .
X2 Xx
Additional catch per firm is simply the MP divided by X2. MP is
X2 X2
.also a declining function of the number of firms in the industry and
is interpreted to be the additional industry landings resulting from
adding one additional firm to the industry with the same characteristics
as all other firms in the industry.
In the empirical analysis of specific marginal products numerical
values of other variables ware held constant at their mean levels.
Traps per firm (X¡) and number of firms (X2) were held constant at 429
traps per firm and 399 firms, respectively. Mean seasonal surface water

58
temperature was 77.591F.
levels gi^es
Evaluating MP (Equation 23) at 1973 input
X1
1,439,976,169
(429)2
7,824 pounds.
(26)
As each firm in the industry increases the number of traps it fishes by
one, total landings for the industry increases by 7,824 pounds. A one
trap increase per firm is equivalent to a 399 total trap increase for
the industry and an increase of 19.59 pounds per trap.
Evaluating the effect of changing the number of firms in the indus
try (Equation 24) gives
465,173,997
(399)2
2,922 pounds.
(27)
Holding traps per firm and water temperature constant and increasing the
number of firms by one increases total industry landings by 2,922
pounds. Increasing the number of firms by one unit and holding traps
per firm constant, brings 429 new traps into the industry. The fishing
power of an additional trap to the industry may be greater if it is the
first trap for a new firm compared to an additional trap for a firm
already fishing. However, the marginal analysis as set forth will not
allow for this difference.
Evaluating the effect of changes in water temperature (Equation 25)
gives
MP = 83 = -239,791 pounds, (28)
A 3
For every one degree increase in the mean surface water temperature for
the season, total industry landings will decrease by 239,791 pounds or
about 5 percent of total landings in 1973. A general concensus among
fishermen is that landings increase shortly after meteorological

59
changes such as storms and weather fronts. These weather changes often
create lower temperatures and partially explain the inverse relation
ship of this parameter.
Maximum Sustainable Yield (MSY) Estimate
One of the initial objectives in this study was to address the
question of "the status of the spiny lobster fishery with respect to
maximum sustainable yield (MSY)." The industry bioeconomic harvest
model indicated that industry landings are approaching a maximum sustain
able yield. The bioeconomic empirical model based on a theoretical cur
vilinear harvest function fitted the data very well (R2 = .75). Explan
atory variables were individually highly significant and the total
"accounted for" variation was significant. At current levels of effort
the percentage increase in landings was much less than the percentage
increases in inputs.
These conclusions were reached observing the range in landings as
inputs were increased to an infinitely large number as shown in Table 4.
Inputs were held constant at 1973 mean values while the remaining vari
ables were varied. Landings were also analyzed with seasonal water
temperature (Xj) which was held constant at its mean, minimum, and
maximum observed values.
The range of maximum landings was from 5.9 million to 8.9 million
pounds. Illustrated in Figure 8 is the harvest function as it reaches
a maximum of 7.89 million pounds with 2,000 traps per firm (Xj), holding
total number of firms (X2) at the 1973 level of 399 and seasonal water
temperature (X3) at its mean of 77.59. Although some fishermen are
fishing 2,000 traps, this number was chosen to illustrate the approximate

60
Table 4. Estimated levels of maximum landings (Q) for given levels of
traps per firm (Xi), number of firms (X2), and seasonal water
temperature (X3), economic study of Florida spiny lobster
industry
Maximum
landings (Q)
Variable
approaching
CO
(infinity)
Level
Xl
of Variables
X2
Held Constant
x3
8,152,905
Xi

287
(MEAN)
77.59
(MEAN)
8,607,871
Xl

399
(MAX, 1973)
77.59
(MEAN)
8,121,094
Xl

399
(MAX, 1973)
79.62
(MAX, 1972)
8,450,247
Xl

287
(MEAN)
76.35
(MIN, 1969)
8,905,212
Xl

399
(MAX, 1973)
76.35
(MIN, 1969)
7,666,129
Xl

287
(MEAN)
79.62
(MAX, 1972)
5,860,742
x2
368
(MEAN)

77.59
(MEAN)
6,416,893
x2
429
(1973)

77.59
(MEAN)
6,786,218
x2
482
(MAX, 1971)

77.59
(MEAN)
6,299,442
x2
482
(MAX, 1971)

79.62
(MAX, 1972)
7,083,559
x2
482
(MAX, 1971)

76.35
(MIN, 1969)
Note: Mean, minimum, and maximum refer to values for Monroe County
time-series data, 1962-73 (Appendix K). Numbers in parentheses
represent year.
point where the bioeconomic harvest function becomes flat for all prac
tical purposes. This represents a 366 percent increase in traps per
firm and a 58 percent increase in landings. Note that the levels of
inputs required to achieve the maximum output levels in Table 4 were
totally unrealistic at levels of infinity. A 18 to 78 percent increase

Figure 8
Spiny lobster bioeconomic industry harvest function

62
in landings would require an infinite percentage increase in inputs.
The same point is illustrated in Figure 8 but traps per firm is presented
in a more realistic range. Predicted landings increase by 40 percent,
from 5.62 to 7.89 million pounds, as a result of a 115 percent increase
in the number of traps per firm (from the maximum observed in the data
of 482 to 2,000).
Estimates of MSY chosen for analysis in this study ranged between
six million and eight million pounds with a realistic estimate probably
in the range of six to seven million pounds. This is not to imply that
landings cannot increase above these figures, but rather that these fig
ures are the levels estimated at which landings could be maintained from
year to yearmaximum sustainable harvest (yield) ceteris paribus.
Actually, the limiting factor probably is that the typical firm does not
have the capacity to reach the required trap level.
In summary, maximum harvest levels considered here are quite liberal
for several reasons. Some illustrations used extremely unrealistic
levels of inputs to achieve the maximum levels of harvest and more impor
tantly, some input levels were beyond the range of data. Estimated
landings may be beyond maximum economic yield, discussed in the next
sectJ-on. In addition, substantial input increases of this nature may
cause irreversible effects on the population, not directly observable
in the existing data on which the analysis was based. Therefore, the
realistic MSY level was concluded to be in the range of six to seven
million pounds annually.
Value Marginal Product Amtlysis
A more comprehensive analysis of maximum economic yield (MEY) is
presented in the section integrating results from the cross-sectional

63
and time-series analyses, but cone knowledge of levels of expenditures
and profit maximization can be gained using results of the time-series
industry analysis thus far.
Value marginal products for given inputs were derived by multiply
ing constant product price times the respective marginal physical pro
duct. The value marginal product equation for traps per firm (Xj) is^
A
Pi
VMP = P MPV = P ( 7) (29)
Xi y Xi y 2
where,
P = annual average dockside price per pound of lobster,
assumed constant;
A
Pi
- -- = marginal product of Q with respect to input X^ (Equation
X1
23).
VMP is the addition to industry total revenue as a result of a roargi-
X1
nal increase in traps fished per firm. VMP,, was divided by the number
X1
of firms in the industry in 1973 (399) to demonstrate the effect of
price changes on an individual firm (Figure 9).
2
Product prices per pound used in the analysis were $1.08, $1.25,
$1.50,and $2.00. In this price range the value marginal product ranged
from approximately $4.81 to $140.00 as traps per firm vary from approxi
mately 900 to 168, respectively. At a product price of $1.08 and traps
per firm at the mean level for 1952-71 (368) the VMP was $23.77. If
X1
the cost for an additional trap were $28.77, this would be the profit
VMP is with respect to the subscript (x^) denoted in Equation 29.
2
Mean ex-vessel price of $1.08 per pound was obtained from a .
survey of 25 Lobster boat captains taken in 1973.

Traps per firm (Xj)
Figure 9. Value marginal product of traps per firm (X^) divided by the maximum number of firms
observed (399) in the industry in 1973

65
maximization level of output. Thus as long as the cost of fishing a
trap was less than $28.77 it would pay to expand.'*' At dockside prices
of $1.25, $1.50,and $2.00, marginal cost per trap could increase to
$33.31, $39.97, and $53.30, respectively, before the input level for
profit maximization would be reached. With traps per firm (X¡) at the
1973 level of 429, VHP ranged from $21.16 (assuming a product price
A1
of $1.08 per pound) to $39.22 (assuming a product price of $2.00 per
pound). Maximum level of traps per firm observed was 482 in 1971. At
this level VMP ranged from $16.77 to $31.07 for product prices ranging
X1
from $1.08 to $2.00 per pound. These values exceed trap costs and en
courage intensification of traps fished per fisherman.
Value marginal product for an additional firm was also analyzed
while holding traps per firm (X^) constant. Value marginal product for
the firm was expressed as
$2
VMPy = P ( t) (30)
x2 y X22
where,
B2
- rr = marginal product of Q (Equation 24) with respect to firms
X2
(X2), holding X} constant.
Estimates of VMP for the mean, minimum, maximum, and 1973 levels of
X2
firms are presented in Figure 10 at the product prices used earlier.
Profit maximization will occur with 399 firms in the industry when the
total cost for the typical firm reaches $3,154, $3,652, $4,383>or $5,844,
given product prices of $1.08, $1.25, $1.50,or $2.00, respectively
'cost of an additional trap includes fixed costs for construction
find craft, and variable expenses incurred to fish the trap such as'
fuel, bait, and labor.

28
26
24
22
20
18
16
14
12
10
b
6
4
2
O'
2S,892
^ - X?
100
200
300
Firms (X2)
500
cn
o
10. Value marginal product of firms (X2)

67
respectively (Equation 30, Figure 10). The difference between industry
total value of landings in 1973 for 399 firms fishing compared with 400
firms fishing was $3,154 at a product price of $1.08. In order to gen
erate a net profit to the industry, the addition to industry total cost
from the 400th firm fishing must be less than $3,154.
Analysis of Firm Harvest Function Model
Time-series data on firms included both part-time and full-time
commercial fishermen. Some of these firms fish in more productive fish
ing grounds than others which can significantly influence the firm har
vest rate. Fishing power and intensity of this power varies substan
tially between firms which influences the firm harvest rate. Aggregate
data measuring explanatory variables such as firms and traps have all of
these production input differences confounded in their estimated effects,
thus making the interpretation of estimated coefficients very difficult
and incomplete. Therefore, one objective of the cross-sectional anal
ysis was to obtain partial estimates adjusted for these other influences.
A second objective was to develop cost estimates which would be used
with the time-series bioeconcmic model to determine maximum economic
yield for given measures of effort. That analysis is presented in this
section along with a brief analysis of optimum resource allocation for
the firm at a given fishery stock level.
Firm Harvest Model
The harvesting process for the typical spiny lobster firm was esti
mated using a Cobb-Douglas functional form. The empirical data must lie
in Stage II of production since diminishing marginal returns are indi
cated by less than unity values estimated for the parameters. The

68
estimated equation is
a .7577 .43991 .37211 .30876 .44455 .13063
q = 4.09000 X2 X3 X4 X5 Xg (31)
Equation 31 was estimated in log linear form using ordinary least
square methods. This entails minimizing the sum of squares of the
logarithms of residuals. The assumptions of BLUE estimaters are still
valid.
Landings per firm (q) were measured in pounds. Average traps
fished per firm (xj) was a weighted average of traps fished per firm.
Tills variable considered the initial number of traps fished at the
beginning of the season, the number of traps lost during each month of
the season, and the number of times a trap was fished before lost.
Rounds per week (X2) was a measure of effort intensity and was defined
as the season average proportion of traps pulled per week for the season.
A round was defined as a single pulling of all traps. Total number of
weeks fished (X3) was another measure of effort intensity. In Florida
a maximum of 36 weeks is allowed in the season by law. Fishing power
of the firm (X4) was taken into consideration by including a size vari
able. The square area of the hull was used as a proxy for size. Influ
ences on harvest levels due to quality differences in fishing grounds
were accounted for by including dummy variables X5 and xg which broadly
characterized the firms into the three areas previously defined.^
The R2 corrected for small sample size showed that the harvest
function explained 82 percent of the variation in a typical firm's
"^Derivations and detailed definitions of the explanatory variables
are presented in Appendix D. Appendix G contains the estimating
equations for landings (q) and marginal products (MP ). Appendix L
contains the data used to estimate the firm harvest Xi function.

Thousand pounds Thousand pounds
Traps per fina (x¡)
Rounds per weeks (x2)
500 1,000 1,500 2,000
Square feet of craft (xi,)
Figure 11. Firm harvest functions with respect to effort measured as gear (Xj),
fishing intensity (X?_, X3), firm size (X^), and adjusted for fishing
grounds (X5, X6)
O'.
o

70
landings (Table 5). The range in error of estimated landings was com
puted by expressing the antilog of the standard error of the estimate
(SEE) as a percentage of the total estimated value. For Equation 31
landings varied from 31.5 percent above to 24.0 percent below the
estimated harvest values.
Table 5. Regression statistics for the cross-sectional firm harvest
function model, economic study of Florida spiny lobster
industry
Independent
Variables (x.)
1
Estimated
Coefficient (8^)
Standard
Error
t-Ratio
Significance
Level of
Probability
Constant (u)
4.09000
1.2500
1.128

Traps per firm
(xi)
.75770
.1099
6.895
.9999
Rounds per week
(X2)
.43991
.2772
1.587
.8700
Weeks fished
(X3)
.37211
.2400
1.550
.8615
Craft size
(x4)
.30876
.1358
2.274
.9645
Upper Keys area
(X5)
.44455
.1493
2.977
.9919
Lower Keys area
(X6)
.13063
.1653
.790
.5603
Note: R2 = .8223
, R2 = .9310, d.f.
= 18, SEE =
.2742, F6>
18 = 19.514.
The relationship of landings to effort (xj, X2, X3 and,x4) for the
firm is presented in Figure 11. Adjustments to the firm harvest function
for the influence of different fishing grounds is also illustrated.
An analysis of the estimated effort coefficients (Equation 31)
indicated that the function is homogeneous of degree 1.87848 and thus
defined an industry exhibiting increasing returns to scale. The theoret
ical interpretation was that the marginal returns to a simultaneous

71
increase in all inputs was positive and total landings were increasing
at an increasing rate. Homogenity of 1.87848 means that if each of the
independent variables of the harvest function are multiplied by a con
stant k, landings will change by a multiple of k1*878if 5. For example,
if XI ... Xg are all doubled (k = 2) landings will more than quadruple.
To illustrate the significance of this, assume that the State of Florida
determined that MSY had been surpassed and landings would have to be
reduced by, say, approximately 50 percent to protect the fishery stock
from irreversible damage. Given homogenity of 1.87848, all inputs would
have to be reduced by only 25 percent to obtain a 58 percent reduction
in landings per firm, and thus, for the industry, assuming homogeneous
firms.^ If the state does not have control over individual effort,
individual firms would have to be provided some inducement to voluntarily
cut back input usage, similar to the objective of the Federal Soil Bank
Program for agriculture in the 1960s. Although this type of analysis
may provide some interesting insights into management of the fishery,
it may be argued that the interpretation is non-sensical. Realistically
speaking, size of craft and number of weeks are definitely limited
beyond some point of expansion.
Estimated Parameters
The estimated coefficients (8^) of the hai'vest function presented
in Table 5 explained the percentage change in landings due to a given one
percent change in the particular input level, assuming all other inputs
^Notationally the derivation is 3S follows:
(. 75) 1 8781,8 q = .58 q
where,
q = firm harvest function (Equation 31).

72
constant. These were defined as output elasticities and can also be
expressed as ratios of marginal and average productivities.
Partial differentiation of the harvest function (Equation 31) with
respect to given explanatory variables, gave the marginal products as
follows:
. 3q 2 3il 62 $3 $4 3s $6
MPxi = ^ = 3ixj x2 x3 Jx4 hx5 '5x6
(32)
MP = |3- = a 32x2B2"2x1ei-e3-
X2 9x2
x3 "X4 'x5 -x6
A A
9q 2 63-1 3i 3p 34 3s 8r
MP = = a 83X3 X! xx2 zx4 4x5 dx6
X3 9x3
A A
mo 2 84-1 81 82 83 85 86
MPx4 = 3x^ = a 134X4 Xl X2 X3 X5 X6
(33)
(34)
(35)
Traps per firms (xi)
The estimated parameter (3i) is interpreted as a 76 percent in
crease in landings due to a one percent increase in number of traps for
the firm. 3i is statistically significant at the 99 percent confidence
level. ^
The marginal increase in landings due to the addition of one trap
by the typical firm is:
-.2423
MP = 62.85xi
X1
(36)
The derivative of MP was negative implying marginal landings per trap
X1
will decrease as additional traps are added by each firm to the total
Alternatively, the probability of randomly obtaining a 3 as large
as 81> if 81 is equal to zero is less than .01.

73
number fished. The marginal return to an additional trap was positive
and also greater than the marginal return for any of the other three
forms of effort.
Rounds per week (x?)
As the firm increased its trap pulling rate by one percent (i.e.,
A
decreases its set period), landings increased by 44 percent (32 = -43991).
Rounds per week is an index measuring fishing intensity as defined in
A
Appendix D. g2 was statistically significant at the 87 percent confi
dence level. The marginal product of x2 was expressed as
MP = 5317 x2-*5601 (37)
x2
As x2 increased the rate of increase in landings decreased. For
example, assume the firm is pulling all of its traps once per week. The
marginal product (Equation 37) of increasing this rate to twice per week
would be approximately 4,500 pounds.
Useful information contained in this index is the expected gain in
landings due to increasing the number of days a fisherman's traps set
between harvest periods."* Rounds per week (x2) was computed by dividing
the average number of days in a set period for the season into seven
days of a week. By substituting this definition for rounds per week
into the firm harvest function (Equation 31) the marginal product of
increasing the set period an additional day was calculated (Table 6).
For example, a fisherman previously harvesting his traps after the
third day can increase his total harvest by 2491 pounds by letting his
This is often referred t.o as "set period" among fishermen.

