Citation
A model for evaluating alternative policy decision for the Florida orange subsector of the food industry

Material Information

Title:
A model for evaluating alternative policy decision for the Florida orange subsector of the food industry
Creator:
Powe, Charles E. ( Dissertant )
Langham, Max R. ( Thesis advisor )
Polopolus, Leo ( Reviewer )
Eddleman, Bobby R. ( Reviewer )
Schulze, David L. ( Reviewer )
Reynolds, John E. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1973
Language:
English
Physical Description:
166 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Advertising expenditures ( jstor )
Agricultural seasons ( jstor )
Boxes ( jstor )
Crops ( jstor )
Marginal revenue ( jstor )
Market prices ( jstor )
Modeling ( jstor )
Prices ( jstor )
Simulations ( jstor )
Weather ( jstor )
Citrus fruit industry -- Florida ( lcsh )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
City of Lakeland ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
A third generation quantitative economic model of the Florida orange subsector was developed and then used to evaluate the effects on subsector performance of alternative inventory, pricing, advertising and supply control policies. The model was composed of ten interrelated sectors, extending from tree planting through consumer demand, and was written in the DYNAMO simulation language. The internal consistency of the model was examined. The model was then validated on the basis of its ability, when given empirical estimates of weather conditions, to reproduce the behavior of the orange subsector over the 1961-71 period. Theil's inequality coefficients were used to measure the correspondence between simulated and empirical data. Calculated values of the coefficients ranged from .55 to .98 and indicated that predictions were better than those that would have been realized with the model p = a , where a and p represent actual and predicted values at time t. After the model had been accepted as an adequate representation of the structure of the orange subsector, a set of simulations was made to establish a base with which to compare the ten policies considered in the study. Comparable results for a variety of conditions were obtained by replicating each simulation with five randomly selected weather patterns. Simulations were started with initial values corresponding to conditions that existed at the beginning of the 1961-62 season and covered a twenty-five-year period. Results were examined from the viewpoints of three major groups of subsector participants: orange producers, processors and distributors, and consumers. It was assumed that the interests of these groups could be evaluated on the basis of the present value and variance of grower profits, crop size, and average FOB price, respectively. These values were computed from model output with the aid of a FORTRAN computer program and along with estimated storage costs provided the information used in policy evaluation. Policies that reduced long-run supplies of orange products caused substantially higher grower profits, lower storage costs and higher retail prices. They also reduced risks for orange producers, but not for other subsector participants. Small gains from policies that failed to alter the long-run behavior of the subsector were partially or completely offset by increased storage costs associated with them. Given the advertising response functions in the model, the alternative advertising proposal, which increased average advertising expenditures from $11.9 million to $19.8 million per season, did not prove to be profitable. However, the study did not confront the question of whether or not one method of collecting and expending advertising funds was superior to the other. The characteristic which dominated policy analysis was the presence of conflicts of interests among subsector participants. In almost every instance, in order for one group of participants to gain, another was placed in a less desirable position. For the policies considered in the study, results provided insights into costs and returns and their distribution among subsector participants. With periodic updating, the model can provide an ex ante method of evaluating future decisions as policy questions develop in the Florida orange subsector.
Thesis:
Thesis (Ph. D.)--University of Florida, 1973.
Bibliography:
Bibliography: leaves 163-165.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Charles Everitt Powe.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
029994417 ( AlephBibNum )
ACG2299 ( NOTIS )
79608163 ( OCLC )

Downloads

This item has the following downloads:


Full Text














A MODEL FOR EVALUATING ALTERNATIVE POLICY
DECISIONS FOR THE FLORIDA ORANGE SUBSECTOR OF
THE FOOD INDUSTRY
















By

CHARLES EVERITT POWE.












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY









UNIVERSITY OF FLORIDA

1973
















ACKNOWLEDGMENTS


The author would like to express his deepest gratitude for the

direction and friendship extended by his chairman, Dr. Max R. Langham.

He is also grateful to Dr. Lester H. Myers for sometimes acting as his

sounding board and for providing many helpful suggestions. In addition,

appreciation is extended to Dr. B. R. Eddleman, Dr. Leo Polopolus,

Dr. David L. Schulze and Dr. J. M. Perry for their services on his

graduate committee, and to Dr. James A. Niles for reading the final

draft of the manuscript and offering many helpful suggestions.

Many others have aided and befriended the author during his graduate

studies. Special appreciation is extended to Dr. K. R. Tefertiller, who

served as chairman of the Food and Resource Economics Department during

most of the author's graduate program. The author would like to thank

the Economic Research Service and the Florida Agricultural Experiment

Stations for the much appreciated financial assistance which supported

the study. Acknowledgment is made of the support and services of the

Northeast Regional Data Processing Center of the State University System

of Florida.

The author is indebted to those who helped in the physical produc-

tion of the thesis. Much of the early typing was done by Mrs. LeAnne

van Elburg who also drew the large diagram of the model. Some of the

figures were drawn by Miss Jan McCartan and the final manuscript was

typed by Mrs. Phyllis Childress. Miss Sandra Claybrook proofread parts

of the manuscript.

















TABLE OF CONTENTS


ACKNOWLEDGMENTS .. ...... . . . . . ..

LIST OF TABLES . . . . ... . . . . . . . iv

LIST OF FIGURES . . . . ... . . . . . . .. vi

ABSTRACT . . . . . . . . ............ viii

CHAPTER

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

The Problem . . . . . . . . .. 1
Objectives . . . . . .... .... . . ... 2
Previous Work . . . . . . . . . 3

II. STRUCTURE OF THE FLORIDA ORANGE SUBSECTOR . . . 6

General Description . . . . . . . . 6
Production . . . . . . . .... .. 7
Dynamics of the Florida Orange Subsector . . 9

III. CHARACTERISTICS OF DYNAMO II . . . . . . . 15

Special Features . . . . . . . ... 15
Time Notation .................. 16
Type of Variables and Computational Sequence . 17

IV. THE MODEL . . . . . . . . ... . . 19

Tree Numbers Sector . . . . . . . .. 21
Weather Effects Sector . . . . . .. 29
Crop Size Sector . . . . . . . .. 32
Grower Profit Sector. . . . . . .. 34
Processor Disappearance Sector . . . ... 35
Advertising Sector . . . . . . . .. 37
FOB Price Sector . . . . . . . ... 42
Retail and Institutional Inventory and Sales Sector 53
Retail and Institutional Price Sector ...... 57
Demand Sector . . . . . . . . ... 60
Initial Conditions . . . . . . ... 63










V. VALIDATION . . . . . . . . . . 68

Long-run Stability . . . . . . ... 69
Retrospective Comparison . . . . ... 72
Conclusion . . . . . . . . ... 83

VI. POLICY ANALYSIS . . . . . . . . ... 84

Policies . . . . . . . .... . 86
Measures of Performance . . . . . ... 91
Analysis of Alternative Policies . . ... 95

VII. SUMMARY AND CONCLUSION . . . . . . ... 110

Limitations . . . . . . . . ... 114
Implications for Future Research . . ... 116


APPENDICES

Appendix A Alphabetized List of Variable Names . . ... 117

Appendix B The Computer Program. ... . . . . . 126

Appendix C Derivation of Marginal Net Revenue Relationships 142

Appendix D DYNAMO Equations for the Alternative Advertising
Policy . . . . . . . .... . 147

Appendix E Miscellaneous Data . . . . . . ... 152

Appendix F A Note on the Calculation of Present Values and
the Variance of Present Values . . ... 160

BIBLIOGRAPHY . . . . . . . . ... ....... 163

BIOGRAPHICAL SKETCH . . . . . . . . ... . . 166

















LIST OF TABLES


Table Page

1 Acreage of bearing and nonbearing orange groves by
Florida counties as of December 1969. . . . . 8

2 Organizational structure for DYNAMO II equations. ... 18

3 Estimated mature productive orange tree equivalents,
movement of orange trees from Florida nurseries
to Florida destinations, and returns above
operating costs for groves averaging over ten
years of age, 1955-56 through 1970-71 seasons . . 26

4 Yield loss, tree loss and hatrack loss factors,
1962-63 through 1972-73 seasons . . . . .. 31

5 Conversion factors for major orange products. . . ... 37

6 Advertising tax rates for Florida oranges by type of
use, 1962-63 through 1970-71 seasons. . . . ... 38

7 Relationship between per capital quantity of an orange
product that would be demanded by retail and
institutional consumers given adequate time for
system adjustment and the FOB price of the
product . . . . . . . . ... .... . 44

8 Mean values associated with estimated demand
relationships . . . . . . . .... . 45

9 Base data periods associated with estimated demand
relationships . . . . . . . .... . 46

10 "Normal" retail inventories of major orange products. . 54

11 Retail and institutional demand relationships for
Florida orange products . . . . . . ... 61

12 Mean values associated with estimated demand
relationships . . . . . . . .... . 62

13 Estimated fruit usage rate by product type,
1961-62 season. . . . . . . . . ... '65










14 Net marginal revenues used to initialize model. ... . 66

15 FOB prices used to initialize model . . . .... 67

16 Observed and simulated fruit usage, by product-market . 82

17 Weather conditions used in the five simulation runs
for each policy . . . . . . . . . 85

18 Discounted values of two hypothetical streams of
income received over a five-year period ...... 93

19 Alphanumeric names used to identify simulation runs . 96

20 The level and standard deviation of the present value
of grower profits, average FOB price and crop
size for twelve sets of simulations . . . ... 98

21 Relative value of the level and standard deviation of
the present value of grower profit, average FOB
price and crop size for policies comparable with
the base (B) run. . . . . . .... ... . 99

22 Size and discounted costs of the carry-overs
associated with alternative policies. . . . ... 100

23 Estimated costs and returns to orange processors,
1961-62 through 1970-71 seasons . . . . ... 103

24 A classification of nonadvertising policies by
preference category relative to the base (B) by
group of participants . . . . . . . .. 107
















LIST OF FIGURES


Figure Page

1 Simplified flow diagram of the orange subsector .... 10

2 Block diagram of major components of the Florida
orange subsector. . . . . . . . . .. 13

3 Size of the orange crop and per box return above
operating costs received by growers for Florida
oranges, 1961-62 through 1968-69 crop seasons . . 14

4 Per box return above operating costs received by
growers for Florida oranges and orange tree
movements from Florida nurseries, 1961-62
through 1965-66. ... . . . . . . . 14

5 Time notation for DYNAMO II . . . . . . ... 16

6 Flow diagram of the DYNAMO model of the Florida
orange subsector. . . . . . . . . ... 20

7 Comparison of output from exponential delay and
empirical yield estimates . . . . . ... 22

8 Relationship between per box returns above operating
costs and movement of orange trees from Florida
nurseries before and after the 1957-58 and
1962-63 freezes.. . . . . . . . . . 25

9 Seasonal pattern of generic advertising and
promotional expenditures for Florida oranges. ... 40

10 Relative price adjustment for three product case. ... 48

11 Simulated time path of selected variables . . ... 70

12 Simulated and actual numbers of mature productive
orange trees, 1961-62 through 1972-73 seasons . . 73

13 Prediction-realization diagram for changes in
numbers of mature productive orange trees . . .. 75

14 Simulated and actual crop size, 1961-62 through
1971-72 seasons . . . . . . . . ... 77

vi










15 Prediction-realization diagram for changes in Florida
orange production . . . . . . . .. 78

16 Simulated and actual on-tree price, 1961-62 through
1970-71 seasons . . . . . . . . . 79

17 Prediction-realization diagram for changes in on-tree
price . . . . . . . . . .. . 81

18 Advertising collections and expenditures for the
alternative advertising policy and base runs,
weather set 1 . . . . . . . .... . .106










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


A MODEL FOR EVALUATING ALTERNATIVE POLICY
DECISIONS FOR THE FLORIDA ORANGE SUBSECTOR OF
THE FOOD INDUSTRY

By

Charles Everitt Powe

December, 1973

Chairman: Max R. Langham
Major Department: Food and Resource Economics

A third generation quantitative economic model of the Florida

orange subsector was developed and then used to evaluate the effects on

subsector performance of alternative inventory, pricing, advertising

and supply control policies. The model was composed of ten interrelated

sectors, extending from tree planting through consumer demand, and was

written in the DYNAMO simulation language.