74
Table 6. Marginal products for various lengths of set periods, economic
study of Florida spiny lobster fishery
- '
Days in
Increase in landing
Fishing effort
set period
due to a one day
intensity in terms
(z)
increase in set period
(MPz)
of rounds per week
(X2>
3
2491
2.333
7
735
1.000
10
440
.700
14
271
.500
traps set four days between harvests. Likewise total landings can be
increased by 735 pounds by increasing the set period from 7 days to 8
days. Increasing from a 10 day set period to an eleven day set period
would increase total landings by 440 pounds, while a 271 pound increase
could be expected by allowing traps to set 15 days instead of 14 days.
Marginal increases in total landings due to increasing the set period
by one day can be estimated for any length of set period by the follow
ing equation:
MP = 12116 z-1*43991 (38)
z
where,
MP is the marginal product due to increasing the set period
by one day,
z is the number of days in the set period or between rounds, and
z = 7/x£.
Equivalent levels of fishing effort intensity measured as rounds per
week (X2) for the examples shown in Table 6 range from 2.333 rounds per
week for fishermen that harvest after a three day set period to .500

75
rounds per week for fishermen that pull all their traps every two
weeks.
Interpretation of these estimates of Mi must be treated with
x2
care. First, the data represent seasonal mean levels of landings re
lated to rounds per week which vary greatly from week to week throughout
the season. During August, the first month of the season, the mean set
period for the 25 total firms in the sample was 5.3 days. By March,
the last month of the season, the mean was 13.3 days. The March mean
was for only 20 of the 25 sample firms since some of the larger, multi
ple specie fishermen usually stop lobster fishing by the end of December
Although this question was not specifically asked in the interview
a considerable amount of information was volunteered that indicated the
maximum level of set period, relative to poaching and vandalism, was
correlated with location of fishing ground to populated areas, distance
from shore, and depth of water. The remarks indicated that approximately
four days was the maximum length of time traps could set between harvest
periods, particularly at the beginning of the season. This could be
extended tc six days if either the traps were in sight of land or firms
banded together in groups to fish an area several miles from shore.
Weeks fished per season (x3)
Landings increased very rapidly the first few weeks of the season,
then leveled off. Recall that in Figure 11 it was shown that approxi
mately 54.5 percent of total landings for the 36-week season are harvest
ed within the first six weeks. This was supported by the estimated out
put elasticity for weeks. £3 shows that landings increase .37 percent
for a one percent increase in weeks fished. Expected weekly landings

76
beginning at various dates within the season can be estimated using the
marginal product of weeks, expressed as follows:
MP = 1093.46 x3--6279 (39)
x3
The second partial derivative of the harvest function for weeks fished
showed MP^ diminishing at an increasing rate.
= -686.58 x3-1-6279 (40)
9x3
Estimated marginal products are presented in Table 7 for various periods
A
throughout the harvest season. g3 was statistically significant at the
86 percent confidence level.
Table 7. Weekly landings expected for given dates within the spiny
lobster season, economic study of Florida spiny lobster
industry
Beginning date of Week
(x3>
Weeks fished
Change in landings
for each addition
week fished (MP )
x3
August
7
1.00
1,093
14
2.00
708
31
4.43
429
September
15
6.57
335
30
8.71
281
October
31
13.14
217
November
30
17.43
182
December
31
21.86
158
February
28
30.29
128
March
31
36.14
115
An additional week of fishing after August 7 would return approxi
mately 1,093 pounds. By the third and fourth week, landings would drop

77
off to 708 pounds and then to 42.9 pounds per week, respectively. After
the 1st of September weekly landings tended to level off dropping to
less than 200 pounds per week by December 1st. Some of the larger firms
with greater capital investments quit lobster fishing by November 1st
and go to other species. The expected net returns from netting mackerel
or long-living yellowtail snapper are evidently greater for at least
these firms. Four out of the 25 firms in. the sample did not fish the
entire season. At least three of these four were always ranked in the
top five in number of traps (xj), fishing intensity (X2X and size of
craft (X4). The cost per pound of fishing extra weeks becomes substan
tial and returns become relatively small. Smaller firms often did not
have the alternative of fishing for other species at higher net returns
and remained in the lobster fishery the entire season. On the other
hand, larger firms have a comparative advantage in other fisheries and
began leaving after the 13th week of the season when approximately 68.6
percent of total landings had been harvested.
By changing species early in the harvest season larger firms can
reduce costs substantially for several reasons. After two months the
trap lines become frayed and traps break off and are lost in hauling.'*'
Those traps not lost to frayed buoy lines require additional repairs
which reduce the efficiency of the harvesting process. Second, by late
summer the probability of ocean storms increases substantially and the
risk of losing traps to high winds and rough waters becomes high. Con
sequently, larger firms fishing in excess of 800 traps have the largest
total risk and pull out of trap fishing early in' the season in an
effort to reduce costs.
-Hauling is defined as pulling a trap out of the water.

78
Craft size (X4)
Craft size, defined as the square area of the hull, was the most
significant of several measures developed from characteristics of the
A
craft. It is reasonable to assume that the effect of craft size (84)
is confounded. There is decreased speed but increased size which allows
A
more traps to be transported and relocated. 84 was statistically sig-
A
nificant at the 97 percent confidence level. From 84, it was concluded
that landings increased .31 percent for each one percent increase in
craft size and the marginal product of craft size increased at a de
creasing rate. This was the smallest response of all the measures of
effort. The range of craft size in the sample was from 80 to 1,045
square feet, while the mean of the sample was 326.88 square feet. Num
ber of craft and hull lengths in each group of the sample were: seven,
16-20 feet; seven, 21-30 feet; seven, 31-40 feet; and four. 40-55 feet.
Appendix H further elaborates various characteristics and practices
classified according to length, for the lobster firms surveyed.
Marginal returns for increases in square footage of the hull (X4)
are presented in Table 8 and were estimated using the following equation
MP = 558.29 x4-*69124 (41)
X4
Marginal product (MP ) due to a foot increase in the hull size
X4
ranged from 27.00 pounds for craft 80 square feet in size to 4.57 pounds
for craft 675 square feet in size. At levels of X4 less than 350 square
feet the marginal product decreased at a greater rate per unit of in
crease in square footage of hull than for craft greater than 350 square
feet. This was determined by the slope of the marginal product curve
in Figure 12, being less than zero. This indicated a decreasing rate

79
Table 8. Marginal products of craft size (X4) for sample sizes
observed, economic study of Florida spiny lobster industry
Change in landings for
Craft size (X4)
(length x width)
Length
Width
each additional square
foot increase in craft
size (MP )
X4
80
16
5
27.00
96
16
6
23.80
140
20
7
18.34
154
22
7
17.17
176
22
8
15.66
200
25
8
14.33
208
26
8
13.95
234
26
9
12.86
240
24
10
12.63
252
28
9
12.22
330
33
10
10.14
340
34
10
9.93
341
31
11
9.91
408
34
12
8.76
432
36
12
8.41
468
36
13
7.96
480
40
12
7.82
574
41
14
6.91
675
45
15
6.18
1045
55
19
4.57
of return. After X4 reached 350 square feet (approximately 34 feet long
times 10 feet wide) returns to increasing the size of the craft began to
level off. For example, in Table 8 marginal product of craft size de
creased by 48 percent compared with a 156 percent increase in craft
size, as the square footage increased from 408 (34 feet x 12 feet) to
1,045 (55 feet x 19 feet). The implications were that marginal decreases
in landings due to increases in the size of the craft were smaller for
larger firms than for smaller firms at mean levels of various inputs.
In summary, the estimated firm harvest model fitted the data well
and all individual explanatory variables were highly significant statis
tically. The model indicated that firms were operating In stage II of

30
Figure 12. Marginal product curve for spiny
lobster craft size (MP )
x4
the production process, defined by diminishing marginal returns to the
inputs. Number of traps (x¡) exhibited the largest returns to increased
input usage, and had the highest statistical significance level of all
explanatory variables. Estimates of rounds per week (X2) revealed that
marginal returns to more frequent pulls or longer set periods would be
positive. Number of weeks fished (X3) by law is limited to 36, although
the analysis of weeks fished indicated that the economic feasibility of
fishing beyond the 13th week is questionable. The diminishing marginal
rate of returns to a firm was smaller for larger firms than smaller
firms.
Optimum Resource Allocation of the Firm
The analysis and results of determining the level of inputs where
profit was maximized for the typical firm are presented in this section.

81
This analysis was expanded to determine the optimum allocation of inputs
for each size of craft classified by the sample stratification.
Optimum level of input usage is customarily determine by solving
a system of equations determine from the first order conditions. In
this case . x4 can be considered as factors of production and X5
and xg are simply area adjustment factors. Notationally, the equilibrium
between value marginal product (VMP ) and marginal factor price for
Xi
each input (x^) can be represented as
VMP = P (42)
x. x.
1 X
Thus the optimum solution for . X4 is determined by simultaneously
solving Equations 43-46.
67.85
-.2423 = p
J X1
(43)
5557.06
5601 = p
X2 r
x2
(44)
1180.39
-.6279 = p
d x3
(45)
602.67
x -.6912 = p
x4
(46)
The terms on the left of Equations 43-46 represent the value marginal
products for the individual factors determined at the means of the other
independent: variables and at a product price of $1.08 per pound. Un
fortunately the factor prices (P ) were not unique exogenous prices.
1.
They were interdependent and thus presented problems in arriving at a
unique solution. Factor price estimates of a trap (P ) are possible
xi
and were the primary concern in this analysis. As ment Lotted earlier,
the traps (x^) variable was the. principle factor through which all

32
inputs were translated into fishing effort. Although analyses of vari
ables measuring effort intensity (xo, X3, and X4) have provided useful-
production information, the principle reason for specification of these
in the model was to allow for partial estimates of the trap effect.
This model adjustment was required because the data base represented a
cross-section of firms which varied with respect to X2, X3, and X4.
Thus an optimum solution in this analysis will be limited to (a) deter
mination of optimal trap use for given (mean) levels of the adjustment
variables and (b) discussion of possible or feasible levels of X2, X3,
and X4.
The price of an additional trap fished (P ) is not simply the
X1
price of the trap but is the price of the trap and the cost of fishing
the additional trap. This latter component presented difficulty in
determining Total cost per firm was regressed on the number of
traps fished per firm. OLS regression technique assuming BLUE estima
tors was used to estimate the total cost function (TC) expressed in
Equation 47:
TC = $1,876 + $11.55 X! (47)
The coefficient of determination corrected for small sample size (R?)
was .53 and the estimated coefficient ($11.55) for traps per firm was
statistically significant at the 99 percent confidence level (t-value
equal 5.328). The constant term ($1,876) was interpreted to represent
fixed costs which do not vary with level of trap use. The coefficient,
$11.55, represented the marginal factor price of an additional trap
fished. Total costs were used for estimation rather than variable costs
because a large component of trap cost was included in fixed cost

83
through depreciation.1 The estimate of optimum number of traps per firm
(xj) using this factor cost estimate is presented in Table 9 with respec
tive landings, profit levels, total revenue, and total cost.
Table 9. Optimum levels of trap usage per firm and resulting levels of
profits, total revenue, total cost, and landings given trap
cost, economic study of Florida spiny lobster industry
Optimum
level of
trap use
Trap
factor
price
(P )
X1
Total
revenue
(TR)
Total
costs
(TC)
Profits
(n)
Landings
(pounds)
$11.55
1,491
$22,742
$17,221
$3,863
21,057
The optimum level of traps given a factor price of $11.55 was 1,491.
Relatively small variations in the factor price of a trap produce signif
icant changes in the estimated optimum level of traps. The highly vari
able nature of the optimum solution is significant in that it offered a
possible explanation for the rapid increase in trap usage in the industry.
Relatively small changes in product price (P ) or factor price of a trap
(P ) resulted in considerable expansion of fishing effort on trap usage.
X1
This finding justifies further consideration of trap usage in management
considerations in the following chapter.
Before closing this chapter consideration of the remaining independ
ent variables is warranted, given the earlier significant estimates of
their marginal effects. One crude method for estimating the factor prices
for X2, X3, and X4 involves dividing total cost or total variable for
each by the mean input levels of each of these factors. Estimates of
Traps have an average life expectancy of three years.

84
total cost (TC), total revenue (TR), firm profit (II), landings (q), and
optimal levels x2, x3, and x4, given the crude factor estimates of P^,
P and P are presented in Table 10. The remaining variables used in
x3 x4
the estimation procedure are assumed constant at their sample mean.
Table 10. Optimum levels of adjustment factors (x2, x3, and x4) and
resulting levels of profits, total revenue, total cost, and
landings per firm, economic study of Florida spiny lobster
industry
Optimum
level of
factor
use
<*i>*
Factor
price
deri
vation
Estimated
factor
price
(P )
x.
X
(dollars)
Total
revenue
(TR)
(dollars)
Total
costs
(TC)
(dollars)
Profits
(n)
(dollars)
Landings
(pounds)
.834
TVC
p
x2 x2
6,149.88
12,084
5,129
6,955
11,189
10.30
p _TC
X3 x3
273.00
7,559
2,812
4,747
6,999
179.11
p
x4 x4
17.70
9,690
2,991
718
8,972
Optimum number of rounds per week, or total percentage of traps
pulled was .834."*" The imputed factor cost for rounds per week was de
rived by dividing average total variable cost per firm from the sample
by the mean level of rounds per week for the sample. Coincidentally,
*
the optimum level of rounds per week (x2 ) was equal to the mean of
rounds per week from the sample (x2) which resulted in a $6,955 profit
for the typical firm. Imputed factor costs for weeks were derived by
Length of set period, measured as days, is derived as follows:
Days set period = ,
Xo

85
dividing total costs by the mean number of weeks in the sample. Optimum
number of weeks was estimated at 10.3 and profit per firm was estimated
at $4,747. Optimum size of craft measured as square footage of hull was
estimated at 179.11 square feet. Factor costs were derived by dividing
total variable costs by mean craft size for the sample. At this level
of craft size profit estimated for the typical firm was $718.
This procedure was presented for illustrative purposes and its use
fulness depends on accurate estimates of factor prices. In addition,
total revenue, total cost, and resulting profits were also dependent on
levels of other inputs which in the above analysis were held at mean
levels rather than "optimal" levels. However, it is interesting to note
that the predicted level for rounds per week and weeks fished in Table
10 were both close to actual observed values in the industry, thus sug
gesting that if firms are maximizing profits, the above estimates of
factor prices for and X3 are reasonable. The factor price estimated
for craft size evidently may be a substantial error because the optimal
hull size of the typical craft was predicted at 179.11 square feet, con
siderably different from the current industry average size of 326.88
square feet. Furthermore, the predicted profit per firm of $718 does
not appear reasonable given the survey data.
At this point, one additional conclusion was indicated with respect
to variations in firm profits due to fishing areas. Fishing in the
upper (X5) and lower (xg) Keys regions produced increased profits. How
ever, only 65 was statistically significant at the 99 percent confidence
level, compared with a 56 percent confidence level for 65. Therefore,
there exists a good chance profits will be greater if firms fish above
Lower Matecumbe Key rather than fish the adjacent area down to Big Pine

86
Key. Fishing in the region below big Pine to Key West most probably
does not increase a firm's profits compared to fishing the area from
Big Pine Key up to Lower Matecumbe Key. The model would have to be
respecified to determine if there exist only two significantly dif
ferent fishing grounds (regions), i.e., above and below Lower Matecumbe
Key. Empirical values for the fishing effort and price variables viere
held at the respective 1973 levels: 618, for ; .834, for X£; 33.08,
for X3; and 326.88, for X4. Product price, P was assumed equal to
$1.08 per pound.

CHAPTER VI
THE MANAGEMENT MODEL
The purpose of this chapter is to present a framework with which
decisionmakers can evaluate management policies. The framework is based
on results from the estimated time-series bioeconomic industry on firm
harvest models in the study. In the first section the analysis of maxi
mum economic yield (MEY) for the industry is presented. Next, analyses
of alternative combinations of traps per firm and number of firms are
presented. Finally, the alternative management considerations outlined
in the study objectives are analyzed.
Maximum Economic Yield for the Industry^
When the quantity of lobster harvested is such that the cost of an
additional unit of input (P ) is equal to the value of the marginal
A,
1
product (VHP ) for that input, then maximum economic yield with respect
A.
1
to the given input (MEY ) is achieved. Maximum economic yield with
Xi
respect to inputs Xj and X2 can be determined by first simultaneously
determining the optimal level of both inputs. These input levels are
then substituted into the production function (Equation 22) to predict
MEY. To determine optimum levels of Xj and X2 for the industry simul
taneously, the profit function (Equation 47) is differentiated with
Recall that capital notations for the variables represent industry
inputs and lower case type for variable notations represent firm inputs.
P represents ex-vessel product price in the firm and industry models.
87

88
respect: to Xx and X2 and set equal to zero to determine a maximum (or
minimum) level of inputs.
nx = TR TC
A A
81 B2
n, = p (K + + )- X2[1876 + 11.55 Xx] (48)
y xi x2
where,
Hi = industry profit,
1876 + 11.55 Xj = per firm total costs expressed as a function
of traps, and other terms are defined as before.
V
11.55 X2 = 0
an_
ax2
- 1876 11.55 X]
0
(49)
(50)
Solving Equations 48 and 49 simultaneously results in 213 firms in
the industry, each fishing 795 traps. Using Equation 22 maximum economic
yield was estimated at 5,778,274 pounds. This estimate was 16 percent
higher than industry landings in 1973. The number of firms in the in
dustry, at 399 in 1973, was 87 percent higher but each firm fished 429
traps, 87 percent less than the estimated value. Several implications
can be drawn from this analysis. First, industry profits have currently
not been maximized nor has total industry landings reached a peak.
Second, firms could be larger and more efficient, maximizing profits
through economics of size. Finally, total industry costs could be re
duced due to fewer firms, resulting in a larger total industry profit.
Maximum economic yield was less than the estimated maximum sus
tainable yield (MSY) and resulted from an optimum allocation of factor

89
resources. However, management authorities allocating factor resources
could consider factors such as "grandfather clause" and minimum levels
of input uses (such as more firms than the optimum 213 firms solved for
in this study). Consequently, only one input at a time will most likely
be considered for regulation. Alternatively, the management authorities
may not strive to reach the most profitable level of utilization, at
least initially, since social and political institutions must be consid
ered. For these reasons the remainder of this chapter will consider
alternative levels of maximum economic yield with respect to given con
straints. That is one input will be analyzed while other inputs are
held at current levels.
Evaluating MEY
Maximum economic yield was estimated in the previous section using
the bioeconomic industry harvest model. In the previous chapter it was
explained that the traps data used to estimate the parameters for the
industry model were not adjusted for influences that make a trap catch
"better" for one firm than another. The reason for this was that data
such as that used to estimate the parameters for the firm harvest model
were not available over time. Trap data in the analysis of the firm
harvest function included these influences making estimation of the
optimal nuaiber of traps a partial effect and probably more accurate.
Consequently, MEY was reestimated constraining the number of traps per
firm to three levels most likely to be politically acceptable based on
analysis in this study. This evaluation involves comparing landings
(MEY), total revenues (TR), total costs (TC) and profits (TI) for the
industry and the firm, among the three levels of traps per firm (Xi).

90
The technique used to reestimate MEY was different than the first
method which involved a simultaneous solution of the industry profit
function. In this case the assumed number of traps per firm (Xj) and
*
the estimated optimal number of firms (X2 ) required for industry profit
maximization was substituted into the original bioeconomic industry har
vest function. In the following equation landings are now defined as
maximum economic yield (MEY) for a given combination of traps per firm
(X^) and number of firms (X2) assuming a constant mean seasonal water
temperature (X3) of 77.591F:
$1 B2
MEY = a + + + $3(77.591).
X1 x2
(51)
The optimal number of firms (X2*) was defined as that number which
maximized industry profit while fishing the number of traps per firm
that was specified for the estimation of MEY. Consequently, total cost
per firm and resulting total industry cost varies according to the num
ber of traps specified.'*' Optimal number of firms was derived for each
level of traps per firm from the following equality between the value
XPV was previously defined as average total cost per firm for the
x2
industry. Alternatively, the estimated value of can be considered
X2
to be a function of the number of traps the firm fishes. The estima
tion of P using OLS regression technique was
x2
Pv = 1,876 + 11.55 X,
x2
where,
SE = 2.168; SE = 1,540; R2 = .74; SEE = 3,752; d.f. = 23 and
A J Ct
pXi $11.55.

91
of the marginal product for number of firms (VMP^ ) and the total cost
per firm (Pv ):
X2
(52)
where,
VMP = MP *P the marginal product of firms multiplied times
X2 X2 y
the ex-vessel price per pound (P ),
P = 1,876 + 11.55 Xi, the firm total cost function, and
X2
X2 = optimal number of firms estimated.
The three levels of traps per firm (X^) selectee to reestimate MEY
were (a) the 1973 mean number of traps per firm for the industry (429),
(b) the mean number of traps per firm in the survey (618), and (c) the
optimal number of traps per firm for profit maximization estimated in
the firm analysis from cross-sectional data. The respective optimal
number of firms (X^*) estimated from Equation 51 are (a) 271 firms fish
ing 429 traps each, (b) 236 firms fishing 618 traps each, and (c) 225
firms fishing 700 traps each. The criteria for evaluation are presented
in Table 11. Comparable values can be derived for the typical firm by
dividing the table values by the appropriate number of firms.
In Table 11, landings were estimated at 4.7 million pounds given the
optimum number of firms (271) estimated from Equation 51. Each of these
firms were assumed fishing 429 traps. If all firms fished 618 traps in
stead (the cross-sectional sample mean), 236 firms would be the optimum
number required for a maximum industry profit which would be $3.8 million.

92
Table 11. Maximum number of firms (X2*), landings, revenues, and costs
for industry profit maximization given desired management
levels of traps per firm (Xj), economic study of Florida
spiny lobster industry
Optimum
number
firms
(x2*)
Traps
per
firm
(xx)
Landings
(MEY)
Total
revenue
(TR)
Total
cost
(TC)
Profit
(n)
271
429
4,700,384
5,076,414
1,851,201
3,225,213
236
618
5,472,346
5,910,134
2,127,304
3,782,830
225
700
5,648,932
6,100,846
2,241,225
3,859,621
Note: Definitions for Table 11:
X2* = Determined as optimum level of X2 given X^ for profit
maximization (VMP,r = Pv ) .
A2 A2
Xi = Assumed desired management levels for Xj as previously
defined.
MEY = Maximum economic yield given X2x and Xi.
TR = Total revenue from landings, assuming 1974 ex-vessel
price (Py) of $1.08 per pound (TR = P^ MEY).
TC = Total operating costs [TC = X2(1,876 + 11.55 Xj)].
II = Profit; total revenue (TR) minus total cost (TC) .
This would result in total landings of approximately 5.5 million pounds.
As number of traps fished per firm increases to 700, the optimum number
of firms required for profit maximization is 225, resulting in landings
of 5.6 million pounds. Thus for given levels of traps per firm which
have either been observed or estimated as typical in this study, the
optimum number of firms required in the industry to maximize industry
profits ranges from 225 to 271 firms. Maximum economic yield for these
input levels was also within a reasonable estimate ranging from 6 per
cent below 1973 landings of 5 million pounds to 12 percent above.

93
Estimated earnings and costs for the input levels are also presented
in Table 11. These estimates are with respect to 1973-74 season stock
levels and environmental conditions.
Policy Implications
The estimated MSY of six to seven million pounds presented in
Chapter IV currently has not been attained. Landings are within 20 to
40 percent of this estimate of MSY. It appears unlikely, given the
estimated MEY of 5.8 million pounds, that fishing effort will cause
landings to surpass MSY, at least in the near future. This is based on
the fact that 7 million pounds are not reached until 649 firms enter the
industry with 700 traps each. With the 400 firms presently in the in
dustry each would have to fish 1,000 traps to harvest 7.2 million pounds.
These levels of inputs are considerably above typical levels found in
the industry. Therefore, the current major concern facing the regula
tory agency is maintaining a politically acceptable maximum economic
yield (MEY) for the industry.
From the evaluation of MEY it is obvious the policy maker is faced
with numerous choices of combinations of traps per firm and number of
firms. The optimum combination of these resources depends on the states
management objectives. For example, objectives based upon a strict pro
fit maximization motive may lead to regulatory legislation that would
reduce the current number of firms to less than 300 (based on Table 11),
allowing only the most efficient firms to operate. Conversely, objec
tives based on a social welfare optimization motive may very well en
courage maximum entry of less efficient firms. The number of firms
would be limited only by the probability of landings surpassing MSY.

94
As more biological information concerning MSY becomes available,
the relationship between MSY and KEY will become more useful in develop
ing management guidelines. An analysis of the impacts of a wider range
of various combinations of inputs and management objectives is presented
in the next section.
Discrete Analysis of Alternative
Combinations of Firms and Traps Per Firm
Extreme variation may occur in the impact of the different manage
ment programs, depending on which resource (X^ or X2) is manipulated and
to what degree. Thus it is extremely important to know the impact of
various combinations of these resources in order to design policy goals
and select parameters for management programs. To illustrate this point
Tables 12 and 13 were developed to show the impact of various combina
tions of traps per firm and numbers of firms, measured as landings
(Q, q), total revenue (TR), total cost (TC), and profit (IT) for the
industry and the average firm. Table 12 was developed for various num
bers of firms in the industry holding traps per firm at 700 traps.
Illustrated in Table 13 are various levels of traps per firm holding
number of firms at the 1973-74 season level of 400 firms.
Alternative Number of Firms in the Industry
Seven hundred traps per firm were assumed because this figure was
felt to be a realistic estimate given results of the various analyses.
In the previous chapter, the average number of traps per firm in the
cross-sectional firm analysis was found to be 842 for the size group with
the highest profits. The average number of traps for the group with the
second highest profit level was 561. For these two groups combined

95
there was an average of 701 traps per firm. Finally, the MEY analysis
using the bioeconomic industry harvest function at the beginning of this
chapter resulted in 795 traps per firm as optimum.
Industry landings (Q) ranged from 3.1 to 7.4 million pounds as the
number of firms has varied from 100 to 1,500 in Table 12. This range
represents only a 141.7 percent increase in total industry landings as
the result of a 1,400 percent increase in effort. Total costs become
greater than tctal revenues when the number of firms exceeds 966. If
the 1973-74 season level of 400 firms were in effect, landings would be
6.6 million pounds with industry profits of $3.1 million. Thus, if each
firm fished 700 traps (selected economic optimum for 1974) 225 firms
would maximize industry profits. Approximately 772 firms would likely
dissipate all industry profits, while the 400 existing firms could
operate at a total industry profit level of $3.1 million. Maximum
industry profits would occur with 225 firms, each fishing 700 traps.
This would result in landings of 5.6 million pounds.
Estimates on a per firm basis presented in Table 12 were derived by
dividing total industry estimates by the appropriate number of firms.
Estimated landings per firm (q) ranged from 4,938 to 30,646 pounds for
the alternative programs. Costs per firm were constant in Table 12.
Estimated average profits per firm ranged from $23,137 for 100 firms in
the industry to $3.00 per firm for 771 firms in the industry. Total
costs per firm were estimated to exceed total revenues per firm when the
number of firms exceeded 771. With these estimates maximum profit per
firm occurred at 121 firms while maximum industry profit occurred at
225 firms.

Table 12. Analysis of alternative levels for number of firms (X?) assuming traps per firm (X-) equals 700, mean seasonal water
temperature (X3)
lobster industry
equals 77.591'F,
and ex-vessel
price per pound (P
) equals $1
y
08, economic study of
Florida spiny
Total Industry
Per Firm
Number of
landings
Total Revenue
Total Cost
Profit
Landings
Total Revenue
Total Cost
Profit
firms (X2)
(0)
(TR)
(TC)
(H)
(q)
(TR)
(TC)
01)
100
3,064,632
3,309,803
996,100
2,313,703
30,646
33,098
9,961
23,137
* 121
3,871,959
4,181,716
1,205,281
2,976,435
32,000
34,560
9,961
24,599*
150
4,615,2.12
4,984,429
1,494,150
3,490,279
30,768
33,229
9,961
23,268
175
5,058,235
5,462,894
1,743,175
3,719,719
28,904
31,216
9,961
21,255
200
5,390,502
5,821,742
1,992,200
3,829,542
26,953
29,109
9,961
19,148
* 225
5,648,932
6,100,846
2,241,225
3,859,621*
25,106
27,114
9,961
17,153
206
5,745.296
6,204.919
2,350,796
3,854,123
24,344
26,292
9,961
16,331
271
5,999,863
6,479,852
2,699,431
3,780,421
22,140
23,911
9,961
13,950
300
6,165,792
6,659,055
2,988,300
3,670,755
20,553
22,197
9,961
12,236
325
6,285,067
6,787,873
3,237,325
3,550,548
19,339
20,886
9,961
10,925
350
6,387,303
6,898,283
3,486,350
3,411,938
18,249
19,709
9,961
9,748
375
6,475,908
6,993,981
3,735,375
3,258,606
17,269
18,651
9,961
8,690
400
6,553,437
7,077,712
3,984,400
3,093,312
16.3S4
17,695
9,961
7,734
425
6,621.845
7,151,592
4,233,425
2,918,167
15,581
16,827
9,961
6,866
450
6,682,652
7,217,264
4,482,450
2,734,814
14,850
16,038
9,961
6,077
500
6,786,024
7,328,906
4,980,500
2,348,406
13,572
14,658
9,961
4,697
* 771
7,113,033
7,682,076
7,679,931
2,145*
9,226
9,964
9,961
3*
1000
7,251,198
7,831,294
9,961,000
-2,129,706
7,251
7,831
9,961
-2,130
1500
7,406,256
7,998,756
14,941,500
-6:942,774
4,938
5,333
9,961
-4,628
Note: Asterisks highlight minimum and maximum positive profits for firms and/or industry and respective number of firms (X2).

97
Alternative Levels of Traps Per Firm
The effects of varying traps per firm from 2C0 to 1,000, holding
the number of firms at the 1973-74 level of 400, is presented in Table
13. Total industry landings (Q) decreased from a maximum of 7.2 mil
lion pounds using 1,000 traps per firm to 1.4 million pounds using 200
traps per firm. At levels less than 205 traps per firm total costs were
greater than total revenues (Table 13). Maximum profit for the industry
and per firm occurred when the average number of traps per firm was 580.
At this level total industry landings were 6.1 million pounds.
Landings (q) per firm ranged from 3,527 to 17,926 pounds for a
variation in traps from 200 to 1,000 traps per firm. Total costs per
firm ranged from $4,186 to $13,426 at these input levels. Profits per
firm ranged from a maximum $7,970 with 580 traps per firm to $39 with
205 traps per firm. At 618 traps per firm (sample mean) total industry
landings (Q) were 6.3 million pounds. This level of landings was
greater than the 5.3 million pounds estimated using the mean number of
traps per firm in the time-series analysis (429 traps per firm).
Evaluation of Estimares
Model estimations thus far appear to be reasonable in comparison
to actual primary and secondary data. In 1973, 399 firms fishing an
average of 429 traps entered the industry and landed 4.99 million
pounds. According to the analysis, 400 firms each fishing 429 traps
would land approximately 5.3 million pounds. The average full-time
firm earned a profit of $8,719 in 1973 fishing 618 traps (Prochaska and
Williams [37]). This compares with the estimated profit of $7,943 per

Table 13. Analysis of alternative levels for number of traps per firm (Xj) assuming number of firms (X^) equals 400, mean
seasonal water temperature (X3) equals 77.591F, and ex-vessel price per pound (F ) equals $1.08, economic study
of Florida spiny lobster industry ^
vO
CO
Note: Asterisks highlight minimum and maximum positive profits for firms and/or industry and respective level of traps per firm (Xj)

99
firm using 618 traps.1 These estimates are not unrealistic when one
considers that the number of firms in the secondary data includes small
part-time and recreational firms with low net revenues as well as large
commercial firms.
Discrete input substitution analysis was limited by the fact that
only a limited number of selected combinations of input levels can be
evaluated. However, it was possible to evaluate all economically fea
sible combinations of number of traps per firm and number of firms in
the industry by analyzing isoquants developed from the bioeconomic
industry harvest model.
Isoquant Analysis
A production isoquant can be defined to show the various combina
tions of traps per firm (Xi) and number of firms (X2) that are capable
of harvesting a given level of landings (Q). The isoquant can then be
used by analyzing the marginal rate of technical substitution between
inputs to illustrate the broad range of alternative combinations of
traps per firm and firms to achieve management objectives and the
2
ultimate limit of the use of a particular resource.
The rate at which traps per firm (X^) and number of firms (X2) are
substituted for each other is important in determining the results of
changes in the combination of inputs. This rate can be defined as the
Total costs do not include opportunity costs such as captain's
salary and returns to investment. Captain's salary was estimated at
$5,130 for the typical firm.
'Notationally Isoquants in Figure 13 can be represented as
- - 8 83
Xi = 81 [Q a -
X2 X3
]

100
marginal rate of technical substitution of traps per firm for firms
(MRTSV ) and is expressed in the following equation:
xlx2
mrtsy
xlx2
dXi
dx7
MP
MP
(53)
MRTS, v is the reduction in number of traps per firm necessary to
xlx2
maintain the same level of landings after an increase in the number of
firms.
Using input levels for the 1973-74 season as set forth in the time-
series data, MRTS v was estimated to be3
xlx2
MRTS
X1X2
A A
Si S2
-1
-2.69.
(54)
Increasing the number of firms in the industry (X2) from 400 to 401
would require decreasing the number of traps per firm (Xi) by three
(2.69 rounded)3to 426 traps to maintain 1973 landings of 5,253,958
pounds. This would result in a total decrease of only 774 traps in
3
the industry. Total cost per firm would decrease by $34.65. Constant
landings would result in an identical level of industry total revenue,
but the additional firm in the industry would decrease average revenue
per firm by $91.23. The reduction of 826 traps would reduce industry
total costs by $7,064 and thus increase industry total profit.
Assuming 429 Xlf 400 X2, $1.08 P TC equal to $1876 + $11.55 X2.
2
MRTS = 2.69 is rounded to 3.0 since inputs are indivisable
XiX2
thus not accurately maintaining the equality of MSY and total revenues.
3(400 x 429) (401 x 426) 774.

101
MRTS diminishes as more firms are substituted for traps per
xlx2
firm and this is illustrated by the concave isoquants in Figure 13.
Tliis condition is recognized as satisfying the principle of diminishing
marginal rate of technical substitution and is caused by two factors.
First, the marginal product of firms (MP ) diminishes as the number of
x2
firms increases while the number of traps per firm is held constant.
This is defined as a downward movement along the MP curve. Second, as
X2
the number of traps per firm decreases, the marginal product function of
firms decreases (thus shifting the >0? curve downward). As more firms
X2
(X2) are substituted for fewer traps per firm (Xj) the marginal produc
tivity of the additional firm in the industry will be less. The oppo
site occurs as the number of traps per firm (Xq) is substituted for the
number of firms (X2). The same two forces act to increase the marginal
product of number of traps per firm (X^) while the marginal product
function of number of firms (X2) decreases.
Analysis of the marginal rate of technical substitution between
inputs can be of importance in providing a priori information to decision'
makers about the results of suggested changes in the structure of the
harvesting sector of the fishery. This analysis includes (a) observing
the effect of movements along an isoquant and (b) determining the loca
tion of ridge-lines (defined).
Movement Along An Isoquant
For firms fishing 700 traps, MRTS ranges from -.0632 for 100
xlx2
firms to -14.2143 for 1,500 (Table 14). MRTS v for 249 firms (-.3922),
xlx2 .
for example, means that if decisionmakers decided to allow the number of
films in the fishery to increase by one to 250, and yet still maintain

- 7,000,000
Q 6.000,000
Q 5,848,203
Q 5,000,000
Q 6,000,000
Figure 13. Spiny lobster harvest isoquants and ridge lines
defining expansion paths where returns equal total
costs, (assuming ex-vessel price per pound (Py)
equals $1.08, industry total cost equals $1,876
plus $11.55 per trap per firm (Xi), and mean
seasonal water temperature (X3) equals 77.591F)
102

103
the previous level of landings (5,848,203 pounds) where industry profits
were maximized, the number of traps per firm would have to be decreased
by 2.55.1 This was illustrated in Figure 13 as moving along the iso
quant where landings (Q) equals 5,848,203 pounds.
Table 14.
Marginal rate of technical substitutions
(mrtsx,x2
) of traps
per firm (Xi) for number of firms (Xi) holding traps per
firm constant at 700, economic study of Florida spiny lobster
industry
Number of
Marginal rate
firms
of technical
(X2)
substitution (MRTSV v )
XiX2
100
- .0632
150
- .1421
200
- .2527
250
- .3922
300
- .5686
350
- .7739
400
- 1.0108
425
- 1.1411
450
- 1.2793
500
- 1.5794
1000
- 6.3175
1500
-14.2143
Carrying this example one step further and assuming a $1.08 product
price and previously estimated total costs per firm, the net effect on
industry and firm profits can be easily approximated. Since each firm
is fishing approximately three (2.55 rounded) fewer traps with the addi
tional firm in the fishery, total costs per firm decreased by $11.55
Notationally this can be expressed as
1
MRTS
XjX2
-AXj.
For Xi = 700 and X2 = 250, the change in Xi was
1
.3922
= -2.55.