The internal consistency of the model was examined. The model was

then validated on the basis of its ability, when given empirical esti-

mates of weather conditions, to reproduce the behavior of the orange

subsector over the 1961-71 period. Theil's inequality coefficients were

used to measure the correspondence between simulated and empirical data.

Calculated values of the coefficients ranged from .55 to .98 and indi-

cated that predictions were better than those that would have been

realized with the model pt = at-1' where at and pt represent actual and

predicted values at time t.

After the model had been accepted as an adequate representation of

the structure of the orange subsector, a set of simulations was made to

establish a base with which to compare the ten policies considered in

viii










the study. Comparable results for a variety of conditions were obtained

by replicating each simulation with five randomly selected weather

patterns. Simulations were started with initial values corresponding

to conditions that existed at the beginning of the 1961-62 season and

covered a twenty-five-year period. Results were examined from the

viewpoints of three major groups of subsector participants: orange

producers, processors and distributors, and consumers. It was assumed

that the interests of these groups could be evaluated on the basis of

the present value and variance of grower profits, crop size, and average

FOB price, respectively. These values were computed from model output

with the aid of a FORTRAN computer program and along with estimated

storage costs provided the information used in policy evaluation.

Policies that reduced long-run supplies of orange products caused

substantially higher grower profits, lower storage costs and higher

retail prices. They also reduced risks for orange producers, but not

for other subsector participants. Small gains from policies that failed

to alter the long-run behavior of the subsector were partially or com-

pletely offset by increased storage costs associated with them.

Given the advertising response functions in the model, the alterna-

tive advertising proposal, which increased average advertising expendi-

tures from $11.9 million to $19.8 million per season, did not prove to

be profitable. However, the study did not confront the question of

whether or not one method of collecting and expending advertising funds

was superior to the other.

The characteristic which dominated policy analysis was the presence

of conflicts of interests among subsector participants. In almost every

instance, in order for one group of participants to gain, another was

ix










placed in a less desirable position. For the policies considered in the

study, results provided insights into costs and returns and their dis-

tribution among subsector participants. With periodic updating, the

model can provide an ex ante method of evaluating future decisions as

policy questions develop in the Florida orange subsector.

















CHAPTER I

INTRODUCTION


The Florida orange subsector1 has been characterized by large

variation in orange production and crop value. Production during the

past fifteen years (1958-72) has ranged from a high of 142.3 million

boxes during the 1970-71 crop season to a low of 54.9 million boxes

during the 1963-64 season. The on-tree value of the orange crop was

208.2 million dollars in 1970-71 as compared to a value of 241.3 million

dollars for the smaller 1963-64 crop. Much of the short-run variation

in crop size and value can be attributed to freeze damage. Freezes

during the 1957-58 and 1962-63 seasons reduced orange supplies and

caused large profits for some growers. These large profits were followed

by new investments in orange groves which after a few years increased

production and caused a period of low aggregate grower profits. During

periods of low profits, grove establishment decreases; however, since

existing orange groves produce over a long period of time, short-run

supplies do not readily respond to low prices.


The Problem


Participants within the orange subsector have been concerned with

the large variations in orange prices and supplies. Individual producers

1
The "Florida orange subsector" is defined in a broad sense starting
with the establishment of orange groves and extending through processing,
marketing and final consumption of oranges and orange products.










have sometimes benefited from short supplies and high prices; however,

high prices allow the introduction of competitive products such as syn-

thetic orange beverages and induce the establishment of new orange groves

which increase supplies and reduce profits in future periods [17, p. 1].

The instability of the orange subsector may be detrimental to the long-

run interests of all subsector participants. Supply stabilization would

allow processors to eliminate excess processing capacity and reduce

costs. Consumer interests may also be best served by stable prices.

Little is known about the effects of alternative industry policies

on the system as a whole and on various subsector participants. The

dynamic and interdependent economic mechanisms operating within the

Florida orange subsector may dampen or amplify the effectiveness of a

policy more than static partial analysis and intuitive judgment would

indicate. Computer simulation provides a method of studying the effec-

tiveness of policy decisions within the dynamic environment of an

abstract model without the risk of experimentation on the actual system.


Objectives


The objective of this study was to develop a third generation,

multiproduct, multimarket model of the orange subsector and to test

policies designed to improve the performance of the orange subsector.

More specific objectives were to:

1. Identify the system structure underlying the orange

subsector's dynamic behavior.

2. Construct a four-product, two-market model of the

orange subsector.










3. Delineate and/or develop measures of performance which

reflect the interest of all participants in the subsector.

4. Use the model to evaluate the effects of policies designed

to improve the performance of the orange subsector. These

policies include:

a. changes in the end of year carry-over of orange products.

b. changes in the Florida citrus industry's generic adver-

tising budget.

c. alternative pricing strategies.

d. alternative supply control policies, including:

(1) elimination of fully productive trees if

grower profits fall below specified levels.

(2) curtailment of new tree plantings when grower

profits are above specified levels.


Previous Work


In 1962, under a grant from the Minute Maid Corporation, Jarmain [9]

developed a first generation industrial dynamics model of the Florida

frozen concentrated orange juice (FCOJ) industry. Jarmain's study indi-

cated that a larger carry-over of FCOJ from one season to the next

would reduce price variability and improve the grower's position.

Raulerson [21] revised and expanded Jarmain's work in a second generation

model in order to appraise the effectiveness of alternative supply con-

trol policies in stabilizing and raising grower profits. Emphasis was

placed on the lack of knowledge in the area of supply response of

oranges--particularly during the periods of low prices. Both Jarmain and

Raulerson used average grower profits as a basis for evaluating the










performance of the frozen concentrated orange juice subsector. These

studies provided a basis for the current study.

Models of the type used in this study require large amounts of

information and it is helpful when this information is summarized in

relatively efficient forms. Information for this model was available

from several sources--the following studies were particularly useful.

A study completed by Polopolus and Black [17] in 1966 concluded that

shifts in the quality and supply of orange juice due to periodic freezes

have fostered the entry and proliferation of synthetic and partially

natural citrus flavored drinks.

The Polopolus and Black study was followed by a study in which

Myers [14] empirically estimated cross elasticities of demand for major

orange juice products, orange drinks and synthetic orange flavored

beverages. Frozen concentrate and chilled orange juice were found to be

strong substitutes. Chilled and canned single strength orange juice

appeared to be weak substitutes. No significant substitution relation-

ship was found between frozen concentrate and canned single strength

orange juice.

Weisenborn [25] completed a study in 1968 in which he used time

series data and least squares regression procedures to estimate price-

quantity relationships for major Florida orange products at the FOB level

of the marketing system. These estimates provided the information necessary

for the construction of net marginal revenue functions which were used to

optimally allocate oranges among product markets for various size crops.

Results based upon the estimated relationships indicated that a 128

million box orange crop maximized industry net revenue at the processor

level.










Priscott [19] carried Weisenborn's study of the export market a

step further in a 1969 study of the European demand for processed citrus

products. In general, the study indicated that the demand for citrus

products in West Europe was elastic and showed development potential.

McClelland, Polopolus, and Myers [12] used time series data to

estimate the response of consumer sales with respect to changes in

generic advertising expenditures. These estimates were used in conjunc-

tion with a quadratic programming model to measure possible gains from

allocating advertising funds more efficiently. Information from this

study provided a basis for specifying the influence of advertising on

product demand.

In a 1971 study, Hall [8] estimated consumer demand in retail gro-

cery stores for frozen concentrated orange juice, chilled orange juice,

canned single strength orange juice, and canned single strength grape-

fruit juice for ten geographic regions of the United States. The

analysis indicated that consumer demand functions for these products

differ by region. Regional price elasticity estimates for canned orange

juice compared closely with Weisenborn's national estimates. Estimates

were lower for chilled orange juice and higher for frozen concentrate

than those reported by Weisenborn.

Parvin [16] used yield estimates and standard regression techniques

to estimate weather effects on early-midseason and Valencia orange pro-

duction for eighteen Florida counties. These estimates provided a basis

for the construction of a weather index for total Florida orange

production.

















CHAPTER II

STRUCTURE OF THE FLORIDA ORANGE SUBSECTOR1


An understanding of the essential relationships which give rise to

a dynamic system's behavior is a prerequisite to the construction of a

simulation model. A verbal description of the system's structure helped

establish this understanding and provided a basis for building a quanti-

tative economic model.


General Description


The Florida orange subsector is composed of five major groups of

participants: producers, processors and packers, wholesalers, retailers

and consumers. Producers are those individuals and business organiza-

tions who are primarily concerned with the production and sale of whole

oranges. Processors and packers are involved with the conversion of

whole oranges into processed products or with the packaging and sale of

fruit in fresh form. Wholesalers and retailers provide marketing services

and are concerned with the movement of orange products from the producing

and processing area into consumer markets. Consumers are those primarily

involved in the consumption of orange products and are the most numerous

subsector participants. For the purposes of this study, final purchasers

of orange products have been classified into two general types: retail

and institutional.

1
Some of the material used in this chapter also appears in an
article by the author [18].










Institutional purchasers are nontax-supported institutions such as

restaurants and drugstore fountains and tax-supported institutions such

as military establishments, hospitals, and school lunch programs. Retail

purchasers are those who buy orange products through retail grocery

outlets.


Production


The production of oranges in a given season depends on the acreage,

variety, age distribution and physical environment of bearing orange

trees plus the cultural and weather conditions that exist prior to

harvest [16]. Weather is the most erratic factor affecting orange pro-

duction. Rainfall, low temperatures, and hurricane winds can cause

extensive damage to fruit and trees. Freezes have historically been the

factor most feared by Florida orange producers.

In addition to the short-term effects of weather on orange produc-

tion, freezes affect tree condition and productivity over long periods.

Freeze damage to orange trees can be roughly divided into two general

types: (1) damage to secondary branches requiring extensive pruning

(hatracking) or (2) damage so severe that the tree dies. Secondary

damage to the tree affects productivity for only a few crop seasons.

More extensive damage requires that the tree be replaced.

Florida orange production is geographically distributed over the

south and central portion of the Florida peninsula. However, following

the 1962 freeze, there was some indication that the producing area was

gradually moving farther south. As of December 1969, two-thirds of the

nonbearing acreage was located in eight south Florida counties. In each

of these counties, the ratio of nonbearing to bearing groves was in










excess of one to five (Table 1). These plantings occurred before the

enactment of the Holland Amendment which was incorporated into The Tax

Reform Bill of 1969 [23]. This amendment requires the capitalization of

all citrus grove development costs and exempts from capitalization

requirements any citrus grove (or part thereof) "replanted after having

been lost or damaged (while in the hands of the taxpayer), by reason of

freeze, disease, drought, pest or casualty . ." [23, p. 574]. Thus,

it provides an incentive for citrus producers to concentrate on the

improvement and maintenance of established groves rather than on new

grove development.

The location of the orange producing area is important from the

standpoint of a model which estimates crop size. If the location of the

production area is rapidly shifting over time, historical data cannot be

used as an estimate of future weather effects on orange production unless

adjustments are made. Since the enactment of the Holland Amendment,

locational movement within the producing area seems to be abridged.

Whether or not this is an effect of the amendment is unknown.


Dynamics of the Florida Orange Subsector


A simplified flow diagram of the subsector is presented in

Figure 1. Whole oranges move from the growing activity into the

processing-packing sector where they are converted into processed orange
2
products. From processed inventory, orange products move into wholesale

or institutional inventories and eventually consumption. Dotted lines

in the diagram represent information flows between various system



Processed products include fresh fruit ready for shipment.