104
times 2.55, or approximately $35.00, but industry total costs increased
by $12.99. This amount is due to increased fixed costs generated by
the additional firm. Furthermore, industry total revenue remains un
changed since product price was held constant and landings were unchanged
due to substitution of inputs along the isoquant. However, total revenues
per firm decrease by approximately $101 because the same level of total
industry revenues was divided by one additional firm.
The analysis of the marginal rate of technical substitution between
inputs can also provide useful information in deciding which inputs
should be changed (limited or allowed to increase) to induce desired
changes in sustainable yield levels. For example, at 400 firms in the
fishery, MRTS v equals approximately unity (1.0108) and substituting
xlx2
either traps per firm (X^) or number of firms (X2) for the other at this
point would not significantly change total industry landings. As more
than 400 firms enter the industry, the marginal increase in industry
landings is greater if increments are made in traps per firm than if
additional firms are allowed in the industry. At 425 firms the marginal
product of traps per firm (MP ) is 14.1 percent greater than the margi-
X1
nal product of number of firms (HP.. ); and at 500 firms, MF* is 57.9
X2 Xi
percent greater than MP^ This suggests that once the number of firms
x2
exceeds approximately 425, further efficiency in industry harvesting
costs is questionable. This is assuming, of course, that proportionate
increases in costs per trap are not unreasonably higher than costs per
firm, which is highly unlikely. Therefore, if some reasonable level of
profit maximization is part of the overall management goal, no more than
425 firms should be allowed to enter the industry, based on the assump
tions of this analysis.

105
Ridgelines
The boundary lines shown in Figure 13 indicate the maximum amount
of one input that can be combined with another input without causing
profits to be negative. This boundary is calculated as those points
1
where the firms total revenue equals total cost. The boundary lines
were calculated by setting total revenue minus total operating cost
equal to zero and then solving for each input in terms of the other.
The economically feasible combinations of traps per firm (Xj) and number
of firms (X2) are shown in Figure 13. The area between the ridge lines
defines the region of profits for the firm. Note that any number of
firms beyond approximately 950 will result in negative returns at any
level of trap use. The minimum number of firms required to yield reve
nues equal to costs was 16. The left-hand ridge-line asymptotically
approached this limit of firms (X2), but beyond the realistic range of
traps per firm (Xj) The production function specified that a minimum
of 51 traps per firm was required to land a positive yield, but when
costs of production are considered, at least 207 traps per firm were
^The right-hand ridge-line is expressed as the following relation
ship :
3l 62
P (K ) = P + TC X2
y xj x2 y
The left-hand ridge-line can be expressed as
A A
$2 61
P K P 1,876 X2 = p 11.55 XiX2
y y X2 z y Xi 1
where,
A
k = a 83X3 977380.707,
X3 = 77.591,
TC = total operating costs (previously defined), and
P^ = $1.08 per pound.

106
required, as indicated by the zero slope of the lower left-hand ridge
line. The feasible range for traps per firm increased above 250 traps
as revenues remained above costs.
Summary of Management Tools
When combined with reliable input cost information, isoquant analy
sis can be a very effective tool in evaluating the impact of management
strategies. Discrete analysis is useful if one of the input levels has
been pre-determined, which may often be the case due to social and in
stitutional constrains!. An unconstrained maximum economic yield can be
determined by solving the first order conditions of the industry profit
function. If inputs are limited, maximum economic yield can be derived
by substituting the particular input constraint and an estimate of the
optimal profit maximizing level cf the other input into the bioeconomic
industry harvest model.
These tools have been developed as a result of this study to aid in
the design and evaluation of management strategies. With this goal in
mind the remainder of this chapter is devoted to analyzing a few selected
traditional management programs and a suggested management strategy de
signed from the tools presented in this study.
Analysis of Traditional Management Programs
Types of traditional management programs considered in this study
were (a) regulating inputs through licensing and (b) issuing landings
quotas. Specific evaluation criteria included were industry revenues,
harvesting costs, and enforcement costs. Revenues to the state to cover
implementation and enforcement costs were analyzed with respect to
revenues available from license fees and/or taxes on landings.

107
For each of the programs analyzed the following assumptions were
made, unless otherwise specified: ex-vessel price per pound (Py) equaled
$1.08 (1974 mean price); number of firms in the industry was 400
(1973 level); traps per firm (X]) was 618 (sample survey mean); desired
level of landings (Q) equaled 5 million pounds (1973 level); and total
cost per firm equaled $1876 plus $11.55 per trap (estimated).
Licensing Traps
Licensing of traps and the charging of a fee increases costs but
appears economically and politically feasible, provided that some form
of "grandfather clause" is included which limits the number of firms in
the industry to at least those that were previously fishing.^ As the
cost of traps increases, the number of traps per firm must be reduced
to obtain higher marginal productivities so that the value of the margi
nal product can equal the higher trap cost. This would reduce effort in
the form of traps as captains attempt to maximize profits.
As a way of illustrating the effects of this program, consider the
analysis in Table 15. Total landings would be 6.28 million pounds and
average firm profits would be $7,325, if 618 traps were employed per
firm. Given assumed desired annual landings of 5 million pounds, a re
duction in average traps to 400 per firm would be required. Industry
profit would be $2.65 million after the reduction, a portion of which
may be taxed through a license to finance the management of the program.
After deducting opportunity costs in the form of captain's wages and
A "grandfather clause" refers to legislation which states that
fishermen licensed prior to the enactment of some limited entry
regulation must be allowed to remain in the fishery.

Table 15. Analysis cf alternative levels for number of traps per firm (X^) assuming number of firms (X2) equals 400, mean seasonal
water temperature (X3) equals 77.591F, ex-vessel price per pound (P ) equals $1.08, and trap license fee equals $1.00
per trap, economic study of Florida spiny lobster industry
Total Industry
Per Firm
Number of
Firms (X;)
Landings
(Q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
Landings
(q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
1000
7,170,570
7,744,215
5,770,440
1,973,815
17,926
19,361
14,426
4,935
eoo
6,810,576
7,355,422
4,766,400
2,509,022 .
17,026
13,389
11,916
6,473
700
6,553,437
7,077,712
4,264,400
2,813,312
16,384
17,694
10,661
7,033
618
6,280,487
6,782,926
3,852,760
2,930,166
15,701
16,957
9,632
7,325
* 557
6,025,310
6,507,335
3,546,540
2,960,795*
15,063
16,268
8,866
7,402*
500
5,730,593
6,139,041
3,260,400
2,928,641
14,326
15,473
8,151
7,322
429
5,253,958
5,674,275
2,903,980
2,700,295
13,135
14,186
7,260
6,926
400
5,010,605
5,411,454
2,758,400
2,653,054
12,527
13,529
6,986
6,633
300
3,810,626
4,115,475
2,256,400
1,859,075
9,527
10,289
5,641
4,648
* 207
1,654,139
1,786,470
1,739,540
-3,070*
4,135
4,466
4,474
-8*
Note: Asterisks highlight minimum and maximum positive profits for industry and/or firms and respective level of traps per firm (Xj).
108

109
returns to investment from each firm's profit, the residual could be
considered the maximum amount in total fees the firm could afford to
pay. This value divided by the number of traps is the maximum trap fee.
If management objectives would insure the maintenance of a minimum
$5,000 salary for the captain and average profit of $7,325 for the firm,
the maximum trap license fee would be $5.81^ per trap. Any difference
between a lower fee and $5.81 would be considered residual returns to
ownership. To compute the values in Table 15, the trap fee was treated
as an additional variable cost to the firm and added to the estimated
$11.55 cost per trap.
The optimum number of traps per firm which resulted in maximum pro
fits per firm ($7,970) was 580 (Table 13) when no license fee was im
posed. Optimum number of traps decreases to 557 if a $1.00 per trap
2
license fee is charged. This results in maximum profits per firm de
creasing to $7,402 (Table 15). The number of traps per firm required to
maintain industry landings at the assumed desirable management level of
5 million pounds would not change, but profit per firm at this level
would drop 5.7 percent to $6,623 due to the trap license fee. Profit
per firm ranged from near zero to $7,402 with the license fee (Table 15),
compared with near zero to $7,970 without the license fee (Table 13).
The percentage difference in firm profits ranged from 6 to 17 percent
and was greatest at the higher levels of traps per firm (Xi). Beyond
207 traps per firm, the firm does not return a profit if a $1.00 license
must be paid. This source compared with 205 traps per firm without a
^($7,325 $5,000) t 400 traps = $5.81 maximum license fee.
2
Considered In the range of a politically feasible fee.

110
license fee. Notice that beyond 400 traps per firm no regulation of
traps is needed to maintain the desired harvest of 5 million pounds if
the number of firms is limited to 400.
As estimates of enforcement and implementation costs increase the
license fee would need to be adjusted accordingly. The estimates pre
sented in this section would change as different management objectives
and values are assumed for ex-vessel price (P ) number of firms (X2) ,
and the trap license fee.
Such a program may be impractical since the number of traps per
firm is not easily regulated. It would be extremely difficult and expen
sive to regulate the number of traps a firm is fishing. However, the
above analysis provides valuable information with respect to the results
expected as number of traps per firm varies. Further analysis of imple
mentation and enforcement costs may be warranted before any attempt to
manage trap numbers can be a feasible management alternative. Otherwise,
this management program may be deferred until more cost-effective means
of regulating traps are discovered.
Licensing Firms
This type of management program is similar to licensing traps in
that it induces an increased cost per firm through a fee. As firm costs
increase only the more efficient fishermen will be able to make a profit
and remain in the industry. A program that restricts the number of firms
could also require restrictions on number of traps and/or landings but
these restrictions were net assumed in this analysis. For illustrative
purposes a license fee of $1000 per firm was assumed feasible (Table 16).1
Refer to Table 12 for some comparable levels of number of firms
(X2) assuming no firm license fee.

Table 16. Analysis of alternative levels for number of firms (X2) assuming traps per firm (Xj) equals 700, mean seasonal
water temperature (X3) equals 77.591F, ex-vessel price per pound equals $1.03, and license fee per firm equals
$1,000, economic study of Florida spiny lobster industry
Total Industry
Per Firm
Number of
Firms (X2)
Landings
CQ)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(1!)
Landings
(q)
Total Revenue
(TR)
Total Cost
(TC)
Profit
(n)
* 121
3,871,959
4,181,715
1,326,281
2,835,434
32,000
34,560
10,961
23,599*
175
5,058,235
5,462,894
1,918,175
3,544,719
28,904
31,217
10,961
20,256
* 211
5,511.756
5,952,696
2,312,771
3,639,925*
26,122
28,212
10,961
17,251
249
5,843,203
6,3)6,059
2,729,289
3,536,770
23,487
25,366
10,961
14,405
400
6,553,437
7,077,712
4,384,400
2,693,312
16,384
17,694
10,961
6,733
400
6,786,024
7,328,906
5,480,500
1,848,406
13,572
14,658
10,961
3,697
* 694
7,046,092
7,609,780
7,606,934
2,846*
10,153
10,965
10,961
4*
966
7,234,825
7,813,611
10,588,326
-2,774,715
7,489
8,089
10,961
-2,872
Note; Asterisks highlight
minimum and maximum profits for firms and/or industry and respective number of firms (X2).
111

112
Profits per firm decreased approximately six percent as a result of the
$1*000 firm license fee with a range from $23,599 for 121 firms to $4
for 694 firms. Total industry costs increased with the license fee and
ranged from $1.3 million for 121 firms to $10.6 million for 966 firms.
As a result, the optimum number of firms for maximum industry profit de
creased from 225 firms (Table 12) to 211 firms. Total industry landings
were reduced by 336,447 pounds due to fewer firms fishing but profit per
firm increased by $2,846 because total industry cost was reduced more
than total industry revenue. The optimum level of firms for maximum
firm profits remained the same at 121 firms as a result of the parallel
shift in the industry cost function.
Implications of this analysis are that inputs (traps) used in the
fishery would be reduced through rational economic behavior of firms
when license fees are charged cr. a per firm basis. License fees could
be set to allow the desired level of firms to maximize profits while
harvesting the level of landings desired by management authorities.
Licensing firms would appear to be a more manageable and enforceable
program for regulating entry of effort into the fishery due to the rela
tively fewer number of firms than traps in the industry and current
craft registration requirements.
The number of licenses issued would be based on desired levels of
traps per firm (Xj), landings (Q) and expected prices of inputs and
outputs. If traps are not regulated, limiting firm numbers does not
guarantee that the desired harvest level selected would not be surpassed
if the harvest level desired is less than MEY. Depending on the impor
tance of maintaining a desired level or landings, a landings quota could

113
be attached to the firm license to insure actual landings equal projected
desired landings.
Landing Quotas
Under this management alternative each firm would be allocated a
percentage of the desired harvest. This percentage could be based on
landing records of individual firms and desired harvest levels. The de
sired harvest level would be announced prior to the opening of the sea
son. For example if each firm of the 400 in the industry were allotted
.25 percent of an estimated 5 million pound harvest level, the landings
quota per firm would be 12,500 pounds. Profits per firm would be a
function of fixed costs plus the number of traps each firm fished since
the number of traps per firm determine total cost. In order that effi
ciency and technological innovation would not be impeded, firms could be
allowed to lease part or all of their quotas at the market price. To
prevent monopolistic practices from developing a maximum number of quotas
per firm could be established.
An alternative to establishing a constant quota per firm would be
to vary the quota per firm based on percentages of previous years' land
ings. For example, percentages could be 60 percent of the first year,
25 percent of the second and 15 percent of the third. This absolute
figure is adjusted up or down by a constant percentage per firm depend
ing on the percentage increase or decrease in the estimated sustained
yield for the coming season. Other activities such as leasing would not
change.
The license fee paid for the quota could be based on estimated pro
fits per firm in conjunction with implementation costs as discussed

114
previously for the. firm licensing program. The quota limits per firm
could be set forth as a percentage of each firm's expected total reve
nues from landings. For example, in Table 12, with 400 firms fishing
700 traps each, profit per firm was $7,734 without any license fee.
Assuming that total implementation and enforcement costs of the program
would be $800,000 or $2,000 per license, firm profits would be 57.6 per
cent instead of 77.6 percent of total costs. To enhance the acceptabil
ity of the fee charge next year's license fee could be set at 11.3 per
cent of the previous year's total revenue ($2,000 v $16,320) instead of
25.9 percent ($2,000 $7,734) of the previous year's profit per firm.
Quotas could be offered for sale on a first come, first serve basis or
more efficiently by some form of auctioning. If firms exceeded their
landing quotas a fine per pound could be levied that would be severe
enough to discourage such practices.
The major advantage of a quota system is the assignment of owner
ship tG the resource. Consequently the quota system allows the free
market system to operate more easily than would the normal conditions
of a common property resource. Free enterprise is conducive to effi
ciency and technological innovation. As the marketing system operates
more freely, less government intervention is required, leading to lower
management costs. The quota system also would have the most direct con
trol over landings and, therefore, could be used for controlling landings
with minimum delay in situations where MSY has been reached or surpassed.
However, several disadvantages are associated with the quota system.
First, the quota system would require accurate information on maximum
sustainable yield levels which might necessitate considerable research
and management costs. Analytical results in this study show that current

115
landings are considerably less than MSY thus highly accurate estimates
of MSY are not required for reasons of over-fishing from a strictly bio
logical point of view. Therefore, it is questionable whether the addi
tional research expense to accurately determine MSY is justified in the
short run for management of the spiny lobster industry.
Another possible misconception is that a quota system leads to MEY.
This is not necessarily true, particularly with respect to an industry
such as the spiny lobster industry where a large percentage of landings
are caught in the beginning of the season. With a quota system, effort
can just as easily become excessive (meaning, fishing as many traps as
without the management program) as fishermen attempt to fill their quotas
early before lobsters become scarce. This situation would cause harvest
ing costs to Increase due to the larger number of traps fished.
A Suggested Alternative: Harvest Rebate Program
The harvest rebate program integrates several features of previously
discussed programs. In this program effort measured by the number of
firms would be limited and would include a license fee. The harvest re
bate program offers the flexibility of allowing each firm to maximize
landings. Finally, this program allows the market system to regulate
harvest since higher license fees will discourage inefficient fishermen.
Landings regulated in this manner could be substantially less costly to
regulate due to less government intervention than in the more traditional
management programs discussed.
These advantages are not to imply that the harvest rebate program
is "the approach" for fishery management. Rather, this program was de
signed to specifically consider problems of the spiny lobster industry,

116
but in some cases it may be applicable to other fisheries. The follow
ing is an illustration of how such a program would operate and the anal
ysis of specific effects on landings, revenues, costs, profits, and
optimum input combinations.
Configuration of the Harvest Rebate Program
Establishing this program would begin with a moratorium on all lob
ster licenses. Using the "grandfather clause" approach the total number
of firms would be initially limited to the 1973 level of 400. Next, an
accurate recording of the average number of traps fished per firm (XO
would be necessary. This parameter would serve as the foundation for
the total program in a given season.
Once the optimum number of traps (x^ ) is established using the firm
harvest model (Equation 31), the maximum number of firms required to har
vest the desired level of landings (Q) would be determined. Those firms
not allowed to enter the industry would receive rebate payments.
Who would receive permits would be a difficult question to answer.
One approach is presented here. As an initial program activity, for
example, an application deadline could be established for licenses and
rebates. At this time a range of probable license fees and rebate pay
ments would be announced. After assessing the ratio of harvesters to
rebate receivers a more accurate estimate of license fees and payments
would be announced and a three-week period (arbitrary) would be allowed
for anyone wanting to change status. The consequences of too many chang
ing status should be made clear to the participants since it could be
detrimental to them. For example, too many rebate receivers could re
duce individual payments.