Table 1. Acreage of bearing and nonbearing orange
counties as of December 1969.a


groves by Florida


Acreage Nonbearing as
County Bearing Nonbearing percentage of bearing

(acres) (percent)


Brevard
Broward
Charlotte
Collier
Desota

Hardee
Hendry
Hernando
Highlands
Hillsboro

Indian River
Lake
Lee
Manatee
Marion
Martin

Okeechobee
Orange
Osceola
Palm Beach
Pasco

Pinellas
Polk
St. Lucie
Seminole
Volusia


6,930
3,327
3,109
1,817
10,763

18,221
8,094
2,887
20,456
19,342

12,436
48,638
3,539
5,994
1,652
18,714

1,465
21,933
6,746
3,972
16,560

1,980
59,527
24,123
2,536
3,412


10.9
3.8
20.7
35.1
22.4

2.4
21.8
1.2
3.0
2.5

18.0
1.4
75.3
2.7
.3
36.2

29.3
1.4
1.4
44.8
2.8


755
125
645
637
2,407

432
1,765
34
613
483

2,237
685
2,666
167
5
6,778

500
299
93
1,781
463

87
1,232
2,574
18
19


Total 328,173 27,500


Source: [5].
a
Counties with


less than one thousand acres are excluded.











































































































Ns._










components. Information may be in the form of order rates or prices.

Associated with information flows are various delay factors. These

delays represent the time lags required for information to move through

the system. Information passed through the marketing system is the

basis for management decisions.

Several allocation problems must be solved by the market mechanism.

The rate at which fruit flows from the growing activity into the process-

ing sector must be controlled. This control is recognized in Figure 1

by hourglass shaped symbols. The solid lines represent physical flows.

Whole fruit must also be allocated among alternative product forms,

markets and consumers.

Given a competitive market system, economic theory indicates that

the allocation of productive resources will be made on the basis of the

value of the marginal product. The marginal increment of a productive

resource will go to the usage where it has the greatest value. Products

will be produced until that output is reached where the value of the

marginal unit of product is equal to its cost of production. The price

system will allocate products among competing customers according to

their ability and willingness to pay. Since information must be

collected, it is reasonable to expect adjustments after a time lag.

The demand for orange products is derived from the utility function

of the individual consumer and product allocation is accomplished through

the interaction of buyers and sellers; however, the allocation process as

visualized in Figure 1 shows the processor-packer sector as a major deci-

sion point. Processor-packers receive information concerning inventory

levels and the rates of flow of various products from inventory. If

inventories are larger than desired or if the demand for a particular










product changes, processors adjust FOB prices. These price signals pass

through the marketing system and eventually affect consumption rates.

As consumption rates change, signals are passed back through the system

in the form of orders. Processors receive information on the adjusted

movement from inventories and evaluate the effects of their pricing

policies. If the effects of the pricing policy are not those desired,

a new FOB price will be forthcoming. An equilibrium price will probably

never result from this process. Consumers react to new prices over a

period of time and while decision makers are considering new pricing

policies, consumers are still reacting to previous prices.

The relationship between short-run supply and price fluctuations

and long-run industry investment patterns is shown in the block diagram

presented in Figure 2. Weather is shown as an exogenous variable which

affects tree numbers and orange supplies. Assuming relatively stable

demand relationships for orange products, restricted supplies following

freeze damage reduce product inventories and increase the FOB prices of

orange products. Historical data indicate a strong inverse relationship

between crop size and the per box return above operating costs received

by growers (Figure 3).

During freezes the orange crops of some producers may be severely

damaged while other producers with relatively undamaged crops benefit

from high prices and high grower profits. These growers, having found

orange production profitable, tend to reinvest in new orange groves

(Figure 4). Thus, the orange subsector is characterized by periods of

restricted capacity followed by periods of large supplies and low prices.
























































Figure 2. Block diagram of major components of the Florida
orange subsector.














Crop size
(million boxes)

140 -

120 -

100 -

80 -

60 -

40 -

20 -

0


Per box returns
(dollars/box)
- 2.80


2.40

2.00

1.60

1.20

.80

.40

0


61-62 62-63 63-64 64-65 65-66 66-67 67-68 68-69 Crop season

Figure 3. Size of the orange crop and per box return above operating costs
received by growers for Florida oranges, 1961-62 through 1968-69 crop seasons.
Source: See Table 3, p. 26, for data on per box returns and [3, 1968-69
season, p. 1] for crop size data.


Per box returns
(dollars/box)


2.80

2.40

2.00

1.60

1.20

.80

.40

0


Movement
(million trees)


63-64 64-65 65-66 Crop season


Figure 4. Per box return above operating
Florida oranges and orange tree movements from
through 1965-66.
Source: See Table 3, p. 26.


costs received by growers for
Florida nurseries, 1961-62


61-62 62-63
















CHAPTER III

CHARACTERISTICS OF DYNAMO II


The subsector model was constructed to meet the design and notational
1
requirements of the DYNAMO II computer compiler. The DYNAMO II compiler

is a set of computer instructions used to translate mathematical models

into tabulated and plotted results. It was developed by the industrial

dynamics group at the Massachusetts Institute of Technology.2


Special Features


DYNAMO II has several special features that facilitate model con-

struction. These features include the following:

1. The compiler will reorder equations within a variable type

whenever necessary in order to perform computations.

Reordering will continue until all calculations have been

made or until the compiler has identified equations that

depend on other equations which in turn depend upon the

equation defined, in which case the system is simultaneous

and DYNAMO II prints an error statement identifying the

equations involved.


Version four was used in this study. It runs on the IBM S/360
computing system operating under OS or CP/CMS and is distributed by
Pugh-Roberts Associates, Inc., 179 Fifth Street, Cambridge, Mass.
02141. See Pugh [20] for detailed documentation.
2
The industrial dynamics approach to problem solving is discussed
by Forrester [7].









3
2. System macros in DYNAMO II includes clipping and limiting

functions, exponential delays, maximum, minimum, random

numbers, pulse, ramp, sample, smooth, step, switch, table,

and trigonometric.

3. The compiler contains a convenient method of specifying output.

The output routine includes various scaling alternatives and

provides output in tabulated and plotted form. Data is out-

putted chronologically with respect to simulated time and can

be requested for each calculation interval or some multiple

of it.


Time Notation


The time notation used in DYNAMO II is presented in Figure 5.




DT DT

JK- --KL-
interval interval Time
J K L

Figure 5. Time notation for DYNAMO II.


In the computational process, DT denotes the period of time

between calculations, K corresponds with the point in time for which

calculations are currently being made, J represents the time for which

calculations were previously made and L denotes the next calculation

time. The intervals between these time points are termed JK and KL.

Once the computer calculates the values of all variables for time K and

the KL interval, the system moves forward one step in simulated time and

3
For definitions see Pugh [20].










the values associated with time K become associated with time J. In

this recursive fashion, the computer moves through the calculation

process and time in the simulation.


Type of Variables and Computational Sequence


The DYNAMO II compiler is designed to handle three principal types

of variables: levels, auxiliaries and rates.

A level is a variable whose value at time K depends upon its value

at time J and on changes during the JK interval. Levels are usually

defined by equations of the form:

quantity at time K = quantity at time J + change during

the JK interval.

Rates correspond to flows over time and are calculated for the KL

interval. They are defined by levels and auxiliaries from time K and

sometimes by rates from the preceding time interval.

Auxiliaries are values calculated at time K from levels at time K

and from auxiliaries previously calculated at time K.

The computational sequence in DYNAMO II is levels, auxiliaries and

rates. In order to assure that the model is recursive and that values

will be available for calculations, equations must be consistent with

the organizational system presented in Table 2. A detailed exposition

of DYNAMO II is given by Pugh [20].










Table 2. Organizational structure for DYNAMO II equations.


e on Time associated Time associated with variables
Variable on
left of equation with variable on right if variable is
on left L A R S C N


L Level K J J JK none none

A Auxiliary K K K JK none none

R Rate KL K K JK none none

S Supplementary K K K JK K none none

C Constant none *

N Initial Value none none none


Source: [20, p. 24].

Not permitted.
















CHAPTER IV

THE MODEL


The model of the Florida orange subsector consists of a set of

relationships between individual system components. These relationships

together with initial starting values provided the information necessary

to simulate system behavior. Much of the effort in this study was

expended in the specification and estimation of model equations and to

a large extent the validity of the study must be judged on the basis of

the confidence placed in them. Some relationships are self-explanatory

given the definitions of the variables involved, others require explana-

tion and justification. The model presented in this chapter represents

a mathematical formulation of the interrelationships that underlie the

dynamic behavior of the orange subsector. It draws heavily on previous

models constructed by Raulerson [21] and Jarmain [9]. No attempt has

been made to acknowledge each duplication. A detailed flow diagram is
I1
presented in Figure 6. Appendix A contains an alphabetic list of

variable names.


The following symbols were used in the flow diagram:

S rates 0 policies

Levels -- material flows

O auxiliaries ---> information flows
- constants




















SENIORS


WEATlHER
EFrrCTs
.KCIp..2


~I, ry
Al


k,- F.7


ri -


DEMAND SECTOR 10


Figure b. Flow diagram of the DYNAMO
model of the Florida orange subsector.


'" w,.l iar 1~
rr*i~uwrr rr~ur
r.,.,. Lz,
"' "' i
L_-
~t;a
Lr~
----- ------~i- -
1


SiU110


RETAI MD INSTITUTIONAL
IMVENTORY ANM SALES SKTOR S


r c I PI S


ADYERTISINb
SECTOR b


" .
*/ fcd. /&4-
, ^ ^. _


.,,Q. KQ.
A?? >


FoB8 PRICV
SECTOR 7


---- i - -


.. ......... ... .' ---- -
---------- ------- aw

- - - - - - -


RETAIL AND
*.-f: INSTITUTIONAL PRICE
SECTOR q


La?: i

~Cr~ ~,
t~'-~~"


N T


""


,i"")

~...i
1.










Tree Numbers Sector


The number of productive trees was increased by trees becoming

productive and decreased by productive trees lost (equation 1). During

an initial period after the start of the simulation, the number of trees

becoming productive was expressed as a fraction of the number of produc-

tive trees in existence (equations 2 and 2A). This procedure allowed

trees planted but not productive at the start of the simulation to be

inserted into the system. After the initial period, trees became pro-

ductive as a result of increases in the productivity of young trees and

the recovery of freeze damage (hatracked) trees (equation 2B). The rate

at which young trees became productive was expressed as a sixth order

exponential delay (actually two cascaded third order delays) with an

input equal to the number of new trees planted and a delay in trees
2
becoming fully productive of 13 years (equations 3 6. The exponen-

tial delay approximated the yield response of newly planted orange trees

by allowing larger proportions of a newly planted tree to come into pro-

duction over simulated time. In Figure 7, the output from the delay in

response to a step input is compared with a weighted average of the

yields estimated by Chern [2, p. 58].

L PT.K = PT.J + (DT)(TBP.JK PTL.JK) 1

ZTBP.JK if TIME.K 156
R TBP.KL = or
NTBP.JK if TIME.K < 156 2

R NTBP.KL = (.178)(PT.K)/WPY 2A

R ZTBP.KL = YTBP.JK + HTBP.JK 2B


2See Forrester for detailed explanation of exponential delays



























Tree
productivity
(percent of
mature yield)


Step input


80 r exponential
yield estimate
of the model


empirical estimate


0 5 10 15 20 25 30 35 Age of
tree
(years)


Figure 7. Comparison of
yield estimates.


output from exponential delay and empirical


Source: Empirical estimates from [2, p. 58].










R YTBP.KL = DELAY3(XTBP.JK, XDG) 3

R XTBP.KL = DELAY3(NTP.JK, XDG) 4

N XDG = DG/2 5

C DG = 676 weeks 6

PT productive trees (trees)

TBP trees becoming productive (trees/week)

PTL productive trees lost (trees/week)

YTBP young trees becoming productive (trees/week)

HIBP hatracked trees becoming productive (trees/week)

NTBP initial trees becoming productive (trees/week)

NTP new trees planted (trees/week)

DG delay in growing (weeks)

XTBP internal transfer variables (trees/week)3

XDG internal transfer variable (weeks)

ZTBP trees becoming productive after initial period (trees/week)

TIME simulated time (weeks)

WPY weeks per year (weeks)

The rate at which new tree plantings occurred was controlled by a

clipping function which set the number of new trees planted equal to

zero or XNTP depending on whether or not a restriction on new tree

planting was in effect (equation 7).