Table 17. Median and mean spiny lobster landing per trap for sample of firms classified according to number of traps pci' firm (Xi),
economic study of Florida spring lobster Industry
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
No.
traps
firm
(Xi)
No.
firms
fishing
(X?*)
Landings
W/0
program
(Qn)
Landings
w I 111
program
Total cost
pee firm
ProfIt8
per
f Lrm
W/0
program
(Tt/X2)
Profltb
por
f I rrn
with
program
(r/x2*)
7.
n /X2
Incl.
lie.
f IC
Maximum
state
revenue
$
$
lb.
lb.
$
$
$
7.
$
1,000
140
7.170,570
5,010,833
13,426
5,935
25,229
325.1
2,701,160
800
156
6,810,576
4,991,626
11,116
7,273
23,441
222.3
2,522,208
700
171
6,553.437
4,996,056
9,961
7,733
21,593
179.2
2,370,060
518
190
6,280,487
4,995,138
9,014
7,943
19,379
144.0
2,172,840
500
246
5,730,593
5,002,577
7,651
7,822
14,312
83.0
1,596.540
429
328
5,253,958
4,998,679
6,831
7,355
9,628
30.9
745.544
350
400
4,496,328
5,000,376
(No limited entry program needed since require
currently exist to harvest an KEY equal to 5
more firms than
million pounds.)
200
400
1,410,665
4,996,381
(No limited
currently i
entry program needed since require
exist to harvest an MEY equal to 5
more firms than
million pounds.)
117

Table 17. Continued
(10)
(U)
(12)
(13)
(14)
(15)
(16)
(17)
Maximum
license
fee
License
fee
7. 4
ir/X2
Excl.
lie.
fee
State
revenue
Admin.
revenue
loan
rebate
payments
7. A
Total
ind.
profit
No.
firms
rcc1d.
rebate
(X2**)
Break
even
harvest
per
trap
(3EC)
$
$
7.
$
$
7.
No.
lb.
IV, 2*34
17,000
38.7
2,380,000
836,900
48.8
260
28.17
16,168
13,500
36.7
2,106,000
331,388
25.7
244
28.49
13,860
11,500
30.5
1,966,500
195,643
19.4
229
28.39
(11,820)
(26.4)
(2,021,220)
(250,363)
(32.25)
11,435
9,500
24.4
1,805,000
136,970
15.9
210
27.74
(10,100)
(16.8)
(1,919,000)
(250,970)
(28.54)
6,490
5,000
19.0
1,230,000
25,412
12.5
154
23.43
(6,000)
(6.3)
(1,476,000)
(271,412)
(25.28)
2,273
1,000
17.3
328,000
-201,560
7.3
72
16.90
(1.535)
(5.0)
(503,480)
(-26,080)
(18.06)
(No limited
entry program needed
since require more
firms than currently
exiat to harvest
an MEY equal
to 5 million pounds.)
(Ho limited
entry program needed
since require more
firms than currently
exist to harvest
an KEY equal
to 5 million pounds.)
118

Table 17.Continued
Note: Assumptions: (1) Commercial fishermen are profit maximizers; (2) Ex-vessel price, P = $i.C8 per
pound; (3) Desired hardest level for MEY = 5 million pounds (or less defined by input
levels); (4) Rebate receivers are maintained at previous levels; (5) Harvesters are
maintained at least at previous profit levels; (6) Initial number of firms, Xo = 400;
(7) TC = (1,876 + 11.55X^)X2, constant per firm with or without the program; (8) Pro
gram is self-supporting.
Definition: (1) X^ ~ assumed trap per firm level; (2) X2* = maximum number of firms required to
^2
harvest MEY, given X- ; X = j ; (3) QD Industry landings before pro-
1 l p,
K MEY
X1
gram given X2 = 400 and Xp (4) = Industry landings after program, given X2* and
X. ; (5) TC/X2 = total cost per firm before and after program, given X2 = 400 and X-p
(6) tt/X2 = profit per firm before program, given X2 = 400 and X^; (7) ir/X2* profit
per remaining firms, X2*, given X^ (including cost of license fee); (8) Maximum State
Revenue = maximum amount total Xy* could pay in license fees and still maintain pre
vious profit (it) ; (9) Maximum License Fee = maximum fee per X2* and still maintain
previous profit (it); (10) License Fee = assumed license fee, given X2* and Xj¡ ;
(11) State Revenue = total state revenue generated, given license fee; (12) Admin.
Revenue = remaining revenue for administrative costs after paying rebates; (13) % A
Ind. it percentage change in total industry profit due to program; (14) X2** = number
of firms receiving rebate (non-lobster fishing firms); (15) B.E.C. = break-even
criterion for firms choosing not to fish this season, defined as average landings per
trap.
Refer to Appendix I for computations.

120
After the three-week deadline licenses and rebate certificates
would be issued. Licenses would be paid in installments of 25 percent
down; 40 percent by September 15th, since August is usually the best
harvesting month; 25 percent by November 1st; and the final 10 percent
by the first of the year. The installment plan would closely parallel
the timing of the majority of landings. The balance of the license fee
would be paid by the first of the year when the majority of the stock
has been landed. Rebate payments would be made at the same time and
rate.
Alternatively, an auction system could be set up to determine the
first round of harvesters and rebate receivers. This has been suggested
in the literature in a theoretical framework that essentially equates
marginal cost and marginal revenue. This approach could also be used if
economic rent is an important consideration of the analysis, a point with
which this study has not been concerned.
Regulation of the harvest rebate program should not be any more
expensive than the cost of current regulatory programs. All craft and
gear must be easily identifiable from the air. More thought should be
given to legislation and regulation of designated fishing areas prohibit
ing trespassing of all non-licensed fishermen.
Hypothetical Example and Analysis of Harvest Rebate Program
The structure and bioeconomic status of the spiny lobster industry
was analyzed under the harvest rebate program assuming various levels of
traps per firm. The levels of traps per firm selected were previously
used throughout this study and ranged from 200 to 1000 traps per firm.
The results of this analysis are presented in Table .17 and include

121
numbers of harvestors and rebate receivers, profits before and after the
program, percentage changes in these profits, revenues and costs to the
state, production revenues and costs, and landings with and without the
program. The remainder of this section discusses the assumptions of the
example and the results of some of the specified levels of traps per
firm.
Assumptions
License fees were arbitrarily assigned and were assumed politically
acceptable as were administrative costs for implementation and enforce
ment of the program. Lobster fishermen were assumed to be profit maxi
mizers and thus would select the alternative which was most profitable
to their individual firm.
The ratio of harvesters to rebate payment receivers was determined
by the minimum number of firms (400 in total) required to land the de
sired industry harvest level of 5 million pounds for a given level of
traps per firm. Rebate receivers were maintained at their previous pro
fit levels. License fees were assigned with several objectives in mind,
one of which was to allow harvesters to earn a profit at least five per
cent higher than their previous level (Column 12).
Another major objective in assigning the level of the license fee
was to collect the required revenue to maintain a self-supporting pro
gram, assuming administrative costs were not greater than $250,000. In
addition, higher license fees were assessed for firms fishing larger
numbers of traps since profit percentages per firm increase as the num
ber of traps per firm increases. License fees ranged from $1,000 for
firms fishing 429 traps each to $17,000 for firms fishing 1000 traps each.

122
Total cost per firm was constant regardless of whether a license
fee was assessed because the number of traps was assumed constant among
firms. Underlying criteria used to arbitrarily assign program costs and
revenues were primarily based on the number of fishing firms (harvesters)
to be supervised and relative profit levels of these firms.
Number of traps per firm at 700
The maximum number of firms required to harvest the desired industry
level of 5 million pounds was estimated to be 171 firms fishing 700 traps
each (Table 17). If only this number of firms choose to participate in
a harvest rebate program as harvesters, 229 firms would elect not to fish
for lobsters and would collect a rebate payment of $7,733 each for the
season (Row 3, Columns 6 and 16). These rebates would cost the state
$1.8 million ($7,733 x 229). Revenues for harvesters in the program
would increase approximately 179.2 percent to $21,593 per firm before
license fee charges (Row 3, Columns 7 and 8). At this rate the state
could charge a maximum license fee per firm of $13,860 and the firm would
be at least as well off than before the program at $7,773 profit per firm
(Row 3, Columns 6 and 10). Approximately $2.4 million (Row 3, Column 9)
in revenue to the state for rebate payments and management of the indus
try would be generated.
Assuming the regulatory agency set the license fee at $11,500 to
cover rebate payments and program expenses, total profit per firm (har
vester), estimated to be $10,093, would be 30.5 percent above profits
before the program. Rebate receivers would collect as much as they were
making before the program without expending any costs. In addition,
these firms could invest their time, skills, and capital elsewhere.

123
Total industry profits could increase (often including license fees) by
19.4 percent. Incomes to fishermen would be improved, resources would
be allocated in an efficient manner and the stock of spiny lobsters
would be in no danger of over-exploitation.
Number of traps per firm at 618 and 500
Assuming 618 and 500 traps per firm (Rows 4 and 5) profits per firm
and total industry profits could also be increased under the harvest re
bate program compared with the profit structure prior to the program.
However, as the number of traps per firm (Xi) would decrease profits for
each firm and for the industry would decrease (Columns 8, 12, and 15).
This situation would occur because the constant rate of increase in
total cost per firm would be greater than the rate at which the MRTS
xlx2
would decrease, thus resulting in a less steep increasing total revenue
function within the range of data. For example, if a decrease in traps
per firm were induced by regulations that limited trap numbers per firm,
total cost per trap would decrease. As the number of traps would de
crease, MRTS would increase. As MRTS v increases along the iso-
xlx2 xlx2
quant (Figure 13) the marginal productivity of a firm decreases, thus
requiring more firms in the industry to harvest 5 million pounds. More
firms increase total industry costs and thus decrease net returns
(profits) to the firms and the industry.
With the harvest rebate program, profits per firm (Column 12) in
creased 24.4 percent to $9,879 and 19.0 percent to $6,490 for firms fish
ing 618 and 500 traps, respectively.^ License fees were assumed at
Profits remaining above the license cost were derived by subtract
ing Column 11 from Column 7 in Table 17.

124
$9,500 and $5,000, respectively, to cover rebate payments plus a balance
of $136,970 and $25,412, respectively, for administrative costs. At 618
traps per firm (Column 16) 210 firms received a rebate for not fishing
(Column 16). Then the number of firms decreased to 154 as traps per
firm decreased to 500 because more firms are needed to harvest the as
sumed 5 million pounds. As a result of the rebate program, total indus
try profits increased 15.9 percent with 618 traps per firm and 12.5 per
cent with 500 traps per firm.
When revenues for administrative costs (Column 14) are not adequate
to meet the $250,000 budget assumption license fees would have to in
crease (Column 11, parentheses) to a level that will generate the re
quired revenues. For example, if the harvest rebate program was imple
mented and each firm was allowed to fish 500 traps, the number of firms
choosing to fish would be 246 while the number of rebate receivers would
be 154. Maximum revenues to the state (Column 9) would be $1,596,540,
while program costs for payments to rebate receivers would be $1,204,588
(154 x $7,822). The $5,000 license fee would pay for rebate payments
but would leave only $25,412 to administer the program. To remedy this
deficit the license fee would need to be increased to $6,000, resulting
in a $271,412 budget for administrative costs, excluding rebate payments.
This situation would decrease profit per firm from 19.0 to 6.3 percent
(Column 12). In the case of 429 traps per firm the required revenues
could not be raised without decreasing profit per firm to less than 5
percent. In this case the program was not able to totally support itself
(Column 14, Row 6).

125
Number of traps per firm at 429
At 429 traps per firm the program could not support itself and would
experience a $201,560 deficit (Column 14). Only $328,000 of the $529,560
(Column 16 x Column 6) rebate payments could be met with a license fee
of $1,000. At this level firm profits would increase 17.3 percent com
pared with profits outside the program. To help make up the deficit in
rebate payments, the license fee would have to be increased to $1,535
which would decrease firm profits to 5.0 percent. Still, a $26,080
deficit in payments would remain with no budget for administrative costs.
Another alternative would be to reduce rebate payments to non-fishermen
to a profit level less than what they were making fishing for lobsters.
Assuming idle capital and labor resources were invested elsewhere, this
may be a feasible alternative.
Number of traps per firm at 350 and 200
If firms were limited to 350 and 200 traps each, all firms would be
needed to harvest the 4.5 and 1.4 million pounds, respectively. Since
more firms would be required to harvest the desired level of 5 million
pounds no management program would be needed since more firms than cur
rently exist are required to harvest MEY (Rows 7 and 8). The average
product per firm with 350 traps was 11,241 pounds and with 200 traps was
3,527 pounds. A total of 445 firms with 350 traps each, or a total of
1,416 firms with 200 traps each, could be allowed in the industry to
harvest an MEY of 5 million pounds.
Overall summary of analysis (Table 17)
For the range of 200 to 1000 traps per firm selected industry land
ings were maintained at 5 million pounds under the program, whereas

126
landings without the program would have ranged from 7.1 to 1.4 million
pounds, assuming all 400 firms in the industry fished (Columns 3 and 4).
No limit on the number of fishermen was required when fishermen were
limited to 350 or less traps each. Firms were limited to 328 if each
fished 429 traps and to 140 if each fished 1000 traps (Column 2). Net
profits for this group increased in the range from 17.3 to 38.7 percent
(Column 12), for 429 and 1000 traps per firm, respectively.
Total program cost ranged from $2.3 million (1000 traps per firm)
to $0.5 million (429 traps per firm) and was paid for by iicesne fees
ranging from $17,000 for firms fishing 1000 traps each to $1,535 for
firms fishing 429 firms each (Columns 11 and 14). Except for a $26,000
deficit assuming each firm fishing 429 traps the program was totally self
supporting and firms receiving rebate payments were maintained at their
previous incomes. The increase in total industry profit with the program
ranged from 7.3 percent assuming 429 traps per firm to 48.8 percent as
suming 1000 traps per firm.
Assuming the harvest rebate program would be feasible, individual
firms, in many cases, would require a careful evaluation of their opera
tions to determine if a license should be purchased or a rebate payment
received. To aid in this decision making process a breakeven criterion
was developed as a result of this study.
Breakeven Criterion
Using the time-series data and primary data obtained from the cross-
sectional survey, an estimate was developed to provide an indication of
which firms might elect to receive payments for not fishing, given the
structure of the industry for a particular season. The breakeven

127
criterion (BEC in Column 17, Tabic 17) was based on the total cost or
total investment of the firm. This information was transformed into
average product per trap required to cover operating costs and license
fee. Thus a given firm may decide to fish a particular season if the
owner feels he is capable of harvesting an amount equal to or greater
than the BEC per trap.
To obtain the values for BEC. total cost per firm (Column 5 plus
Column 11, Table 17) was divided by the number of traps fished per firm
(Xi, Column 1, Table 17) which was multiplied times the ex-vessel price
(P ). Total firm cost includes the new license fees. The result was
y
the average product per trap (Q/X^) required to cover costs.
To evaluate this criterion, landings per trap derived from the
various data used in this study were compared with estimates of BEC for
comparable input levels. Landings per trap (Q/Xq) for the industry from
1963-73 ranged from a low of 29 pounds in 1973 to a high of 49 pounds in
1966. Landings per trap in the cross-sectional sample ranged from a mini
mum of 10.68 pounds to a maximum of 54.86 pounds for firms fishing 665
and 401 traps, respectively. The median for the sample was 21.43 pounds
for firms fishing 560 traps. The data in Table 18 illustrate the median
and mean landings per trap for the given range of number of traps fished
(X¡) in the sample.
The relatively low values of average landings per trap in the time-
series and cross-sectional data may be due to over-capitalization in
traps since no limits exist on traps. Estimated average landings per
trap (Q/Xj) with the harvest rebate program are higher than comparable

128
Table 18. Median and mean spiny lobster landings per trap for sample
of firms classified according to number of traps per firm
(Xj). economic study of Florida spiny lobster industry
Landings
Number of
traps fished per
firm
per trap
<200
200-399
400-499
500-599
600-699
700-899
>900
Total
Median
21.80
22.67
17.07
24.10
26.28
19.33
16.32
21.43
Mean
26.02
22.92
27.45
24.10
22.54
19.26
16.93
21.37
Observations 3
4
3
2
C
.)
5
3
25
breakeven estimates (BEC) as illustrated in Table 19. Estimated land
ings per trap (Q/Xj) were derived by dividing the total number of firms
in the industry after the harvest rebate program into estimated landings
after the program. Since the breakeven criterion of landings per trap
was below the estimated actual landings per trap the firm would have
some flexibility in its decision on whether to fish or not.
BEC ranged from 16.09 pounds per trap for 429 traps per firm to
28.17 pounds per trap for 1,000 traps per firm. The figures in paren
theses (Table 19) represent BEC after adjustments in the license fee
were made to compensate for deficit program costs illustrated in Table
17 (parentheses in Column 11). Estimated landings per trap ranged from
35.02 to 42.54 pounds per trap, thus resulting in a range of 54 to 21
Q/Xj can be represented notationally as
o/x Qa
Q/Xl 0S*KXi7
where,
Q/Xi = estimated average landings per trap,
Q = estimated landings with harvest rebate program
(Column 4, Table 17),
X2 = maximum number of firms required to harvest Q ,
given Xi (Column 2, Table 17), A
Xj assumed number of traps per firm (Column 1, Table 17).

129
Table 19. Analysis of landings per trap required to break-even under
the harvest rebate program for alternative levels of traps
per firm (Xj), economic study of Florida spiny lobster
industry
Number of traps
per firm
1,000
800 700
618 500
429
Q/Xi
35.79
40.00
41.74
42.54
40.67
35.02
BEC
28.17
28.49
28.39
27.74
23.43
16.90
(32.25)
(28.64)
(25.28)
(18.06)
% A
21.29
28.78
31.98
34.79
42.39
54.05
Max. No.
140
156
171
190
246
328
Firms
Note: Q/Xi is estimated landings per trap under harvest rebate program.
BEC is landings per trap required to break-even under price and
cost assumptions of harvest rebate program (break-even criterion).
% A is the percentage difference in Q/X¡ and BEC. Max. No. Firms
is the maximum number of firms allowable in the industry for
given levels of traps per firm under the harvest rebate program.
percent above BEC, respectively. For example, at 700 traps per firm BEC
was 31.98 percent below the estimated average landings per trap. At 500
traps BEC was 42.39 percent below (Q/Xj) and at 425 traps BEC was 54.05
percent below Q/X^. As traps per firm decrease, the difference between
estimated landings per trap and the breakeven level became larger. This
is due to the law of diminishing marginal rate of returns resulting in
an increasing margina] product for a trap as the number of traps per
firm decreases. Thus the program does appear realistic when compared
with expected changes in the industry structure and performance as a
result of the harvest rebate program.
One question that may be of concern about the harvest rebate program
is, "What happens if firms do not select the appropriate plan designed
for them?" Several problems could cause the estimated number of rebate
receivers and harvesters to change.