The restriction on new tree plantings was effective when average

grower profit was greater than the new tree planting restriction (equa-

tion 8). The effect of the policy was to prevent new trees from being

planted when average grower profits were high. The rate at which new

3
Internal transfer variables will be defined in the future only
when their meaning is not readily apparent.










tree plantings would have occurred without considering the restriction

policy was expressed (equations 9, 11 and 12) as a fraction of the

number of productive trees in existence and was dependent upon the level

of average grower profits per 90 pound field box (hereafter box).

Figure 8 presents the basis for the assumption concerning this

dependency. Supporting data are presented in Table 3.

fXNTP.JK if NTPR AGP.K
R NTP.KL = or 7
0 if NTPR < AGP.K

(1.50 if the policy was to be operative
C NTPR or 8
1,000.0 if the policy was to inoperative

R XNTP.KL = (PT.K)(FA.K)/WPY4 9

C WPY = 52 10

A FA.K= TABHL(FAT, AGP.K, 0, 3.00, .50) 11

C FAT* = .022/.054/.086/.118/.150/.182/.214 12

XNTP the rate at which new tree plantings would have occurred

without the planting restriction (trees/week)

NTPR the value above which the planting restriction

became effective (dollars/box)

FA fraction of new trees added

Hatracked trees becoming productive were expressed as a ninth order

delay with an input equal to the number of trees hatracked (equations

13 17). The number of trees hatracked was expressed as a fraction of

the productive trees in existence (equation 18). The output from this

delay in response to a unit input was faster and the average delay time

shorter than for the sixth order delay that controlled the rate at which


The division of WPY was necessary since XNTP was expressed as trees
per week.





















25
Tree
movement
(percent)

20




15 after /
1957-58
freeze after
Il eI 1962-63
/ freeze
10
before
before 1962-63
1957-58 freeze
freeze
freeze ,r





I I I I I
0 .50 1.00 1.50 2.00 2.50 3.00

Returns above
operating costs
(dollars/box)

Figure 8. Relationship between per box returns above operating
costs and movement of orange trees from Florida nurseries before and
after the 1957-58 and 1962-63 freezes.

Source: Table 3.
a
Movement as a percent of mature tree equivalents.



















am)







0



eH
a) W
0 I


'4-1 CW


C)






0 m




ud
0
4J0








o11

OW
1) 0

00














0 4JH
> 4





u a)
0 o
-Wo







m >
a4 0 a




>00





Cdr
0-1













a)
E0





'0 4J















C 1






30
40


0

>d0


0o

a)0)
3 0.






41 0





Q8
0














Ca
Cd
4J i4 >

0 -H











e 0
>0


0. 4








0 0

a)i













C 0
o i










5
0











a C
0 4-
.0 04


41-i



0 0

)a N
4-1









a)
4 )
0 U)0
CI


Nc C Lnno 00' CO4 C- Cl C4 0' w"
S0 t-i tLoM'ON 0 V)iI- Ln 00'-T'

















0 ClI Ln C-4 N 4 0' -4 r4
-----l^ -- s -- o --4.04.0.04
NlCl4 l -40 N -
-4 -4 4 4 -4 -1 -4

















M m LIn N N -4 VI C 1 0

000MON0m'O-4N-4Cnco00044 40
Ln oo w C m N N o'd r-C-

-lr- NiNNMlN l















'mCLICmml-om0-' i o0 -4 o
N4-M N4 Ln -' w 0 r- a0
q, CfCNClCIN 0 4 0
----------4-4-4-

vr- 4 r4r-4 1n- N 4 cN N












Co r- N o m 0 v-i cN Cn I- Llo rC oO 0' 0 '-4
Ln I In I I I o o I o o I o D I- r-
iCo I o"I-N t LC N 0' 0'o 0
LI Li Ln Ln irn DD D C o C D C D C o C D C 0 C 0 CC -
-4-4 -4-4 r- -1 -4- -4 -4 r- -1 -f
????? ???????? ~
NamoHoNMmme>@mo


0



e ed
4 (0
44
0)
4Ja
,-4 Ca


'4J,
N4
4-1

04

u
a'.
ICa





0)
co
N '0

O4
00jia
-H *r4
dC-






00
4a





44 C
0o
41
ON












.0
Ssr
0a











>4-
0) 4






414
lcu
434J







:g


0


a) C








0
-0>
0 44
'4)44



















p4
4-iJ
3





















44

440
0

00
do
0. 0














bW
ai) a
00














NW









W
S01
0
(J00


4.r-I

900

0 4
44
'4-1
1410
00
WO


S.S

Cd 0

4J4<


44
ad










newly planted trees became productive. This difference reflected the

rapid increase in the productivity of hatracked trees. The length of the

delay was equal to 208 weeks. The rate at which productive trees were

lost depended on the stochastic impact of weather and the "normal"

losses associated with the passage of time (equation 19). Productive

trees lost as a result of freeze damage was determined by fractions

generated within the freeze effects sector of the model and by the

number of productive trees in existence (equation 20). The "normal"

loss was expressed in a similar fashion (equation 21).

R BTBP.KL = DELAY3(XHTBP.JK, XDP) 13

R XHTBP.KL = DELAY3(YHTBP.JK, XDP) 14

R YHTBP.KL = DELAY3(THR.JK, XDP) 15

N XDP = DP/3 16

C DP = 208 weeks 17

R THR.KL = (FHR.K)(PT.K) 18

R PTL.KL = PTLA.JK+ PTLF.K 19

A PTLF.K (1/DT)((FTLF.K)(PT.K) + (FHR.K)(PT.K))5 20

R PTLA.KL = (PT.K)(FL.K)/WPY 21

THR number of trees hatracked (trees/week)

DP length of delay in recovery of hatracked trees (weeks)

PTLA productive trees lost as a result of "normal" aging

factors or tree abandonment (trees/week)

PTLF productive trees lost as a result of freeze damage (trees)

FTLF fraction of productive trees lost as a result of freeze

damage

FHR fraction of productive trees hatracked

5
Division by DT is necessary as a result of the multiplication that
occurs in equation 1.










FL fraction of productive trees lost "normally" or as a result

of tree abandonment

The value of the "normal" fraction lost variable was controlled by

a clipping function (equation 22) which set FL equal to a tabular value

which reflected "normal" tree losses (equations 23 and 24) or to a value

that simulated a consciously applied policy of tree abandonment on the

part of orange producers. The tree abandonment restriction could be

made inoperative by setting its value at a sufficiently low level

(equation 25). When the policy was effective, trees were removed from

production whenever grower profit was less than $.15 per box. The rate

at which trees were removed from production was positively related to

crop size through the DD variable (equations 26 and 27).

XFL.K if GP.K = TAR
A FL.K= or 22
YFL.K if GP.K < TAR

A XFL.K = TABHL(XFLT, AGP.K, -.50, 2.00, .50) 23

C XFLT* = .08/.06/.04/.03/.02/.015 24

f.15 if tree abandonment policy was operative
C TAR= or 25
-1000.00 if the tree abandonment policy was
inoperative

A YFL.K = ( )(DD.K YDD) 26

C YDD = 2.012E6 27

XFL "normal" fraction of trees lost

YFL fraction of trees lost when tree abandonment restriction

was operative

GP grower profit (dollars/box)

TAR tree abandonment restriction (dollars/box)

DD disappearance desired (boxes/week)










YDD disappearance associated with grower profits of $1.00
6
per box (boxes/week)


Weather Effects Sector


Values which determined weather effects were obtained in one of two

ways depending on whether historical data were needed (for model valida-

tion purposes) or whether values were to be generated stochastically.

When historical values were desired, option I was used; otherwise, values

were generated by option II. Weather effects were divided into three

categories: tree effect, hatracking effect, and yield effect. In the

model each effect was treated as a pulse input which occurred once each

season (equations 28 30).8

A FTLF.K= PULSE(XFTLF.K, 52, 52) 28

A FHR.K= PULSE(XFHR.K, 52, 52) 29

A FYLF.K = PULSE(XFYLF.K, 52, 52) 30

Option I

Option I allowed predetermined values which reflected historical

weather conditions to be incorporated into the model. These values were

expressed as table functions dependent on simulated time (equations

31 36).

6
A disappearance rate of 2.012 million boxes per week was associated
with grower profits of $1.00 per box only when weather and inventories
were normal, the demand shifter was equal to its mean value, advertising
influences were equal to 1, U.S. population was 193.89 million and the
yield of oranges was 4.9 single strength gallons per box.

During initial stages of model validation it was desirable to
control as many factors as possible and to observe model performance
under relatively stable conditions. In order to partially accomplish
this a third weather option was constructed. This option maintained
"average" weather conditions. For details see Appendix B, p. 129.

SWeather effects for the first season are reflected in initial values.










A XFTLF.K =TABHL(XFTLFT, TIME.K, 52, 572, 52) 31

C XFTLFT* = See Table 4. 32

A XFHR.K = TABHL(XFHRT, TIME.K, 52, 572, 52) 33

C XFHRT* = See Table 4. 34

A XFYLF.K = TABHL(XFYLFT, TIME.K, 52, 572, 52) 35

C XFYLFT* = See Table 4. 36

A WI.K = SWITCH(1, 1, TIME.K) 36A9

A WIY.K = CLIP(WI.K, 1, WI.K, 1) 36B


Option II

When option II was used, a weather influence was selected from a

population that was normally distributed with mean one and standard

deviation .06 (equation 37). The total effect of this distribution was

consistent with the "weather index" estimated by Parvin [16]. The

weather influence selected was subtracted from one to arrive at an

adjusted weather influence (equation 38). The yield effect was set

equal to the adjusted weather influence when the value of the weather

influence was less than one; otherwise, it was set equal to zero (equa-

tion 39). Good weather was accounted for through a weather influence

which increased yield (equation 40). Tree and hatracking effects were

expressed as functions of the yield effect (equations 41 44).

A WI.K = NORMRN(1, .06) 37

A XAWI.K = 1 WI.K 38

A AWI.K = MIN(XAWI.K, 1) 38A


9
Equations 36A and 36B have only mechanical significance in
option I. They set to constants variables determined stochastically
under option II.










Table 4. Yield loss, tree loss and
through 1972-73 seasons.


hatrack loss factors, 1962-63


Lossa (proportion)
eason Tree Hatrack Yield Total


1962-63 .226 .080 .066 .372

1963-64 .185 0 .051 .236

1964-65 0 0 .246 .246

1965-66 0 0 .155 .155

1966-67 0 0 -.189 -.189

1967-68 0 0 .176 .176

1968-69 0 0 -.029 -.029

1969-70 0 0 -.057 -.057

1970-71 0 0 -.058 -.058

1971-72 0 0 .012 .012

1972-73 0 0 0 0


aNegative fractions indicate
increase crop size above expected.


that the effect of the factor was to










0 if WI.K 1
A XFYLF.K = or 39
AWI.K if WI.K < 1

WI.K if WI.K = 1
A WIY.K = or 40
1 if WI.K < 1

A XFTLF.K = TABHL(XFTLFT, XFYLF.K, 0, .35, .35) 41

C XFTLFT* = 0/.15 42

A XFHR.K = TABHL(XFHRT, XFYLF.K, 0, .35, .35) 43

C XFHRT* = 0/.35 44

WI weather influence

AWI adjusted weather influence

WIY weather influence on yield


Crop Size Sector


Crop size was equal to the quantity of fruit remaining plus the

quantity of fruit used to date (equation 45). The quantity of fruit

remaining at time K was equal to the quantity remaining at time J plus

fruit added minus fruit used or lost during the JK interval (equation

46). Fruit usage was accumulated as a level which was cleared at the

end of each season (equation 47). This was accomplished through a fruit

discarded pulse which occurred once each year (equation 48). The pulse

that cleared the level equation was a function of the quantity of fruit

used (equation 49).

A CS.K = CR.K + FUTD.K 45

n
L CR.K = CR.J CLF.J + NCA.JK (DT)( Z FU(I).JK) 46
I=
n
L FUTD.K = FUTD.J + (DT)( E FU(I).JK FD.JK) 47
I= 1

R FD.KL = PULSE (FDP.K, 52, 52) 48










A FDP.K = FUTD.K/DT 49

CS crop size (boxes)

CR crop remaining (boxes)

FUTD fruit used to date (boxes)

NCA new crop added (boxes/week)
th 10
FU(I)- fruit used in I product0 (I = 1, . 7) (boxes/week)

CLF crop lost as a result of freeze damage (boxes)

FD fruit discarded (boxes/week)

FDP fruit discarded pulse (boxes)

N number of orange products considered in the model

New crop added was a function of the new crop pulse which occurred

at the beginning of each new crop season (equation 50). The size of the

pulse depended on the number of productive trees, yield per tree and a

stochastic weather influence on yield (equation 51). Yield per tree was

considered a function of(lagge) average grower profit and reflected the

improved cultural practices provided by growersin response to higher

prices (equations 52 and 53).

R NCA.KL = PULSE(CSP.K, 52, 52) 50

A CSP.K = (PT.K)(BPT.K)(WIY.K) 51

A BPT.K = TABHL(BPTT, AGP.K, -.50, 2.00, .50) 52


10The following numerical code was used to identify the Ith product.

Market
Product Retail Institutional
(Ith product)

Frozen concentrated orange juice 1 5
Chilled orange juice 2 6
Canned single strength orange juice 3 7
Fresh oranges 4 *

Not included.












ATTENTION!


Error Note

The influence of weather on grower costs (equation 60) was intended

to be determined once at the beginning of each season and then to be held

constant until the start of the next crop year. During years when weather

was favorable (WI>1) grower costs per box would be decreased. On the other

hand, unfavorable weather (WI<1) would cause a cost increase. Due to an

error in programming, this was not what actually occurred in the operation

of the model. The weather influence was an auxiliary (equation 37) which,

with DT specified as .5 was calculated twice per week. This caused grow-

er cost per box (equation 60) to be subject to a stochastic influence.

The major effects of the error are the following.

(1) On the average, grower profits were overstated (understated) dur-

ing seasons of unfavorable (favorable) weather.

(2) The rate at which new trees were planted was affected through

average grower profits; however, since the averaging period was two years

the stochastic effect was small.

(3) When the tree abandonment policy was operative (equations 22 and

25), the rate of tree abandonment was influenced since it was based directly

on the level of grower profits.


Correction

The problem may be corrected by changing equation 60 to

A GC.K=CPB/XWI.K 60

and adding the following equations:











fWI.K if WP.K>52
A XWI.K or 60A
LWI.K if WP.K<52

L LWI.K=XWI.J 60B

N LWI=1 4 60B


Comparison

A comparison of results from uncorrected and corrected versions of

the model is presented below for two of the policies (B and TA2, see page

96) considered in the study.



Grower profits Average FOB price Crop size
Policy Presenta Std. Presentb Std.b Presenta Std.b
value dev. value dev. value dev.

(Uc 1000.98 106.59 7.16 .20 1746.39 61.82
Base (B)
C 1007.48 100.02 7.15 .20 1747.96 64.33

Tree U 1165.11 61.35 7.43 .15 1649.96 47.60
abandonment
(TA2) C 1139.58 63.11 7.36 .17 1673.84 52.07


a Large values preferred.

b
Small values preferred.

cU uncorrected; C corrected.










C BPTT* = 4.5/4.6/4.7/4.8/5.0/5.3 53

CSP crop size pulse (boxes)

BPT yield per tree (boxes/tree)

AGP average grower profit (dollars/box)

The crop lost as a result of freeze damage was the sum of the loss

from each of the three freeze effect categories (equation 54). Each of

these losses was the product of the appropriate loss factor (from the

freeze effects sector) and the crop size pulse (equations 55 57).

A CLF.K = TLOSS.K + HLOSS.K + YLOSS.K 54

A TLOSS.K = (FTLF.K)(CSP. K) 55

A HLOSS.K = (FHR.K)(CSP.K) 56

A YLOSS.K = (FYLF.K)(CSP.K) 57

TLOSS crop loss associated with tree kills (boxes)

HLOSS crop loss associated with hatracking (boxes)

YLOSS yield loss (boxes)


Grower Profit Sector


Grower profit per box was the difference in on-tree price per box

and grower cost (equation 58). Grower cost was initially set at .85

dollars per box and remained at that level until option II was employed

to generate a weather influence (equation 59). When option II was used,

grower cost was influenced by weather conditions (equation 60). On-tree

price was a function of the weighted average FOB price paid for orange

products (equations 61 and 62). Average grower profit was an exponen-

tially smoothed function of grower profit (equations 63 and 64). Profit

was calculated by multiplying profit per box times the number of boxes

used (equation 65). It was then accumulated for each year in a level

equation (equations 66, 66A and 66B).










A GP.K = OTP.K GC.K 58

C CPB = .85 dollars per box 59

A GC.K = CPB/WI.K 60

A OTP.K = TABHL(OTPT, AFOB.K, .35, 1.25, .18) 61

C OTPT* = .03/1.00/1.96/2.94/3.90/4.86 62


L AGP.K = AGP.J + (DT)(TG)(GP.J AGP.J) 63

C TAGP = 104 weeks 64

R PROFT.KL = (GP.K)(TFU.K) 65

L CP.K = CP.J + (DT)(PROFT.JK CPD.JK) 66

R CPD.KL = PULSE(CPDP.K, 52, 52) 66A

A CPDP.K = CP.K/DT 66B

OTP on-tree price (dollars/box)

GC grower cost (dollars/box)

CPB cost per box (dollars/box)

AFOB weighted average FOB price of orange products

(dollars/gallon single strength equivalent)

TAGP time for averaging grower profits (weeks)

PROFT profit (dollars/week)

TFU total fruit usage per week (boxes)

CP cumulative profit per year (dollars)

CPD cumulative profits discarded (dollars)

CPDP cumulative profit discard pulse (dollars)


Processor Disappearance Sector


Weeks of crop (supply) remaining was a function of crop remaining

and average fruit usage (equation 67). Average fruit usage was equal










to fruit usage exponentially smoothed with a four week averaging period

(equations 68 and 69). Fruit usage associated with the Ith product

depended on the disappearance of product I and a conversion factor

(equations70 76). The constant portion of the conversion factor was

based on yield figures for the 1969-70 and 1970-71 seasons (Table 5).

The conversion factor remained at the constant level until the weather

influence was generated. When the weather influence was available,

yield was influenced by weather conditions (equations 77 90). Pro-

cessor disappearance was a function of retail and institutional demand

and processor availability (equations 91 97). Processor availability

was related to the number of weeks of crop remaining (equations 98 and

99).

A WCR.K = CR.K/AFU.K 67

n
L AFU.K = AFU.J + (DT)(T ) Z (FU(I).JK AFU.J) 68


C TAFU = 4 weeks 69

R FU(I).KL = (PD(I).JK)(BPG(I).K) 70-76

n
A TFU.K= E FU.JK 76A
1=1

A BPG(I).K = ( I.K77-83
(GPB(I))(WI.K)
C GPB(I) = See Table 5. 84-90

R PD(I).KL = (D(I).JKXPA.K) 91-97

A PA.K= TABHL(PAT, WCR.K, 0, 15, 5) 98

C PAT* = 0/.84/.97/1.0 99

WCR weeks of crop remaining (weeks)

AFU average weekly fruit usage (boxes)

TAFU time for averaging fruit usage (weeks)










PD(I) processor disappearance product I (gallons

single strength equivalent/week)

BPG(I) conversion factor for product I (boxes/gallon

single strength equivalent)

GPB(I) conversion factor for product I (gallon

single strength equivalent/box)

D(I) order rate for the Ith product (gallons

single strength equivalent/week)

PA processor availability


Table 5. Conversion factors for major orange products.


Conversion factors
Product Gallons single strength
equivalent per 90 pound box


1 4.90
2 5.29
3 5.20
4 5.29
5 4.90
6 5.29
7 5.20


Source: Based on yield estimates for 1969-70 and 1970-71 seasons.


Advertising Sector


Advertising revenue was equal to fruit usage times the advertising

tax less administrative and other nonadvertising costs (equation 100).

Administrative and other nonadvertising costs were assumed to be a

constant $26,306 per week (equation 101). The advertising tax rate

was based on actual values for the 1962-63 through 1970-71 seasons

(Table 6). After the 1970-71 season, the tax was assumed constant at










Table 6. Advertising tax rates for Florida oranges by type of use,
1962-63 through 1970-71 seasons.


Season Advertising tax rate
Fresh Processed

(cents/box)

1962-63 9 9

1963-64 9 9

1964-65 10 8

1965-66 10 8

1966-67 10 8

1967-68 10 8

1968-69 10 8

1969-70 10 8

1970-71 10 10


Source: Personal interview with
Florida Department of Citrus.


the Economic Research Department,










10 cents per box (equations 102 and 103). Advertising tax revenue

accumulated at time K was equal to revenue accumulated at time J plus

revenue collected minus revenue spent during the JK interval (equation

104). The weekly advertising expenditure was the product of revenue

available for advertising and the fraction spent each week (equation

105). The fraction spent each week reflected the seasonal expenditure

pattern presented in Figure 9 and was a function of the number of weeks

remaining in the season (equation 106 and 107). Trademark advertising

was not considered in this study.

n
R ATR.KL = ( E FU(I).JK)(AT.K) AC 100
I=i

C AC = 26,306 101

A AT.K = TABHL(ATT, TIME.K, 0, 416, 52) 102

C ATT* = .09/.09/.08/.08.08/.08/.08/.08/.10 103

L ATRA.K = ATRA.J + (DT)(ATR.JK ATS.JK) 104

R ATS.KL = (ATRA.K)(FSPW.K) 105

A FSPW.K = TABHL(FSPWT, WP.K, 1, 52, 1) 106

C FSPWT* = See Figure 9. 107

ATR advertising tax revenue (dollars/week)

AC administrative cost (dollars/week)

AT advertising tax (dollars/box)

ATRA advertising tax revenue accumulated (dollars)

ATS advertising tax spending (dollars/week)

FSPW fraction spent per week

WP weeks passed (weeks)

Consumers were assumed to respond gradually to advertising expendi-

tures in the model. The magnitude of their response at a given time was







40



















Weighting
factor


160


.02439
120 I I
.02033a | .02033

80



40 I .00813



0
40 .------------------------- ---



Sept. 10 Dec. 10 Mar. 10 June 10 Months

Figure 9. Seasonal pattern of generic advertising and promotional
expenditures for Florida oranges.

Source: Personal interview with the Economic Research Department,
Florida Department of Citrus.
a
Fraction of tax revenue spent per week.










determined on the basis of the average advertising expenditure for the

preceding two years (equations 108 117).

Since little data were available, advertising responses for insti-

tutional products were based on the assumption that customer oriented

institutional purchasers such as restaurants and drugstore fountains

were affected by advertising programs in the same manner as retail con-

sumers. Noncustomer oriented institutions such as hospital and military

establishments were assumed to be unaffected by advertising programs

(equations 118 123).11

L AA.K = AA.J + (DT)(1/TAA)(ATS.JK AA.J) 108

C TAA = 104 weeks 109

A AI1.K = TABHL(AI1T, AA.K, .5E5, .3E6, .5E5) 110

C AIlT* = .96625/.9810/.9925/1.0030/1.0095/1.015 111

A AI2.K = TABHL(AI2T, AA.K, .5E5, .3E6, .5E5) 112

C AI2T* = .9445/.9720/.9895/1.0055/1.0195/1.027 113

A AI3.K = TABHL(AI3T, AA.K, .5E5, .3E6, .5E5) 114

C AI3T* = .9555/.9920/.9990/.9990/.9910/.9840 115

A AI4.K = TABHL(AI4T, AA.K, .25E5, .225E6, .5E5) 116

C AI4T* = .74/.92/1.068/1.116/1.146 117

A AI5.K = TABHL(AI5T, AA.K, .5E5, .3E6, .5E5) 118

C AI5T* = .97604/.98651/.99468/1.00213/1.00675/1.01065 119

A AI6.K = TABHL(AI6T, AA.K, .5E5, .3E6, .5E5) 120

C AI6T* = .96781/.98376/.99391/ 1.00319/1.01131/1.01566 121

A AI7.K = TABHL(AI7T, AA.K, .5E5, .3E6, .5E5) 122

C AI7T* = .97419/.99536/.99942/.99942/.99478/.99072 123


11For the data on which these relationships were based, see
Appendix E.