130
First, the estimation of traps per firm could be reevaluated. As
previously mentioned, considerable effort and funds could be spent to
accurately estimate average traps fished per firm. Second, the license
fee could be too high if too many firms have applied for a rebate. On
the other hand, the license fee could be too low if too many firms have
applied for a license. In the short-run, the rebate could be increased
before the suggested three-week deadline if too many license applica
tions were received. If too many applications were received for re
bates the license fee could be lowered during this period.
Finally, another problem might be that estimates of input and output
prices could be different from various sectors of the industry. The
state should be prepared to absorb the inaccuracies of the program
should the ratio still be out of proportion after short-run remedies
have failed. Program adjustments could be made the following year based
on experiences in the previous year(s).
In summary, the harvest rebate program is offered as a non-tradition-
al alternative. Its features include increased profits to the industry
and firm, depending on estimated levels of traps per firm. Since inputs
would be reduced, current over-capitalization would be reduced, allowing
more efficient harvesting through such activities as economies of scale.
More importantly the rebate program would allow the fishermen to make
the decision of whether or not to fish. It could also lead to improved
stock and fishing grounds since fewer traps and craft would be employed
in the harvesting process of the industry.

CHAPTER VII
SUMMARY AND CONCLUSIONS
Florida's spiny lobster (Panulirus argus) industry achieved tremen
dous growth during the past two decades and is presently the second most
important fishery in the state in terms of dockside value of landings.
Spiny lobster landings in Florida exceeded 11 million pounds in 1973
with an estimated retail value of over $40 million. Florida landings
represent approximately 98 percent of total U.S. landings.
The tremendous growth in landings is a result of a disproportionate
increase in inputs into the fishery. Number of spiny lobster firms,
number of traps, and size of firms (gross tonnage) have increased
throughout the past two decades. The rate of increase lias been greatest
since 1965. The increase in number of firms and total traps fished was
80 percent and 242 percent, respectively, between 1965 and 1972. During
this same period total industry landings increased only 16 percent,
while landings per firm actually decreased by approximately 60 percent.
An increase in the retail price of lobster tails from $1.50 per pound in
1960 to over $9.00 per pound in 1975 has induced the growth in inputs
employed in the spiny lobster harvesting process. Thus the immediate
problem addressed in this dissertation was that of answering economic
questions relative to industry growth. "Over investment" in capital
(gear and craft) and labor (fishermen) has occurred in an effort to
harvest a relatively fixed supply. The increased fishing effort in
131

132
the fishery also raises concern about the possibility of "over-
exploitation" of the fishery stock.
The primary objectives of this study were to (a) evaluate the
extent of fishing effort in the industry and determine both the maximum
sustainable yield and the maximum economic yield, and (b) analyze alter
native management programs which would allow for a more efficient utili
zation of the fishery stock. To achieve these objectives, two analytical
models were developed for the Florida Keys spiny lobster fishery. A
bioeconoroic model was estimated for a time period in which the biologi
cal stock was allowed to vary. The second model (firm harvest function)
was estimated for a given stock of lobster resources. With these two
models the impacts of selected management programs were analyzed by
simulating the industry with respect to estimated optimum levels of
inputs.
The scope of the study was defined to include only the Florida
spiny lobster fishery. The data for the empirical analysis represented
Monroe County, Florida, since approximately 80 percent of Florida
domestic landings are landed in Monroe County.
Theoretical considerations and industry data availability required
that the bioeconomic model be estimated as a function of traps per firm,
number of firms employed in the industry, and mean seasonal water tem
perature. The mathematical form of the model was a reciprocal equation
which represented behavior consistent with suggested theory and the cur
rent status of the industry with respect to sustainable yield and pre
sent management policies. Annual time-series data from 1963 to 1973
were used for estimation. The overall explanatory power was high.and
each coefficient was statistically significant in the model.

133
The firm harvest function was estimated from a cross-sectional
sample of lobster firms. Spiny lobster fishermen selected by a statis
tically designed sample were interviewed in 1974 concerning specific
aspects of the spiny lobster harvesting process. This data was used to
analyze the lobster harvest function for a given stock level on a per
firm basis. A Cobb-Douglas functional form model was used to relate
firm landings to the number of traps fished and fishing intensity.
Fishing intensity was measured as percentage of traps pulled per week,
number of weeks fished, and size of the craft. Location of fishing
grounds was entered in the model to adjust for area differences in fish
ing conditions. All variables with the exception of one location vari
able were highly statistically significant. The cross-sectional harvest
model was used to estimate the profit maximizing level of traps per
firm. This value was then substituted into the bioeconoxnic industry
function for traps per firm to complete the industry analysis.
Maximum sustainable yield for the industry was approximated by
observing the range of estimated maximum industry landings as traps per
firm and then firms were increased to practical feasible limits. While
one input was varied the other was held constant at actual mean, minimum,
and maximum levels employed in the industry. The estimated range in
maximum sustained yield was between 5.9 to 8.9 million pounds. For the
purposes of ths study, 8 million pounds was defined as an extreme esti
mate of maximum sustainable yield while 6 million pounds v/as defined as
a conservative estimate.
Maximum economic yield was estimated for the industry allowing both
traps per firm and number of firms to be simultaneously determined such
that maximum economic profit would be attained. Maximum economic yield

134
was estimated to be 5.8 million pounds. The optimum level of firms was
determined to be 213, each fishing 795 traps. Estimates were based on
1973-74 ex-vessel prices ($1.08 per pound) and 1973-74 total costs per
firm and per trap. These optimum levels would require a reduction of
47 percent in number of firms and a slight reduction of 1,836 traps in
the total industry from 1973 levels. Total industry landings would be
increased approximately 16 percent over 1973-74 season harvest. Esti
mates will change depending on relative changes in the cost of produc
tion and product prices. As usual, maximum economic yield was less than
the predicted maximum sustained yield.
Recognizing that maximum economic yield may not be the immediate
goal for management because of the political and social consequences of
extreme adjustments in the short-run, further analyses were completed.
The analyses considered (a) parameters from the firm harvest function
which represented current stock levels and thus would be relevant for
current management programs and (b) alternative levels of one input
while holding the other input at politically realistic levels. These
analyses provide information to regulatory agencies which could be used
in assessing benefits and costs of alternative management programs.
Fewer than the optimum number of firms would be allowed to enter
the industry if the major objective of the regulatory agency was to
maximize average net return per firm. This objective was evaluated
using value marginal product analysis with respect to the industry har
vest function. The results showed only 121 firms could be allowed to
eater the industry assuming 700 traps per firm and 1973-74 factor costs
and product price. Total industry profits would be maximized w'ith 225
firms using value marginal product analysis, thus defining the range of

135
number of firms that could enter the industry based on rational profit
maximizing objectives of the regulatory agency. As a result, total in
dustry landings would range from 3.87 million pounds with 121 firms to
5.65 million pounds with 225 firms.
Considerable substitution between number of traps per firm and num
ber of firms can be made without changing the level of landings thus
providing numerous policy alternatives. Rates of substitution between
numbers of traps per firm and number of firms were determined. Beyond
400 firms substantial increases in number of firms would be required to
maintain landings due to a reduction in traps per firm. An analysis of
the possible range of combinations of traps per firm and number of firms
where profits are positive was presented with the use of isoquant map.
The conclusion was that profits would not be possible if more than 900
firms would enter the industry, nor would it be feasible for a firm to
fish with less than 75 traps.
For purposes of this study "management" was defined to include
maintaining current levels of inputs, as well as increasing or decreas
ing their levels. Traditional programs were analyzed by simulating the
behavior of the spiny lobster fishery under programs which would license
traps, license firms and issue landing quotas. Finally, an alternative
management scheme, entitled "harvest rebate program," was suggested.
This program would incorporate aspects of the traditional system.
Programs were analyzed under the previously stated factor costs
and product price assumptions. The desired value for landings was as
sumed to be 5 million pounds. Seven hundred traps were determined as
optimum for 1973-74 stock levels for profit maximization.

.136
Licensing of traps appears feasible in a theoretical framework if
performed in conjunction with some form of "grandfather clause" legisla
tion. The objective would be to increase costs per trap to a level
where the level of traps fished would be such that the value of the mar
ginal product would be equal to the marginal factor cost of a trap.
Data for this analysis was obtained from the survey of spiny lobster
firms and results showed that typical firms in the industry would be
required to reduce number of traps fished. Assuming 400 firms in the
industry, firm and industry profits are maximized at 557 traps per firm.
No profits are returned if a firm fishes less than 207 traps. Further
more, if less than 400 traps per firm are fished, no regulation of traps
would be needed to maintain the desired 5 million pound level for land
ings. Licensing of traps from a pragmatic standpoint, however, may not
be feasible since policing the number of traps per firm would be diffi
cult and expensive to regulate.
The firm licensing program was essentially based on the theoreti
cal motive of increasing marginal factor costs of the firm to a level
where the value of the marginal product of an additional firm added to
the industry is equal to the marginal factor cost of the firm. Such a
program may or may not limit the number of traps fished and/or landings.
Seven-hundred traps fished and a $1000 license fee were assumed per
firm for the simulated example.
The analysis showed profit per firm was maximized with 121 firms,
while total industry profit was maximized with 211 firms in the indus
try. Total landings were 3.87 million pounds for 121 firms compared
with 5.51 million pounds for 211 firms in the industry. If more than
694 firms entered the industry no profits were earned. If each firm

137
fished 700 traps, no more than 175 firms could be allowed in the industry
in order to maintain a desired harvest level of 5 million pounds.
Licensing firms appeared to be a more manageable program for regu
lating entry of effort into the fishery than licensing traps since a
much smaller number of units (number of firms) would have to be regu
lated. The number of licenses issued would be based on the regulatory
agency's objectives and selected parameters for traps per firm, landings,
and expected prices of inputs and outputs. Furthermore, if traps were
not regulated, limiting the number of firms would not guarantee that
the desired level of landings would be achieved.
Landing quotas could be useful as a management tool for expedient
adjustments to precisely control industry landings. Since current land
ings were less than the estimated range of maximum economic yield levels
precise control of landings was not viewed as an immediate concern in
the Florida spiny lobster fishery. Consequently, an example of the in
dustry structure and behavior regulated through landing quotas was not
simulated. However, a quota fee could be assessed in a similar manner
to the firm licensing program. The major advantage of the quota system
would be that it would allow the harvesting process to operate freely
to optimally combine inputs. Free enterprise is conducive to effi
ciency and technological innovation, which could lead to reduced total
industry costs in the long run.
Conversely, disadvantages of the quota system are: (a) that an
accurate estimation of maximum sustainable yield would be needed which
could generate high research costs; (b) maximum economic yield would
not necessarily be attained since the incentives of over capitalization
still remain; and (c) the fisherman's motivation due to dreams of "the

138
big catch" would be destroyed if he were limited to a predetermined har
vest level.
An alternative approach to management, the "harvest rebate program,
was offered for further consideration. This program integrated several
features of the previously discussed traditional management programs.
Effort in the form of firms would be limited and license fee would be
required. The harvest rebate program offers the flexibility of allow
ing each firm to maximize landings. Finally, this program would allow
the market system to regulate harvest since higher license fees should
discourage inefficient fishermen. Landings regulated in this manner
could be substantially less costly to regulate due to less government
intervention than would be the case in the more traditional management
programs discussed.
The harvest rebate program was analyzed simulating the industry
behavior under various levels of traps per firm. License fees were
ranged from $17,000 to $1,000 per firm, with the optimal number of firms
ranging from 140, each fishing 1,000 traps, to 328, each fishing 429
traps. Those fishermen choosing not to fish would receive a rebate pay
ment equivalent to the average firm profit without the program for a
specified level of inputs. The increase in profit per firm for those
fishermen electing to pay the license fee ranged from 38.7 percent with
140 firms in the industry to 17.3 percent with 328 firms in the indus
try. Profits for each of the 400 firms before the management program
ranged from $5,935 for firms fishing 1,000 traps to $7,943 for firms
fishing 618 traps. Maximum revenue to the state, given the assumptions
of the analysis, ranged from $745,544 for 328 firms to $2,701,160 for
1!
140 firms.

139
Finally, a breakeven criterion was developed to help the fisherman
decide whether he should fish under the harvest rebate program, or elect
not to fish and receive a rebate payment. The criterion was in terms of
the minimum pounds per trap necessary to maintain a profit level equal
to or greater than the profit level without the program. The conclusion
was that a firm must harvest an average of 16.90 pounds per trap (assum
ing 328 firms, each fishing 429 traps) to 28.49 pounds per trap (assum
ing 156 firms, each fishing 800 traps) before it would be economically
feasible to purchase a license to fish. Thus, fishermen participating
in the program would operate with considerable flexibility, firm and
industry profits would be equal to or greater than would be the case
without the program, and the program would be totally self-supporting.

APPENDICES

APPENDIX A
Table Al. Spiny lobster landings and dollar value, Florida and U.S., 1952-73, economic
study of Florida spiny lobster industry
u.
s.
Florida
Cent 8
Cent 6
Percent of U.S.
1,000
1,000
per
per
Year
Pounds
Dollars
Pound
Pounds
Dollars
Pound
Pounds Dollars
1952
2,419
740
30.6
1,612,400
403,100
25.0
67
55
195.5
2.745
752
27. 4
1,995,000
399,000
20.0
73
53
1954
2,849
837
29.4
1,947,300
428,4U5
22.0
68
51
1955
3,154
962
30.1
2,295,400
527,9/2
25.0
73
55
1956
3,849
1,210
31.4
3,113,000
825,056
26.5
81
68
1957
4,687
1,500
32.0
4,039,800
1,123,545
27.8
S6
75
5 958
3,588
1,226
34.2
2,954,307
836,651
28.3
32
68
1959
3,698
1,268
34.3
3,130,733
954,605
30.0
36
75
I960
3,210
1,344
41.9
2.S48.540
1, i 00, ?. ? 4
33.6
89
82
1561
3,235
1,263
39.0
2,603,439
969,303
34.6
S7
77
1962
3,664
1,561
42.6
3,107,000
1,187,127
38.2
35
76
595 5
4,130
1,798
43.0
3,535,194
1.407,746
39.3
86
78
1564
4,063
1,830
46.0
3,631,130
1,362,163
43.0
89
83
1?65
6,237
3,626
58.1
5,714,093
3,219,741
56.3
92
89
1966
5,844
2,832
49.3
5,350,266
2,*68,969
46.1
92
86
1967
4.86S
S.PS
64.2
4,413,5 .7
2.732,724
61.9
91
88
1966
7,476
5,367
71.8
C 155,056
-,6 08, o 9
71.6
82
82
1969
8.781
6,310
71.9
7,571,733
5,257,5-2
69.4
86
S3
1970
10,345
6, 332
61.2
9,S59,*£2
5.918.479
60.0
95
9/4
1571
3,439
7,907
93.7
p
7,0*36,538
86.0
97
89
197?
* \ 02 i
i 1.TSg
7 03. t
10,r
10,986,234
1C 3..3
95
96
1972a
il.807
12,173^
103.1
1) ,416,?82
U,771,425
103. J
Yt
97
1973
9,872
10,567
107.0
v, o',:
10,221,2 42
105.7
98
97
1973*
11,376
12,007
105.5
li J72 ."fs'1
11,661 ,l-*l
104.4
53
97
Source
National
Marine
Fisheries S
erv.c.*. Fishery
Statistic. cf the I n
ited States
(fore il ly Bureau
i o Comercial Fishery's),
i.S. Government Prin
ting Office,
Washington, D.C.
Annual I-
sues, 19*32-71.
National
Marine
Fisheries 5
civ ice, Flori da
-endings (fn:
r.ierly E
urc.au of
Comercial Fisheries), U.S.
Government Pri
r.:ing Or ice,
hashing
ton, D.C.
Monthly
and annual issues,
19/1-73.
Note:
From per so
n&I interviews with
staff of the Statistics and
H*3 rke t
!ciws Division.
;;hfs ,
of.DC, it was indicated that ap
proxi.-vate.ly 80-
93 per-cat. o
acta I
:and:.:*s are
doc ur
need. For
example,
ic\ 1973 it
is c-cin-ited that two ;vlh
on
-of unrecorded
spiny lobster landings from Florida
were mike ted l
n Geo eg a. I
ven., are
based on
person
al opinions
of scat
1st leal analysts collect In
g and analyzing the d
ata icd are
not documented facts.
*0ui o
f soasen landing? I
Deluded for
1972 2nd 1973
were 782,974
i: d 1 5C
4,480.
reapec
lively. These arc
lanelags iu
Florida ports
from foreign 1
witers daring the
closed
season in
Florida
allowed due
co nev 1972 legislation.
The following data for out of season
landings were
obtained from
ishori
es Statistics,
Southeastern Fisheries Center, U.S.D
C., boAA, NMFS
, Miami, Florida.
To.r
East
Coast
West
Coast
Florida
Toral
Cents
Founds
Dollars
Pounds
Do 11 a r 3
Pounds
Dollars
-* per
Pound
1972
530.734
532,907
252,240
252,224
782,974
785.131
100.3
3973
1,25f,351
1,JOG.551
245,179
249,348
1,504,489
1,4 JV.S89
95.7
t,
Eat lifted by 11,807 x $1,031 12,173.017
141

zn
Table Bl. Spiny lobster capital and labor inputs, Florida west coast, 1952-72, economic study of Florida
spiny lobster indusLry
Fishermen
Boats
Vessels
Traps
Firms
Traps
Per Firm
On
Vessels
On Boats
Regular Casual
Total
No.
No.
Cross
Tonnage
No.
No.
No.
1952
0
71
0
71
54
0
0
4,500
54
83
1953
0
70
0
70
55
0
0
6,500
55
118
1 9 Vi
u
83
28
115
71
2
13
11,490
7 3
160
1955
4
61
10
75
61
2
14
12,700
63
202
1956
28
80
18
126
57
14
104
16,775
71
236
1957
49
138
10
197
83
25
126
21,720
103
201
1958
33
106
8
347
88
17
142
23,221
105
221
1959
30
174
20
224
159
17
134
33,612
176
291
1960
29
192
18
239
132
16
171
54,640
168
325
1961
32
170
11
213
124
16
166
38,990
140
279
1962
40
192
7
239
151
20
212
58,250
171
341
1963
44
233
12
289
162
24
261
60,050
186
323
1969
68
2 J!i
104
410
214
34
338
79,553
248
297
1965
56
306
24
386
188
23
308
89,700
216
415
1966
104
300
12
416
210
58
824
74,550
263
278
1967
14 3
330
24
497
224
75
1189
91,300
299
307
1968
323
214
12
549
135
137
34 33
93,500
272
362
1969
184
255
20
459
176
92
2185
96,955
268
362
1970
287
331
17
635
214
123
3534
150,050
337
445
1971
364
259
39
662
195
142
4184
147,037
337
436
1972
350
333
37
720
238
155
4006
174,490
393
445
Source:
National
Narine Fisheries
Service,
Fishery
Statistics
of the
United Sta
,tes, (Formerly Bureau of
Commercial Fisheries), U.S. Government Frintlng Office, Washington, D.C., Annual Issues, 1952-72.
APPENDIX B