AA average advertising (dollars/week)

TAA time for averaging advertising (weeks)

AI(I) advertising influence on demand for the Ith product


FOB Price Sector


The FOB price of orange products was the mechanism through which

allocation was accomplished. Allocation occurred in a resursive fashion.

A time lag existed during which the model waited for consumers to respond

to the most recent price adjustment. When price adjustments did not pro-

duce the desired effect or when conditions changed, new prices would be

forthcoming. In making price changes, the model considered the size of

the orange crop, the time that remained in the marketing season, the

rate at which fruit was being used and the relative profitability of

orange products. When fruit usage was less than desired, the model

attempted to increase consumption and order rates by reducing prices.

When it appeared that shortages would occursthe model increased prices.

Price adjustments designed to alter fruit usage were accompanied by

adjustments in the relative price of orange products. The model adjusted

relative price whenever the marginal net revenue from the sale of one

product was different from another. For example, when the marginal net

revenue from product I was greater than that from product J, the model

increased the price of J, reduced the price of I, or both. Thus, the

model attempted to equate marginal net revenues among orange products.12

The marginal net revenue of product I at time K was specified as a

function of the FOB price of the Ith product at time J (equations 124 -

12
Refer to pp.47-49 for a discussion of the allocation problem. Net
marginal revenue functions were derived from cost and revenue relation-
ships. For details see Appendix C.










130). Marginal net revenues were weighted by the quantity of each

product to arrive at a weighted average marginal net revenue per gallon

single strength equivalent (equation 131). This weighted average was

used to suggest an FOB price for each product (equations 132 138).

Suggested FOB prices along with demand equations and advertising influ-

ences on demand provided estimates of the monthly per capital quantity

of product demanded (equations 139 145). When multiplied times an

estimate of U.S. population, summed and converted to boxes per week,

these estimates suggested processor disappearance (equations 146 153).

Tables 7, 8 and 9 show the demand functions, mean values of variables

and the data periods, respectively, for the demand relationships.

L MNR(I).K = Al(I) + (A2(I))(FOB(I).J) + (A3(I))(DS.J) 124-
130


n
E (MNR(I).K)(XQD(I).K)
A AMNR.K = I=1 131
n
S XQD(I).K
I=1

A XFB(I)S.K = A4(I) + (A5(I))(AMNR.K) + (A6(I))(DS.K) 132-
138

n
A XPQS(I).K = (AI(I).K)(A7(I) + Z ((A8(I))(XFB(I)
I =

S.K)) + (A9(I))(DS.K) 139-145

A XQS(I).K = (XPQS(I).K)(POP.K)/4 146-152

n
A PDS.K = E ((BPG(I).K)(XQS(I).K)) 153
I =1

MNR(I) marginal net revenue of Ith product (dollars/

gallon single strength equivalent)










Table 7. Relationship between per capital quantity of an orange product
that would be demanded by retail and institutional consumers
given adequate time for system adjustment and the FOB price
of the product.


Quantitya FOB price
(gallons single (dollars/gallon Seasonal
strength equivalent Intercept single shifterb
per capital per month) strength equivalent)



QC .145935 -.106017 -.009218
FCOJ

QR .035136 -.047900 -.000294
COJ

QR .023731 -.027704 .000131
CSSOJ

O .126176 -.117840 c

1 .052886 -.055452 c
TFCOJ

Q .078273 -.058530 c
COJ


QCSSOJ .173864 -.185287

Source: Retail demand relationships for processed products were
obtained from the Economic Research Department, Florida Department of
Citrus. The fresh orange relationship was derived from elasticity esti-
mates reported by Langham [10, p. 20]. Demand relationships for insti-
tutional products were obtained from [26, 27]. All relationships have
been adjusted.
a
Superscript represents retail or institutional market. Subscript
indicates product type.

bSeasonal shifter = 0 Sept. Mar.
[1 Apr. Aug.
c
Not included in regression model.










Table 8. Mean values associated with estimated demand relationships.


FOB price Quantity
Product (dollars/gallon (per capital gallons
single single strength
strength equivalent) equivalent/month)


FCOJR .5242 .0867


COJR .5532 .0085


CSSOJR .5547 .0084


FOR .7618 .0364


FCOJI .7492 .0113


COJI 1.0600 .0162


CSSOJI .9043 .0062


a
The subscript refers to the retail or institutional market.






46


Table 9. Base data periods associated with estimated demand relationships.


Product Market
Retail Institutional


FCOJ January, 1968 December, 1963 -
April, 1971 November, 1966

COJ January, 1968 December, 1963 -
April, 1971 November, 1966

CSSOJ January, 1968 December, 1963 -
April, 1971 November, 1966

Fresh oranges August, 1962 a
July, 1963


aNot applicable.










FOB(I) FOB price of Ith product (dollars/gallon single

strength equivalent)

AMNR weighted average marginal net revenue (dollars/

gallon single strength equivalent)

XQD(I) quantity of the Ith product demanded at time J

(gallons single strength equivalent/week)

XFB(I)S suggested FOB price for product I (dollars/

gallon single strength equivalent)

XPQS(I) monthly per capital consumption of product I

suggested (gallons single strength equivalent

per capita/month)

POP U.S. population

XQS(I) suggested consumption of Ith product (gallons

single strength equivalent/week)

PDS suggested processor disappearance (boxes/week)

In order to maximize profits, economic theory indicates that a

product should be allocated among markets so as to equate the marginal

net revenue from the sale of the product in each market. The use of the

average marginal net revenue to suggest new FOB prices insured that this

condition was met. Perhaps this should be illustrated by an example.

Assume that the FOB prices (PI, P2 and P3) of products 1, 2, 3 yield the

marginal net revenues (MNR1, MNR2 and MNR3) shown in Figure 10. Further

assume that the marginal net revenue of product 1 is less than the

marginal net revenue of product 2 and greater than that of product 3.

Since prices and marginal net revenues are positively related, profit

maximization requires that the price of product 2 be reduced relative to

product 1 while that of product 3 should be increased. A simple average






















4,
0



0
o






o
.0
-4J













0 *


u
0
N


-4

M




00 -


S41
C o
00









44 co
4 -
41 4
$) 44








- a

o o
4 m


4 4











p y
3 -ri4
J4 0-
0 4
U 44













-4 44>
--4-4o)








11)


SC


E 0

0 4
a 0o


m
CO


-4 -4
0H










044
pt 0
O 00




















4 0
- o.-n
044)
'O 00










of the three marginal net revenues yields a value equal to AMNR.13

Prices suggested by this average value will be associated with equal

marginal net revenues. In the example, the FOB price for product 1

would be unchanged while prices of products 2 and 3 would be reduced

and increased, respectively. This technique adjusts relative prices;

however, it does not consider adjustments in overall fruit usage relative

to desired. In order to make this adjustment, it was necessary to com-

pare processor disappearance suggested with processor disappearance

desired.1

Desired disappearance was a function of crop remaining, the number

or weeks left in the marketing season, and the end of season carry-over

(equation 154). The carry-over was set equal to an eight week supply,

except when an increased carry-over was operative in which case the

desired carry-over increased to a 16 week supply (equation 155). Weeks

passed were accumulated by a level equation which was reset to zero at

the beginning of each season (equations 156 158).

A DD.K = (CR.K)/(WPY WP.K + WCO) 154


13The weighted average actually used in the model reduces the mag-
nitudes of the fluctuations in aggregate fruit usage that result from
relative price adjustments.

14Bharat Jhunjhunwala has pointed out that an alternative approach
would be to solve the constrained maximization problem and to use the
resulting relationships as the basis for selecting the new price set.
This method would allow the selection of prices that equate marginal net
revenues while conforming to a quantity constraint. If the constraining
quantity was set equal to desired disappearance, the movement suggested
by the new price set would be that required to deplete available orange
supplies (less carry-overs). This method was not used since it was
believed that the iterative technique provided a closer approximation of
real world behavior and was computationally less demanding than a solu-
tion to the constrained maximization problem. The constrained maximiza-
tion problem becomes computationally complex if the B matrix defined in
Appendix C is nondiagonal.










8 if the increased carry-over policy was
inoperative
C WCO = or 155
16 if the increased carry-over policy was
operative

L WP.K = WP.J + (DT)(1 WD.JK) 156

R WD.KL = PULSE(WDP, 52, 52) 157

N WDP = (WPY/DT) 158

WCO weeks of carry-over (weeks)

WD weeks discarded (weeks)

WDP weeks discarded pulse (weeks)

Processor disappearance relative to desired was the variable that

determined whether an adjustment in product flow was necessary (equation

159). When its value was not equal to one, an overall price adjustment

was indicated; however, whether or not the adjustment was made depended

on the value (either 0 or 1) of R (equation 160). The value of R

depended on the value of V which in turn depended on the values of E, H

and TIME (equations 161 165). These equations allowed specification

of a minimum time period during which price adjustments could not occur.

A PDRD.K = PDS.K/DD.K 159

1 if V.K 0
A R.K = or 160
0 if V.K < 0

A V.K = (TIME.K/H) E.K 161

L E.K = E.J + (DT)(Z.J) 162


15The mechanics of the mechanism was as follows: no adjustment was
allowed when R.K was equal to zero. R.K was equal to zero whenever V.K
was negative. V.K was negative when the ratio TIME.K/H was less than
E.K. When the ratio was equal to E.K, V.K became zero and R.K was set
equal to one allowing the adjustment to be made. In order to prevent
continuous price adjustments beyond time H, the value of E.K was
incremented by one. Then, the process was repeated.










A Z.K = R.K/DT 163

.5 if the price adjustment restriction
was inoperative
C H = or 164
4 if the price adjustment restriction
was operative

N E = 165

PDRD processor disappearance relative to desired

When adjustments were allowed, average marginal net revenue was

adjusted and prices increased or decreased according to processor dis-

appearance suggested relative to desired (equation 166). When suggested

disappearance was greater than desired, average marginal net revenue was

adjusted upward. When suggested disappearance was less than desired, the

average net marginal revenue was adjusted downward. The magnitude of the

adjustment was increased by the Q variable as the disappearance ratio

moved further from its equilibrium value (equations 167 and 168). A

policy option allowed the specification of a limit below which average

marginal net revenue could not be adjusted (equations 168A and 168B).

Once the average marginal net revenue had been adjusted and new prices

suggested they became the basis for new FOB prices (equations 169 189).

Thus, when the policy was effective lower limits were placed on the

prices of the orange products. Finally weighted average FOB price was

smoothed (equations 189B and 189C).

A ZAMNR.K= AMNR.K+ (R.K)(PDRD.K- 1)(Q.K) 166

A Q.K= TABHL(QT, PDRD.K, .94, 1.06, .01) 167

C QT* = 20/18/16/14/12/10/1/10/12/14/16/18/20 168

A XAMNR.K = MAX(FLOOR, ZAMNR.K) 168A

-.20 if lower limit on XAMNR was operative
C FLOOR = or 168B
-1000 if lower limit on XAMNR was inoperative










A FOB(I)S.K = A2(I) + (B2(I))(XAMNR.K) + (B4(I))

(DS.K) 169-175

A AQS(I).K = (POP.K)(AI(I).K)(A3(I) + (B3(I))

(FOB(I)S.K) + (B4(I))(DS.K)) 175A-175G

n
A AQS.K = E (AQS(I).K)(BPG(I).K) 175H
I=i

L FOB(I.K = FOB(I).J + (DT)( 1 )(FOB(I)S.J -
TCFP(I)
FOB(I).J) 176-182

C TCFP(I) = 4 weeks 183-189

n
E (FU(I).JK)(FOB(I).K)
A AFOB.K = I = 1 189A
TFU.K
1
L SFOB.K = SFOB.J + (DT)( )(AFOB.J SFOB.J) 189B
TSFOB
C TSFOB = 12 weeks 189C

ZAMNR average marginal net revenue before considering

the policy limit

FLOOR lower limit on XAMNR

XAMNR average marginal net revenue after the overall adjust-

ment (dollars/gallon single strength equivalent)

FOB(I)S FOB price of Ith product suggested after the overall

adjustment (dollars/gallon single strength equivalent)

AQS(I) quantity of the Ih product suggested after price

adjustment (gallon single strength equivalent/week)

AQS total quantity suggested after the price adjustment

(boxes/week)

TCFP(I) smoothing period used in determining FOB price for

I product (weeks)










SFOB smoothed weighted average FOB price (dollars/box)

TSFOB time for smoothing weighted average FOB price (weeks)


Retail and Institutional
Inventory and Sales Sector


Sales of orange products were equal to the product consumers

demanded as long as adequate supplies were available at the consumer

level (equations 190 196). The model's ability to satisfy consumer

demand depended on the number of weeks of product inventory on hand

relative to "normal." Data collected by the A. C. Nielsen Company and

a priori knowledge provided a basis for estimating "normal" inventory

levels for orange products (Table 10). When inventories dropped below

"normal," a portion of consumer demand went unsatisfied (equations

197 210).