APPENDIX C
Table Cl. Input/Output relationships, Florida west coast, 1952-72,
economic study of Florida spiny lobster industry
Year
Pounds
Per Trap
Dollars
Per Trap
Pounds
Per Firm
Dollars
Per Firm
1952
213
53
17,717
4,429
1953
134
27
15,887
3,177
1954
62
14
9,896
2,177
1955
93
21
18,802
4,324
1956
137
35
32,408
8,363
1957
154
42
30,957
8,437
1958
100
28
22,205
6,218
1959
78
23
14,987
4,421
1960
39
15
12,674
4,879
1961
54
18
15,010
5,148
1962
42
16
14,238
5,436
1963
46
18
14,896
5,808
1964
39
16
11,473
4,885
1965
49
28
20,301
11,423
1966
49
22
13,672
6,191
1967
30
18
9,154
5,601
1968
40
29
14,415
10,398
1969
48
34
17,360
12,406
1970
46
27
20,332
12,131
1971
32
28
14,068
12,145
1972
20
21
13,069
14,003
143

APPENDIX D
CROSS-SECTIONAL DATA COMPUTATIONS
Definitions:
x\ = (TR) average number of traps fished for the season.
X2 = (PWK), average number of rounds per week for the season.
X3 = (WK), number of weeks fished during season (36 maximum).
X4 = (LOWD), size of hull in square feet; computed as hull length
(LO) times hull width (WD).
X5 = (DU), dummy variable for upper Keys; DU = e if included
and 1 if excluded.
xg = (DL), dummy variable for lower Keys; DL e if included
and 1 if excluded.
i = months, 1, 2, ... 8 (August March).
PULL = pulling a trap out of the water once (also termed hauling).
TOTAL PULLS = total number of times a trap was pulled (P) out of
the water (could be same or different trap(s)).
ROUND = pulling all traps fished, once.
R. = total rounds per month i.
x
TOTAL ROUNDS = total number of times all traps fished were pulled
(R).
SET PERIOD = length of time a trap sets between pulls (SP).
SF^ = set period for month i.
D, = days per month i.
LG = hull length.
WD = hull width.
T^ = traps fished in month i.
DATA COLLECTED (or known): T SPj[> D x3, LO, WD, x5, and x6.
144

145
DERIVATIONS:
xi
P
F.
i
R
x2
x4
P
R (1)
8
I (T ) (R ) (2)
1=1
Pi
SP.
8
E
i=l
R.
(3)
(4)
R_
x3
(5)
(LO) (WD)
(6)

9 VI
Table FI. Spiny lobster landings and dollar values, Florida east and vest coasts, and Monroe County, 1952-73, economic study of Florida spiny
lobster industry
Y?d r
FTOPIfiA
FAST COAST
WEST
COAST
MOSROE
COUNTY
Pound*
Dollnrs
c/lb.
Founds
On]lnra
C/Jb.
Pounds
Pollnra
C/lb.
2 Florida
lbs. Dollars
Founds
Dollars
c/lb.
2 Vest
lbs.
Co%st
Dollars
1552
1.612,400
403.100
25.0
655.700
163,925
25.0
956,;o0
739,175
25.0
59
59
447,396
Na
NA
47
NA
1 VO
1.975.000
397,000
20.0
1,171,200
224.740
20.0
M73,MOO
174,760
21.0
44
44
573.847
NA
NA
66
NA
1534
1.947,300
428,406
22.0
1,223,300
269,126
22.0
/24,000
159,280
22.0
37
37
722,444
NA
NA
100
NA
1555
2.295,400
527,942
23.0
1,079,400
24B.262
23.0
1,216,000
279,680
23.0
53
53
1,210,109
NA
NA
100
NA
1956
3,113,000
825,056
26.5
793,800
227,818
28.5
2,314,200
597,238
25.6
74
72
2,308,836
NA
Na
100
NA
1957
4,039.800
1,123,545
27.8
651,300
200,112
30.7
3,388,500
923,433
27.3
84
82
3,333,541
NA
NA
100
NA
1 VO
2.954,J07
834,451
28.3
677,787
383,772
29.3
7 "ll 570
f 9
28.0
79
78
2,328,406
NA
NA
100
NA
1959
3,180,733
954,605
30.0
542,9/9
176,468
32.5
2,637,754
776,137
29.5
83
82
2,635,118
NA
NA
100
NA
I960
2,848.540
1,100,284
38.6
719,344
280,544
39.0
2,129,19.;
819,740
38.5
75
75
2,126,349
813,664
38.5
100
100
1961
2,803,439
969,303
34.6
702,041
248,523
35.4
2,101,398
720,700
34.3
75
74
2,099,829
720,241
34.3
100
ICO
1942
3.107,000
1,187.177
38.2
672,400
259,546
38.6
2,434,600
927,581
38.1
78
73
2,434.148
929 3 '* *
53.2
100
100
1663
3.585,194
1,407,746
39.3
814,604
327,377
40.2
2,770,590
1,080,369
39.0
77
77
2,770,100
1,080,339
39.0
100
100
1964
3,631,130
1,562,163
43.0
735,718
350.537
44.6
2,845,412
1,211,576
42.6
78
78
2,843,888
1.21G.928
42.6
100
ICO
1965
5,714,093
3,219.741
56.3
1,328,998
751,851
56.6
4,385,095
2.467,390
56.3
77
77
4,379,496
2,464,780
56.3
100
100
1966
5,350,266
2.468,969
46.1
1,686,333
809,852
48.0
3,664.12.3
1,659,117
45.3
68
67
3,650,142
1,654,460
45.3
100
100
196 7
4,413,567
2,732,724
61.9
1,676,595
1,053,000
63.1
2,736,972
1,674,724
61.2
62
61
2,719,173
1,668,216
61.4
99
100
15o5
6,155,036
4,403,569
71.6
2,234,177
1,530,336
70.7
3,920,359
2,823,183
72.1
64
64
3,891,736
2,313,336
72.3
59
99
1969
7,581,133
5.257,542
69.4
2,928,569
1,932,852
66.0
4,652,564
3,324,690
71.5
61
63
4,620,746
3,309,355
71.6
99
100
16 70
9.669,462
5,913,479
60.0
3,017,745
1,330,199
60.
6,851,717
4,008,280
59.7
69
69
5,235,225
3,125.429
59.7
76
76
1971
8,205.S03
7,066,538
86.0
3,417,767
2,932,268
85.8
4,783,036
4,124,270
86.1
58
58
4,653,137
4,017,561
86.3
97
97
1972
10,633,808
10,986.294
103.3
5,736,746
5,721,281
99.7
4,857,062
5,265,013
107.5
46
48
NA
NA
NA
NA
NA
1973
9,667,228
10,221,242
105.7
4,371,265
4,556,980
104.2
5,295,943
5,664,262
107.0
55
55
NA
NA
NA
NA
NA
1572a
11,416,782
11,771,425
103.1
6,267,480
6,254,188
99.8
5,149,302
5,517,237
107.1
45
47
4,314,013
5,176,026
107.5
93
94
1573a
11,171,708
11,661,141
104.4
5,621,636
5,747,531
102.2
5,550,072
5,913,610
106.6
50
51
5,247,409
NA
NA
95
Includes out of season landings. See Footnote a, Table A1, Appendix A
APPENDIX E

APPENDIX F
Table FI. Spiny lobster landings in Florida ports caught in foreign
waters, 1964-73, economic study of Florida spiny lobster
industry
Total
Florida Landings
Florida Landings
Florida
From Domestic
From
Foreign
Year
Landings
Waters
Wa
ters
Quantity
Quantity
Quantity
Percent of
(Pounds)
(Pounds)
(Pounds)
Florida
1964
3,631,100
2,632,547
998,553
27.6
1965
5,714,100
4,719,847
994,253
17.4
1966
5,350,000
3,151,150
2,198,850
41.1
.1967
4,414,000
1,915,676
2,498,324
56.6
.1968
6,155,000
2,880,540
3,274,460
53.2
1969
7,582,000
4,086,698
3,495,302
46.1
1970
9,862,462
6,745,924
3,116,538
31.6
1971
8,205,803
4,669,102
3,536,701
43.1
1972
11,986,221a
5,488,338
6,497,883a
54.2
1973
12,676,188a
6,621,122
6,055,066a
47.8
Source: Foreign water landings obtained from unpublished data collected
by the Statistical Reporting Service of the National Marine
Fisheries Service, Miami, Florida.
dOut of season landings included for 1972 and 1973 were 782,974 pounds
and 1,504,480 pounds, respectively. These are landed in Florida from
foreign waters during the Florida closed season.
147

APPENDIX G
TOTAL PRODUCT AND MARGINAL PRODUCT
EQUATIONS FOR FIRM HARVEST FUNCTION MODEL
(x j) TRAPS
In q = A.41843 + .7577 In x3
In MP = 4.07715 .2423 In x,
*1
(x2) PWK
In q = 9.367628 + .4399 In x2
In MP = 8.5787272 .5601 In x2
x2
(x3) WEEKS
In q = 7.985825 + .3721 In x3
In MP = 7.101433 .6279 In x3
x3
(x4) LOWD
In q = 7.4999502 + .3088 In x4
]n MP = 6.526395 .6912 In x4
x4
(z) DAYS IN SET PERIODS
x2 = 7/z
|* 4.23501 x1Plx363x4^z~(62 + 1} = 12116 z"1-43991
In MPz = 9.40232 1.43991 In z
148

APPENDIX H
Table HI. Comparison of spiny lobster production practices by craft
length for firms sampled, Florida Keys, 1973-74 season,
economic study of Florida spiny lobster industry
Craft length
(feet)
Item
Unit
16-22 24-28
31-36
40-55
Traps fished
no.
341
561
842
809
Traps lost:
Number
no.
98
193
318
371
Percent
%
29
34
38
46
Traps fished per day
no.
139
190
202
272
Hours fished per day
hrs.
7
8
8
9
Pulls per season
no.
27
27
25
27
Weeks fished
wks.
35
36
33
25
Trips per season
no.
66
103
89
48
Boat and vessel size:
Length
ft.
20
26
34
46
Width
ft.
7
9
12
15
Volume of Lobsters:
Per trap
lbs.
18
22
22
20
Per week
lbs.
175
339
549
636
Per trip
lbs.
93
118
204
331
Note: Data reflect averages for classes of craft size.
149

APPENDIX I
(Table 18 Computations)
1. Xj assumed equal to 1000, 800, 700, 618, 500, 429, 350, and 200,
A
X2 -
465,173,997.252
(4,773,480.707) 1,439,976,169
Xi
3. Q = 8,610,545.714 =
4. Q = 9,773,480.707 -
1,439,976,169 465,173,997.252
Xi
x2
5. TC/X2 = 1,876 + 11.55Xj
Qr (1.08)
6* ^/X2 = -^T TC/X2
7. tt/X
2a
400
* Q. (1-08)
- TC/X2
8. % A
1T/X2.
Column 7
Column 6
- 1
9.
10.
11.
Maximum State Revenue = (Column 10) x (Column 2)
License Fee assumed:
(Column
7) -
(Column 6)
$20,000
for
1000
traps
per
firm
18,000
for
800
traps
per
firm
15,000
for
700
traps
per
firm
13,000
for
618
traps
per
firm
10,000
for
500
traps
per
firm
5,000
for
429
traps
per
f irm
4,000
for
350
traps
per
firm
3,000
for
200
traps
per
firm
12. % A
tt/X,
A*
- [Column (7) Column (11)] : [Column (6)] 1
-A
State Revenue = (Column 11) x (Column 2)
150

151
14. Administrative Revenue = (Column 13) [(Column 6) x (Column 16)]
15. % A
Tot. Ind. = [(Column 7) x (Column 2)] = [(Column 6) x 400] 1
77
16. X2 400 Column (2)
17. B.E.C. = [(Column 5) + (Column 11)] [(Column 1) x (1.08)]

APPENDIX J
Spaces provided for answers have been omitted from the original
thirteen page questionnaire for inclusion in this text. The questions
and multiple choice answers are the same. A map of the study area used
to identify the actual fishing grounds for each fisherman has also been
excluded.
(CONFIDENTIAL: Please do not give name)
SPINY LOBSTER FIRM SURVEY QUESTIONNAIRE
Please answer all questions based on 1973-74 season. Answer all
questions as accurately as possible. If the exact answer cannot be
recalled, please give your best approximation. If additional space is
needed to answer (or simply comment on) a question use the back of that
page and properly indicate additional comments.
I.DESCRIPTION OF LOBSTER PRODUCTION UNIT
A. Operation Unit: ( ) Vessel, Boat
1. Fabrication (i.e., wood, fiberglass, steel, etc.)
2. Length (feet), Breadth (width) (feet)
3. Depth (feet), Draft feet (loaded) (feet)
4. Gross Tons, Net Tons
5. Engine Make, Horsepower
6. Age of Vessel, Age of Engine
7. Top speed: Empty, Loaded, Average Speed
E. Method and Crew:
1. Type ( ): Trap, Diving, Bull Net, Other
2. If trap: Single, Trot Line
3. Number of men in crew excluding captain
4. Approximate age of regular crew members (4 blanks)
5. Does a single trip involve more than one day away from port?
Yes, No. If yes, what is the average length of time away
from port per trip? (Days)
C. Gear:
1. Traps: a. Average number of traps fished in each month.
b. Maximum number of traps fished at any one time:
2. Electronic equipment on board. Give make and model number.
3. Method used to haul traps. If hydraulic, please give capacity,
size, and make if known.
4. Preservation techniques used? Live, Ice, Freeze, Other
5. Please list other gear used but not listed above.
152

153
II. FISHERMAN'S LOBSTER PRODUCTION TECHNIQUE
A. Materials and Style of gear.
1. Trap Design
a. Briefly describe trap style
b. What type of throat structure is used?
c. How many entrances do you have and where are they located?
d. Is a bait cup used? Yes, No
e. Type of material used? Is it readily available?
2. a. What type of bait do you use?
b. Why do you prefer this type?
c. On the average, how often do you have to replace the bait
in a trap?
d. Is it easy to acquire the bait you are using?
B. Description of fishing ground and fishing intensity.
1. Please draw areas on the map on the next page as shown in the
example. Then number each area consecutively (beginning with
#1) based on the amount of fishing you do in that area. (i.e.,
area I is fished most by you)
2. For the areas you have indicated on the map please give your
best answer to the following questions describing each area.
Area V (see map) (1 . 2 . 3 . 4 . 5 . 6 . 7 . 8)
(1) Approximate distance from home port (miles)
(2) Average traveling time from home port to each area (minutes)
(3) Botton conditions (enter letter): a. rocky/coral; b. sandy;
c. grass; d. ether
(4) Average depth (feet)
3.Please indicate your best estimate of the following information
for the three major areas you fished for the following months:
(a)average depth, (b) average water temperature, (c) average-
number of traps. (See map attached to back of questionnaire).
1973-74 season (Aug Sept Oct
Area if (get from map)
(a) Average # traps
(b) Average water temperature
(c) Average number traps made
Nov Dec Jan Feb Mar)
(Dotted lines used to
separate mere than one
area fished for a month.)
4. List all ports at which you landed during season. (8 blanks)
5. Daily Activity:
a. What is the average hours per day worked? (From departure
of port to return) (Hours)
b. Of the above hours, approximately how many are spent
actually hauling traps? (Excluding traveling between
fishing grounds) (Hours)
c. How many traps can your operation pull and shoot per hour?
d. On the average, approximately how many trips diu you make
per week for each month? (1973-74 season) (Aug. Mar.)
e. What is the average length of time traps set between hauls
for each month? (Days)
f. Approximate number of days of bad weather which prevented
you from fishing for each month? (If unknown, give best
estimate for total season. (Season total) (Aug. Mar.)

154
III. COSTS OF PRODUCTION
A. Initial Costs (fixed costs):
1. Value of vessel (boat) (Excluding gear, electronic, and
hydraulic equipment)? ($ )
2. Type (make) and value of electronic equipment on board?
Value $ Describe
3. Replacement value of engine? $
4. Value of Hydraulic and other equipment on board? Value $
Describe.
5. Cost of insurance?
a. Protection and indemnity (P & I)? ($ )
b. Hull ($ )
6. Interest on Loan? ($ )
7. Fishing and vessel (boat) licenses and permits? ($ )
8. Trap construction:
a. Number of traps built for 1973-74 season?
b. Cost of line? ($) Type used
c. Cost of wood? ($) Type used
d. Cost of buoy? ($) Type used
e. Cost of labor used in building traps? ($)
f. Other costs (i.e., cement, oil, nails, wire)? (Specify
amount)
9. Please describe and give value of other miscellaneous initial
expenses?
B. Operating Costs (Variable Costs). 1973-74 season. Please leave
blank if the item does not pertain to your operation.
Item .... Amount Used .... Total Cost ($)
1. Fuel (gals.)
2. Oil (gals.)
3. Bait (lbs.)
4. Ice (lbs.)
5. Groceries
6. Other miscellaneous trip expenses
7. Labor costs
a. Captain share (%)
b. Crew share (%)
c. Boat share (%)
d. Wages (hours)
e. Bonuses
f. Labor taxes
g. Other (specify)
8. Maintenance and repair costs
a. Hull
b. Engine
c. Electronic equipment
d. Other machinery
e. Gear (traps)
f. Other (specify)
9. Cost of trap losses No. of traps lest
10.Other expenses (Specify)

155
TV. PRODUCTION AND EARNINGS
1. What percent of your total income is earned from lobster fishing?
2. Please complete the following table on monthly landings and values
to the best of your knowledge: (1973-74 season)
1973-74 Season: Landings & Value (August March) Total
Lobster (lbs.)
Lobster ($)
Finfish (lbs.)
Finfish ($)
Other (lbs.)
Other ($)
3. Please answer the following questions to the best of your knowledge.
Space for answers is provided in the table.
A. What is the average size of legal lobsters landed for each
month?
B. How many pounds of "shorts" do you see in your traps per trip,
on the average, for each month?
C. What is the average number of traps lost each month?
D. How many pounds of lobsters do you believe were stolen from
your traps, on the average, each month?
1973-74 (August March ) Total
Quest. A
Quest. B
Quest. C
Quest. D
4. Please check the range of your total earnings from lobster fishing
only for the 1973-74 season. (Below $2,000 to above $30,000)
5. If you fished and if you recall, what was your approximate total
season landings and total number of traps fished each season as
shown in the table.
(72-73) (71-72) (70-71) (69-70) (68-69)
Total Landings
Total Traps Fished
6. What do you feel would be the most efficient combination of the
following if you could design the ideal operation unit?
A. Vessel: Make, Length, Width, Gross Tonnage, Fabrication
B. Engine: Make, Horsepower
C. Size of crew
D. Electric Equipment
E. Hydraulic Equipment
F. Total Number of Traps
G. Approximate Cost of Complete Operation Excluding Crew and
Traps ($)
H. Given this "Dream" Operation Unit Approximately How Many
Pounds Do You Believe You Could Have Landed in 1973-74 Season?

156
V. ABOUT THE CAPTAIN AND HIS VIEWS ON MANAGEMENT AND REGULATION
1. Toe Captain
A. Age (years)
B. Years lobster fishing (years)
C. Father's occupation
D. What generation lobster fisherman are you
E. Education (grade school, high school, college)
2. Is your lobster operation considered single firm, partnership, or
Corporation?
3. Is there any cooperative activity with other fishermen (i.e. sharing
of labor)? Explain.
4. Do you find that the size of lobsters has decreased over the years?
Yes. No. If so, by how much or in what manner?
5. What are the major factors used by you to determine when and where
to fish certain areas? (i.e. with respect to such things as tides,
month, wind, moon, temperature, barometer readings, etc.)
6. If the landing of shorts \ you have landed in the 1973-74 season in addition to the legal
lobsters you landed? (lbs.)
7. How many pounds of shorts do you feel were landed in your area in
the 1973-74 season? (lbs.)
8. If you were not a lobster fisherman x^hat other occupation would you
have chosen based on your qualifications.
A. Other fishing (specify) Estimated income ($)
B. Non-Fishing (specify) Estimated income ($)
9. What kind of regulation or management xrould you recommend xcith
respect to the following:
A. How long should the season be? Why?
B. What months should the season include? Why?
C. Should the number of licenses be limited? If so, how and to
whom?
D. What is the maximum amount you are x^illing to pay for a license?
E. What should a lobster's legal carapace length be set at? (inches)
F. Other comments.

Table K1
Spiny 1bfcter Input, outputs, and values, Monroe County, Florida, 1963-73, econonic study of Florida opiny lobster industry
1973a
1972"
1971
1970
1969
1S68
1967
1966
1965
1964
1963
Total landings (lb.)
4,993,230 .
4,639.773
4,653.387
5,235,255
4,620,766
3,891,736 ;
2,719.178
3,650,142
4,37V,496
2,843,888
2,770,100
Total value ($)
5,322,836b 4,967,756
4,017,561
3,123,429
3,309,855
2,813,336 :
1,668,216
1,654,460 i
2,464,780
1,210,528 :
1,080,339
Prlc- (c/lb.)
1C6.6
107.5
86.3
59.7
71.6
72.3
61.4
45.3
56.3
42.6
39.0
Tc-ir* (gcJt)
171,240
133,044
155,229
134,300
96,935
98,500
91,800
74,550
89,700
73,353
60,050
Pounds per trap
29.16
34.87
2S.98
38.98
47.66
39.51
29.62
48.96
48.82
38.66
46.13
Dollars per trap
31.08
37.49
25.88
23.26
34.14
28.56
18.17
22.19
27.48
16.46
17.99
Kli(ier?ien: Ven l
421
370
329
251
134
323
143
104
56
08
44
Boat (reg.)
319
325
253
330
255
214
330
300
306
238
233
Casual
30
37
39
17
20
12
24
12
24
104
12
TOTAL
770
732
621
598
459
549
497
416
386
410
239
Boat b
211
2 34
192
212
176
135
224
210
188
214
162
Fishermen per boat
1.51
1.39
1.32
1.56
1.45
1.59
1.47
1.43
1.63
l.u
1.44
Vessels
188
123
130
111
£9
137
75
58
28
34
24
Fishermen par vessel
2.24
3.01
2.53
2.26
2.07
2.35
1.91
1.79
2.CO
2.00
1.33
Cron* Tannage
4,<)00t
2,874
3,243
2,491
2,135
3,433
1,189
824
308
2S0
261
Cros tonnspe per vessel
21.28
23.37
24.55
22.44
24.55
25.06
15.85
14.21
11.00
8.24
10.63
Firms (Em's and Vessels)
399
357
322
323
25
272
299
268
216
248
136
Pounds per lira
12,514
12,997
14,451
16,208
17,4.17
14,303
9,094
13,620
20,275
11,467
14,893
Dollars per. firm
13,340
13,971
12,477
9,670
12,430
10.343
5,579
6,173
11,411
4,883
5,808
Traps per fina
429.17
372.67
482.08
415.79
365.87
362.13
307.02
277.99
415.28
296.58
322.85
Water Temperature
79.09
79.62
78.57
76.62
76.35
76.94
77.79
76.64
77.91
77.52
77.45
Source: U.S. Department of Coirnerce, NOAA, NMFS, Southeast Fisheries Center, Miami, Florida.
aAdjusted for out-of-scasoo landings. Actual data recorded for Monroe County, before
adjusting for out of season landings v re: Landings 5,247,409 (1973); 4,314,013 (1972);
Total value $5,593,73b (1973); *5,176,026 (19/2).
b
973 total value eatic*.
ed ly 4,993,230 x 106.6
5,322,836.
Monroe County
Out of Season Landings
April May
1972 0 84,318
1973 36,008 83,661
June July Total
49,104 40,818 174,240
83,119 46,341 254,129
Estimated.
Water temperature was calculated from the monthly mean surface water temperaturu for August thru March of each season
The data for South Klmi and Key West station were averaged to obtain this value.

158
APPENDIX L
Table LI. Data used to estimate firm harvest function, 1973-74 survey of spiny lobster captains,
economic study of Florida spiny lobster industry
Landings
(pounds)
Traps
(xi)
Rounds
per week
(x?_)
Weeks
(X3)
Craft
size
(x4)
Area
fished
(x5,x6)
Length
Width
Landings
(dollars)
Survey
I.D.
Code
3052
140
.6240
36
154
1, 0
22
7
3336
105
14000
832
.8860
36
80
1, 0
16
5
1498
108
10254
377
1.1200
28
140
1, o
20
7
10254
110
2963
85
.7980
36
96
1, 0
16
6
3200
111
5000
448
.6750
36
154
0, 0
22
7
5350
204
6616
365
.9120
36
176
0, 1
22
8
7148
302
2996
140
.8300
36
176
0, 1
22
8
3176
305
13613
851
.6790
36
234
1, o
26
9
14566
101
22000
401
.6610
36
234
1, o
26
9
23540
109
7103
665
.7700
36
200
0, 0
25
8
7600
201
12000
560
1.0390
36
252
0, 0
28
9
12840
203
8000
260
.7620
36
240
0, 1
24
10
8560
304
16531
800
.6330
36
252
o, 1
28
9
20664
306
6171
396
.6670
36
208
0, 1
26
8
7171
307
15000
776
.5000
36
341
1, 0
31
11
16050
102
15973
597
.7950
36
408
1, 0
34
12
17055
103
17000
648
.7980
36
432
1, 0
36
12
18190
104
17000
647
.7950
36
340
1, 0
34
10
18190
106
18000
1103
.9300
15
468
0, 0
36
13
19260
202
8500
498
.5720
36
330
0, 0
33
10
9095
205
35308
1625.
1.0480
36
468
0, 0
36
13
37780
206
16333
1281
.8900
13
690
0, 0
46
15
17966
207
16575
716
1.0810
36
574
o, 1
41
.14
17520
303
16724
619
.9900
36
480
0, 1
40
12
17903
308
13979
622
1.3950
15
1045
0, 1
55
19
14800
310
APPENDIX L

REFERENCES
[1] Allen, Bennet M. "Notes on the Spiny Lobster (Panulirus inter
rupts) of the California Coast," University of California
publication in Zoology, Vol. 16, No. 12, 1916.
[2] Barnhart, P. S. "Notes on the Artificial Propagation of the Spiny
Lobster," California Fish and Game, Vol. 5, No. 2, 1919.
[3] Bell, Frederick W. "Estimation of the Economic Benefits to Fish
ermen, Vessels and Society from Limited Entry to the Inshore
U.S. Northern Lobster Fishery," BCF, DER, W.P. No. 36, March,
1970.
[4] _. The Economics of the New England Fishing
Industry: The Role of Technological Change and Government
Aid, Federal Reserve Bank of Boston, Research Report No. 31,
1966, 215 pp.
[5] "The Relation of the Production Function to
the Yield on Capital for the Fishing Industry," Recent Devel
opment and Research in Fisheries Economics, Frederick W. Bell
and Jared E. Hazleton (eds.), published for the New England
Economic Research Foundation, Dobbs Ferry, New York: Oceana
Publications, Inc., 1967.
[6] "The Pope and the Price of Fish," The American
Economic Review, Vol. LVIII, December, 1968.
[7] Bell, Frederick W. and Richard F. Fullenbaurn. "Economic Impact of
Alternative Management Strategies for the Northern Lobster
Fishery," NMFS, ERD, File Manuscript No. 108, August, 1972.
[8] Bromley, D. W. "Economic Efficiency in Common Property Natural
Resource Use: A Case Study of the Ocean Fishery," BCF, DER,
W.P. No. 28, July, 1969.
[5] Butler, J. A. and N. L. Pease. "Spiny Lobster Explorations in the
Pacific and Caribbean Waters of the Republic of Panama," U.S.
Department of Interior, Fish and Wildlife Service, BCF,
Fisheries Report No. 5U5, 1965.
[10] Carlson, Ernest V/. "Bio-Economic Model of a Fishery," BCF, DER,
W.P. No. J2, March, 19b9.
159

160
[11] "An Economic Theory of Common Property Fishery
Resources," NMFS, ERD, File Manuscript No. 66, July, 1970.
[12] "The Biological and Economic Objectives of
Fishery Management," NMFS, ERD, File Manuscript No. 140,
September, 1971.
[13] Carlson, Sune. A Study of Price Theory of Production, New York:
Kelly and Millman, Inc., 1956.
[14] Cheung, Steven N. S. "Contractual Arrangements and Resource
Allocation In Marine Fisheries," Economics of Fisheries
Management: A Symposium. Edited by A. D. Scott, 1960.
[15] Chislett, G. R. and M. Yesaki. "Spiny Lobster Fishery Explora
tions in the Caribbean," UNDP/FAO Caribbean Fishery Develop
ment Project, Bridgetown, Barbados, 1971.
[16] Christy, Francis T., Jr. and Anthony Scott. The Common Wealth in
OceanFisheries, Baltimore: The John Hopkins Press, 1965.
[L7j Cope, C. E. "Spiny Lobster Gear and Fishing Methods," U.S.
Department of Interior, Fish and Wildlife Service, BCF,
FL No. 487, 1959.
[18] Council of Economic Advisors, Economic Report to the President,
Annual Report of the Council of Economic Advisors, Washington,
D.C.: U.S. Government Printing Office, 1975.
[19] Crawford, D. R. and W. J. J. DeSmidt. "The Spiny Lobster,
Panullrus argus, of Southern Florida: Its Natural History
and Utilization," Bulletin of the U.S. Bureau of Fisheries,
Vol. 38, 1923.
[20] Crutchfield, J. A. "Economic Objectives of Fishery Management,"
The Fisheries: Problems in Resource Management, ed. J. A.
Crutchfield, Seactle, Washington: University of Washington
Press, 19o5.
[21j Crutchfield, James and Arnold Zeliner. "Economic Aspects of the
Pacific Halibut Fishery," Fishery Industrial Review, U.S.
Fish and Wildlife Service, Vol. 1, No. 1, April, 1962.
[22] Dees, L. T. "Spiny Lobsters," U.S. Department of Interior, Fish
and Wildlife Service, BCF, FL No. 523, 1968.
[23] DeWolf, A. Gordon, The Lobster Fishery of the Maritime Provinces:
Economic Effects of Regulations, Bulletin of the Fisheries
Research Board of Canada, Bulletin 187, Ottawa, 1974.
124] Dow, Robert L., Frederick WT. Bell and Donald M. Harrimgn. "Bio-
Eccnomic Relationships for the Maine American Lobster Fishery,
with Consideration of Alternative Management Schemes," NMFS,
ERL', File Manuscript No. 149, April, 1973.

161
[25] Ferguson, C. E. The Neoclassical Theory of Production and Distri
bution, Homewoods, Illinois: Cambridge University Press,
1969.
[26] Fullenbaum, R. F. "A General Equilibrium Demand Model for Living
Marine Resources: An Application of General Equilibrium and
Common Property Resource Theory to the U.S. Seafood Sector,"
NMFS, ERD, FL No. 116, August, 1971.
[27] Gates, J. M. and V. J. Norton. "The Benefits of Fisheries Regu
lation: A Case Study of the New England Yellowtail Flounder
Fishery." Sea Grant Resource Economics, University oi Rhode
Island, Marine Technical Report No. 21, Kingston, R.I., 1974.
[28] Gordon, H. Scott. "The Economic Theory of a Common Propertv
Resource: The Fishery," Journal of Political Economy, Vol.
62, April, 1954, pp. 124-142.
[29] Herrington, William C. "Some Methods of Fishery Management and
Their Usefulness in a Management Program," U.S. Fish and
Wildlife Service, Special Scientific Report No. 18, 1943.
[30] Huq, A. M. and H. I. Hasey. "Socio-Economic Impact of Changes
In the Harvesting Labor Force in the Maine Lobster Fishery,"
NMFS, ERD, File Manuscript No. 142, January, 1973.
[31] Idyll, C. P. "Spiny Lobster of the Caribbean (Abstract)," F.A.O.
Fish Report No. 71.1, 1969.
[32] Lampe, Harlan C. "The Interaction Between Two Fish Populations
and Their Markets," Frederick W. Bell and Jared E. Hazleton
(eds.), Recent Development and Research in Fisheries Econ
omies Published for the New England Economic Research
Foundation. Dobbs Ferry, New York: Oceana Publications,
Inc.., 1967, pp. 179-195.
[33] Mendenhall, W., et al. Elementary Survey Sampling, Belmont,
California: Dunberry Press, Wcrdsworth Publishing Co., 1971,
p. 40.
[34] Nesbitt, Robert A. "Biological and Economic Problems of Fishery
Management," U.S. Fish and Wildlife Service, Special
Scientific Report No. 13, 1943.
[35] Pontecorvo, Giulio. "On the Utility of Bio-Economic Models for
Fisheries Management," Ocean Fishery Management: Discussions
and Research, U.S. Department of Commerce, NOAA and NMFS,
NOAA Technical Report NMFS CIRC-371, April, 1973.
[36] Prochaska, F. J. and J. R. Baarda. "Florida's Fishery Management
Programs: Their Development, Administration and Current
Status," Florida Agriculture Experiment Station Bulletin No.
768, University of Florida, Gainesville, 1975.

162
[37] Prochaska, F. J. and J. S. Williams. "Economic Analysis of Cost
and Returns in the Spiny Lobster Fishery by Boat and Vessel
Size," A Florida Sea Grant Publication No. SUSF-SG-76-004,
University of Florida, Gainesville, July, 1976.
[38] Rich, Jack. "Natural Resources and External Economics: Regula
tion of the Pacific Halibut Fishery," Ocean Fishery Manage
ment : Discussions and Research, U.S. Department of Commerce,
NOAA and NMFS, NOAA Technical Report NMFS CIRC-371, April,
1973.
[39] Robinson, M. K. "Atlas of Monthly Mean Surface and Subsurface
Temperature and Depth of the Top of the Thermocline: Gulf
of Mexico and Caribbean Sea," Scripps Institute of Oceano
graphy, University of California, San Diego, S10 No. 73-8,
March, 1973.
[40] Russell, E. S. "Some Theoretical Considerations on the 'Overfish
ing' Problem," Journal of Conservation and International Ex
ploration, March 6, 1931.
[41] Schaefer, Milner B. "Some Considerations of Population Dynamics
and Economics in Relation to the Management of the Commercial
Marine Fisheries," Journal of Fishery Research Board of
Canada, Vol. 14, No. 5, 1957, pp. 669-681.
[4V.J SmJ'b, F. G. W. "The Spiny Lobster Industry of the Caribbean."
Caribbean Research Council, Fisheries Series, No. 3, 1948.
[43] _ "The Spiny Lobster Industry of Florida," Florida
State Board of Conservation, Educational Series No. 11,
Marine Laboratory, University of Miami, 1958.
[44] Smith, V. L. "On Models of Commercial Fishing," Journal _of
E'olitlcal Economy, Vol. 77, No. 6, March/April, 1969.
[45] Sokoloski, Adam A.