The number of weeks of product inventory on hand was calculated by

dividing the inventory level by average consumer demand (equations 211 -

217). Inventories were increased by processor disappearance and

decreased by product sales (equations 218 224).

R S(I).KL = (QD(I).K)(IA(I).K) 190-196

A IA1.K = TABHL(IA1T, WIA1.K, 0, 1.5, .5) 197

C IA1T* = 0/.85/.98/1.0 198

A IA2.K = TABEL(IA2T, WIA2.K, 0, 1.5, .5) 199

C IA2T* = 0/.85/.98/1.0 200

A IA3.K = TABHL(IA3T, WIA3.K, 0, 4, 2) 201

C IA3T* = 0/.85/1.0 202

A IA4.K = TABHL(IA4T, WIA4.K, 0, .6, .2) 203

C IA4T* = 0/.85/.98/1.0 204










Table 10. "Normal" retail inventories of major orange products.


Product


Inventory level (C(I))


(weeks)

FCOJR and 1.3
R and I

COJ 1.2
R and I

CSSOJ 3.7
R and I


FOR .5


Source: The estimate for fresh oranges was based on a priori
knowledge. Estimates for processed products were based on data collected
by the A. C. Nielsen Company.










A IA5.K = TABHL(IA5T, WIA5.K, 0, 1.5, .5) 205

C IA5T* = 0/.85/.98/1.0 206

A IA6.K = TABHL(IA6T, WIA6.K, 0, 1.5, .5) 207

C IA6T* = 0/.85/.98/1.0 208

A IA7.K = TABHL(IA7T, WIA7.K, 0, 4, 2) 209

C IA7T* = 0/.85/1.0 210

A WIA(I).K = I(I).K/AQD(I).K 211-217

L I(I).K = I(I).J + (DT)(PD(I).JK S(I).JK) 218-224

S(I) sales of the Ith product (gallons single strength

equivalent/week)

IA(I) influence of product availability on sales of the

Ith product

QD(I) quantity of the Ith product demanded (gallons single

strength equivalent/week)

WIA(I) number of weeks of inventory available (weeks)

I(I) inventory level (gallons single strength equivalent)

AQD(I) average quantity of Ith product demanded (gallons

single strength equivalent/week)

Retail and institutional order rates depended on the level of

average consumer demand, the inventory level relative to "normal" and a

competitive influence which was associated with future price expecta-

tions (equations 225 231). When inventories were below "normal"

regular order rates were increased in an effort to rebuild inventories,

while above "normal" inventories caused a reduction in orders (equations

232 245). The competitive influence was expressed as a function of

processor disappearance relative to desired and reflected the influence

of price expectations on current order rates (equations 246 247).










When the ratio of suggested and desired processor disappearance

was larger than unity, a price increase was expected at the FOB level

and retail and institutional purchasers increased their orders in an

attempt to take advantage of the lowest possible price. Similarly,

when processor disappearance relative to desired was less than unity,

order rates were reduced in anticipation of lower FOB prices.

R D(I).KL = (AQD(I).K)(II(I).K)(CI.K) 225-231

A Il.K = TABHL(IIIT, WIA1.K, .3, 2.8, .5) 232

C IIlT* = 2.2/1.4/1.0/.9/.85/.82 233

A II2.K = TABHL(II2T, WIA2.K, .2, 2.7, .5) 234

C II2T* = 2.2/1.4/1.0/.9/.85/.82 235

A II3.K = TABHL(II3T, WIA3.K, .7, 6.7, 1.5) 236

C II3T* = 1.5/1.2/1.0/.9/.85 237

A II4.K = TABHL(II4T, WIA4.K, .1, .9, .2) 238

C II4T* = 3.0/2.4/1.0/.81/.72 239

A II5.K = TABHL(II5T, WIA5.K, .3, 2.8, .5) 240

C II5T* = 2.2/1.4/1.0/.9/.85/.82 241

A II6.K = TABHL(II6T, WIA6.K, .2, 2.7, .5) 242

C II6T* = 2.2/1.4/1.0/.9/.85/.82 243

A II7.K= TABHL(II7T, WIA7.K, .7, 6.7, 1.5) 244

C II7T* = 1.5/1.2/1.0/.9/.85 245

A CI.K= TABHL(CIT, PDRD.K, .6, 1.4, .2) 246

C CIT* = .9/.97/1.0/1.03/1.1 247

II(I) inventory influence associated with Ith product


CI competitive influence










Retail and Institutional Price Sector


Retail prices of orange products normally adjust to levels suggested

by FOB prices. The length of the adjustment period and the degree to

which retail prices respond to changes at the FOB level depend on several

factors, among these is the price protection policy of processors. At

the time of this study, price protection was offered for processed prod-

ucts for a two week period. No protection was offered for fresh oranges.

Factors such as the magnitude of the FOB price adjustment, the rate of

product sales, and the level of inventories probably influence the

length of the adjustment period. For this study, the time to correct

the retail price of each product was assumed constant. Once the FOB

price of a product was known, it was used to suggest a price which

exponentially smoothed over an adjustment period determined the retail

price of the product (equations 248 263). These retail prices were

averaged and used as inputs to the consumer demand sector (equations

264 268).

A XFOB1.K = (2.2501)(FOB1.K) 248

A XFOB2.K = (3)(FOB2.K) 249

A XFOB3.K = (4.3119)(FOB3.K) 250

A XFOB4.K = (2.645)(FOB4.K) 251

A RPS1.K = 4.60 + (8.3333)(XFOB1.K) 252

A RPS2.K = 16.91 + (8.3333)(XFOB2.K) 253

A RPS3.K = 12.38 + (8.3333)(XFOB3.K) 254

A RPS4.K = 2.34 + (4.0)(XFOB4.K) 255

L RP(I).K = RP(I).J + (DT)( T( )(RPS(I).J -

RP(I).J) EI = 1, 2, 3, 4) 256-259










C TCRP1 = 2 weeks 260

C TCRP2 = 2 weeks 261

C TCRP3 = 4 weeks 262

C TCRP4 = .5 weeks 263

L ARP(I).K = ARP(I).J + (DT)(T- )(RP(I).J -

ARP(I).J) (I = 1, 2, 3, 4) 264-267

C TARP = 2 weeks 268

XFOB1 FOB price of frozen concentrated orange juice

(dollars/dozen 6 ounce cans)

XFOB2 FOB price of chilled orange juice

(dollars/dozen quarts)

XFOB3 FOB price of canned single strength orange juice

(dollars/dozen 46 ounce cans)

XFOB4 FOB price of fresh oranges

(dollars/45 pound carton)

RPSI retail price suggested for frozen concentrated

orange juice (cents/6 ounce can)

RPS2 retail price suggested for chilled orange juice

(cents/quart)

RPS3 retail price suggested for canned single strength

orange juice (cents/46 ounce can)

RPS4 retail price suggested for fresh oranges (cents/pound)

RP(I) retail price of the Ith product (same units as retail

price suggested)
th
TCRP(I) time for correcting the retail price of the I

product (weeks)










ARP(I) average retail price of the Ith product (same units

as retail price suggested)

TARP time for averaging retail price (weeks)

The heterogeneity of the institutional market makes data collection

and analysis at the consumer level difficult and costly. The difficulty

is further complicated by the fact that many institutional outlets pur-

chase orange products through retail stores. For example, restaurant

sales accounted for the consumption of about 88 million gallons of

orange juice during 1971 [1]. Of this, 19 percent was reported to have

been purchased by restaurants through retail outlets. The total insti-

tutional consumption of orange products during 1971 was estimated to be

196 million single strength gallons. This represented about 28 percent

of total 1971 orange juice consumption.

Demand estimates for institutional products at the FOB level were

available from a study by Weisenborn [25]. This information was used

as the basis for predicting consumption in the institutional market. It

should be noted that the model estimates neither wholesale nor consumer

prices for orange products sold through institutional outlets.

The FOB prices of institutional products were converted to units

consistent with Weisenborn's equations (equations 269 271). They

were then exponentially smoothed and used as inputs to the demand

sector (equations 272 275).

A XFOB5.K = (12)(FOB5.K) 269

A XFOB6.K = (3)(FOB6.K) 270

A XFOB7.K= (4.3125)(FOB7.K) 271

L IP(I).K = IP(I).J + (DT)(-T -)(XFOB(I).J IP(I).J) 272-
TCI 274
(I = 5, 6, 7)










C TCIP = 2 weeks 275

XFOB5 FOB price of FCOJ (dollars/dozen 32 ounce cans)

XFOB6 FOB price of COJ (dollars/dozen quarts)

XFOB7 FOB price of CSSOJ (dollars/dozen 46 ounce cans)

IP(I) smoothed institutional FOB price of the Ith product;

(I= 5, 6, 7) (same units as XFOB prices)

TCIP time for correcting institutional price (weeks)


Demand Sector


Relationships used to estimate product consumption are presented

in Table 11 and the mean values for prices and quantities are given in

Table 12. Advertising and price information (inputs to the sector) were

used in conjunction with the demand equations to predict the quantity of

each product demanded (equations 276 282). Estimates were made on a

monthly per capital basis. These estimates, converted to weekly per

capital quantities and multiplied times projected U.S. population, pro-

vided an estimate of the total weekly consumption of each product (equa-

tions 283 290). Population was accumulated in a level equation and

was dependent on a growth rate which was related to time (equations

291 293). Average quantity demanded was an input to the retail and

institutional inventory and sales sector (equations 294 301).

4
A PQD(I).K = (AI(I).K)[A(I) + E (B(I))(ARP(I).K) +
I = 1
I=1

(B8)(DS.K)] (I = 1, 2, 3, 4) 276-279

7
A PQD(I).K = (AI(I).K)[A(I) + Z (B(I))(IP(I)).K]
1=5


(I = 5, 6, 7)


280-282










Table 11. Retail and institutional demand relationships for Florida
orange products.


Quantitya Retail or
(gallons single Pricing institutional Seasonal
strength equivalent InteUnit price shifter
per capital) coefficient

R
QFJ .171943 cents/6 ounce -.005654 -.009218


QR .067536 cents/quart -.001916 -.000294
COJ

Q .033276 cents/46 ounce -.000771 .000131
CSSOJ

R
QFO .152239 cents/pound -.011138 c


Q .052886 dollar/dozen -.004621 c
FCOJ 32 ounce

Q .078273 dollar/dozen -.019510 c
COJ 32 ounce

Q .173864 dollar/dozen -.042965 c
CSSOJ 46 ounce


Source: Retail demand relationships for processed products were
obtained from the Economic Research Department, Florida Department of
Citrus. The fresh orange relationship was derived from elasticity
estimates reported by Langham [10, p. 20]. Demand relationships for
institutional products were obtained from [26, 27]. All relationships
have been adjusted.

aSuperscript represents retail or institutional market. Subscript
indicates product type.

b Jo Sept. Mar.
Seasonal shifter = Apr. Aug.

cNot included in model.










Table 12. Mean values associated with estimated demand relationships.


Quantity
Product a Price/Unit (per capital
gallon single
strength equivalent)


FCOJR 14.43 cents/6 ounce .0867


COJR 30.74 cents/quart .0085


CSSOJR 32.31 cents/46 ounce .0084


FOR 10.40 cents/pound .0364


FCOJI $8.99/dozen 32 ounce .0113


COJI $3.18/dozen 32 ounce .0162


CSSOJ $3.90/dozen 46 ounce .0062



The subscript refers to the retail or institutional market.










A DS.K = CLIP(1, 0, WP.K, 30.3) 283

A QD(I).K = (PQD(I).K)(POP.K)/4 (I = 1, . 7) 284-290

L XQD(I).K = QD(I).J 290A-290G

L POP.K = POP.J + (DT)(PG.JK) 291

R PG.KL = (.01)(PGR.K)(POP.K) 292

A PGR.K = .0232 + (.0462/TM.K) 293

A TM.K = MAX(4, TIME.K) 293A
1
L AQD(I).K =AQD(I).J + (DT)(TAQD)(QD(I).J -

AQD(I).J) (I = 1, . 7) 294-300

C TAQD = 2 weeks 301

PQD(I) per capital quantity of the Ith product demanded

(gallons single strength equivalent/month)

DS demand shifter = Sept. Mar.
1 Apr. Aug.

PG U.S. population growth (people/week)

PGR weekly U.S. population growth rate (percent)

TM TIME proxy (TM -4)

TAQD time for averaging quantity demanded (weeks)


Initial Conditions


In order to start the computation process, a requirement of com-

puter simulation is that initial conditions be specified. The values

specified in this section roughly approximate subsector conditions at

the beginning of the 1961-62 season. Once the starting conditions were

specified, the DYNAMO compiler had the information required to compute

initial values for level equations. These values were then available

for the solution of auxiliary and rate equations. Within the computing










sequence (levels, auxiliary, rates), the DYNAMO compiler rearranges the

solution order of equations when necessary.


PT = 18.7E6

WI = 1

CR = 108.8E6

FUTD = 0

AGP = GP

CP = 0


n
N AFU = FU(I) (I = 1 . 7)
I=I

N FU(I) See Table 13. (I = 1, . 7

N ATRA = (AT)(CS) (.15)(AT)(CS)

N AA = ATS

N MNR(I) See Table 14. (1 = ,

N WP = 0

N FOB(I) See Table 15. ( = 1, . ,

N SFOB = AFOB

N I(I) = (C(I))(AQD(I)) See Table 10 for

values of C(I). (I = 1, . ,

N RP(I) = RPS(I) (I = 1, 2, 3, 4)

N ARP(I) = RP(I) (I = 1, 2, 3, 4)

N IP(I) = XFOB(I) (I = 5, 6, 7)


Initialization for
Sector Equation(s)

1 1

2 37

3 46

3 47

4 63

4 66


) 5

6

6

7) 7

7

7) 7

7


XQD(I) = QD(I)

POP = 184.8E6

AQD(I) = QD(I)


70-76

104

108

124-130

156

176-182

189B



218-224

256-259

264-267

272-274

290A-G

291

294-300


(I = 1, . 7)









65






4J
a) 0 a 0 0
SI r-, 0 oa
a A D a) o
'a -4 0
a)


1-
ca
4J
0 1



*i 4 0 Co ) 0 r.

m 0 0 m on
O 4 "
., l C








4J

a) U n
a) a n -4 -
0 I i c* I
w 'I aO
a) 0
U -ML
4J4



*> a3 'i- r r^

'a a. Cl C- CA C1 4
0 a' 0 r -. .




4J



p1 4J rQ rQ '--
a.



0 144



.0 CA -4 C! O






00 4J OD I In in c- o7 0
ra ) to



a 44 Cl a' a' 0 CJ (1) G) 4-
-t A Cl 3 o 0 -L c- a) a. 2
34 44 A .. .' 0
a) 0 H o- w 'a W a)
4 3 C a O j a) a
14 1 Cl C- I W 0 -4
a- .. .. 0a .l 0,


a) -4 a) a)

4.3 a) -4
4J a) a)

) Ca .. *u i C ) a)
3 -i 4

Cl 4 U 0 U 0 a O m
rr U uu rx E-1 0 CY W <
a' a) 0 Ca
a)
i-4

E0










Table 14. Net marginal revenues used to initialize model.


Product Market
Retail Institutional

(dollars/gallon single
strength equivalent)

FCOJ .105654 .516743

COJ .410560 1.043205

CSSOJ .145009 .523586

FO .560814 a


Source: Calculated.

aNot applicable.










Table 15. FOB prices used to initialize model.


Market
Product Market
Product Retail Institutional

(dollars/gallon single
strength equivalent)

FCOJ .862362 .856507

COJ .660564 1.278780

CSSOJ .688240 .918408

FO .911312 a


Source: Calculated.

aNot applicable.

















CHAPTER V

VALIDATION


The usefulness of the model presented in the preceding chapter

depends upon its ability to characterize the response of the Florida

orange subsector to changes in economic conditions. If the model is a

"good predictor" of subsector response,it should be useful as a tool for

policy analysis. If not, its value for studying economic policies may

be limited. The predictive ability of a model can be evaluated on the

basis of a set of criteria established for this purpose. However, the

choice of criteria is a subjective process. The model can also be

evaluated from the standpoint of the reasonableness of the estimates

and assumptions presented in Chapter IV. The purpose of this chapter

is to provide insight into the model's ability to predict.

In his book, Computer Simulation Experiments with Models of

Economic Systems, Naylor makes the following statement:

In general, two tests seem appropriate for validating
simulation models. First, how well do the simulated values
of the endogenous or output variables compare with known
historical data, if historical data are available? Second,
how accurate are the simulation model's predictions of the
behavior of the actual system in future time periods? [15, p. 21]

In this study, a simulation was made to determine whether or

not the model would converge when run for a long period of time with

weather conditions held constant. The model was then evaluated on the

basis of its ability, when given empirical weather data, to reproduce

the behavior of the orange subsector during the 1961-71 period.

68










Long-run Stability


The model was intitialized to reflect, as nearly as possible,

conditions that existed in the orange subsector at the beginning of the

1961-62 crop season. During the run stochastic weather generation was

suppressed and weather effects were set equal to constants that reflected

average weather conditions. With 1961-62 initial conditions, there was

reason to expect the model to start from a disequilibrium position.

However, a run period of one hundred years was believed long enough to

allow the model to overcome initial disequilibrium and to provide an

opportunity for observing whether the model, if left undisturbed, would

come to a stable position. Partial results of this run are presented

in Figure 11.

In Figure 11 variables were plotted against time and the appropriate

vertical scale. The vertical scales are identified by groups of numbers.

Each number is associated with a respective variable identified by

letter. The number of mature productive orange tree equivalents,

represented by T, was initialized at 18.7 million. After the start of

the simulation this figure increased at a rapid but decreasing rate for

approximately sixteen years. After this period, tree numbers remained

relatively stable within the 40-41 million range for about six years,

before taking a slight dip and beginning a substained increase that

lasted the remainder of the run. At the end of the simulation the

number of mature productive orange trees stood at 94.7 million and had

been increasing by 1.2 million trees per year. This behavior may be

compared to the behavior of average grower profit during the same period.

At the beginning of the run, prices were initialized at levels which

yielded an average grower profit of $1.99 per box. The fact that this














m a
) 0I
4J 4J


C O

44
U 441

o cl


I I

S 4


4d b 444

44 044 0 0
*-4 l-4 60 4J .Q -
'o rlM M -

o W 040 4 01


t4 bH- I' 4 0 (b P






Id P 4
> 1 4 il 4


0~N0 '440~ C'N~0
'44 -.1 c-i'
10 oom


44



O
U)


dG d




F) X
4 4J
440 44









-.






-a










m
.L)
4







a)
4








O 4





a
'-A



















u

a )
4 4
0







o 4


"IVIo


44
-4



0

0 441 441








.
4 4J









z4 4
M 0r
44*
44 U t
'44 44-
44 .44a
44 4
a4










figure was immediately adjusted downward by the model seemed consistent

with the behavior that would have been expected from the orange sub-

sector, if rather than having experienced the 1962-63 freeze, "normal"

weather conditions had been encountered. The absence of freeze damage

would have resulted in an estimated 42-44 million additional boxes of

fruit during the 1962-63 season and would have prevented the temporary

or permanent loss of approximately 13.5 million trees. In the simula-

tion, average grower profit ranged from $1.99 to $.09 per box. Compared

to a realized range during the 1961-70 period of $2.52 to $.21 per box,

the simulated range seemed reasonable, particularly considering that the

model, operating with "normal" weather conditions generated larger

supplies than those experienced by the orange subsector. Other variables

in Figure 11 follow similar patterns.

Average marginal net revenue stabilized at a negative 16 cents per

box. This behavior seemed inconsistent with the behavior required to

maximize long-run net revenue at the FOB level and reflected a tendency

of the model to overplant trees even under "normal" weather conditions.

This overplanting tendency may represent a hedge against recurring crop

damage. At any rate, it resulted from the specification of new tree

plantings relative to average grower profits. As specified in Chapter

IV (equations 11 and 12), the response table required that new tree

plantings occur at the minimum rate of 2.2 percent of productive orange

trees even when average grower profit was zero or negative. An earlier

simulation, which used a response function that allowed new tree plantings

to fall to zero, reached a stable position after approximately the same

number of years with an average marginal net revenue of $-.03 per box.

Differences between the two runs indicate behavior of the model is

sensitive to changes in this relationship.










The purpose of this run was to determine whether the model would

stay within reasonable ranges and exhibit relatively stable behavior or

whether it would explode if given time to overcome its initial disequi-

librium. Results of the run seemed to affirm reasonable behavior, i.e.,

the model converged.


Retrospective Comparison


A simulation was made with initial values corresponding to

conditions that existed at the beginning of the 1961-62 season and with

weather effects specified to replicate as nearly as possible those that

occurred during the 1961-62 through 1971-72 period. Results were com-

pared with empirical data reflecting the behavior of the Florida orange

subsector during the same period.


Tree Numbers

Figure 12 presents a comparison of simulated and observed numbers

of mature productive orange tree equivalents during the 1961-62 through

1971-72 period. In the simulation, the tree numbers variable was

initialized at 18.7 million and had increased to 22 million trees by the

end of the 1961-62 crop season.I As a result of the freeze which

occurred in the simulation at the beginning of the 1962-63 season, tree

numbers were reduced to 16.9 million by mid-season. Carry-over effects

of the freeze also caused a reduction in productive trees during 1963-64.

During this period, an almost identical pattern of change was reflected


Ilnitialization of tree numbers at 18.7 million probably over-
stated the number of trees in existence at the beginning of the 1961-62
season. Reflection indicated that this figure was more nearly associated
with the end than with the beginning of the season.










































































































04J 0 > ) 4 0
Z ) 0 0 4 -4
0 9 0-r- 0 0

0d a- -o I --


00

CM




04
0
4i
I
















0
ct

















o
13 1
()








0
co




4J
s-i












0 co
1-4







1)
0






















4 0
'o

0 a
CO


cl












r n
lC'










in the observed data; however, levels of observed tree numbers were

approximately ten percent lower than those generated by the model.

Following the 1963-64 season, the combined effect of new trees becoming

productive and damaged tree recovery produced a sharp increase in tree

numbers. This increase was particularly evident in the time path of the

observed variable and may have partially resulted from the reassessment

of freeze damage. At any rate, there were 3.5 million more trees

observed than simulated in 1964-65. Further comparison of the time

paths revealed high correspondence between observed and simulated tree

numbers during the 1966-67 and 1968-69 seasons. However, after the

1968-69 season, simulated tree numbers increased at a rate faster than

the rate based on the observed data point.

A summary of observed versus simulated changes in tree numbers is
2
presented in Figure 13. In this diagram, completely accurate predic-

tions fall on the line of perfect forecasts. As points move away from

this line, predictive accuracy decreases. The second and fourth quad-

rants of the diagram map turning point errors, i.e., the prediction of

a change in direction when no change occurred or a change in direction

not predicted. For the six points for which comparable tree numbers

data were available, the model overestimated realized changes three

times, underestimated once and predicted one point on the perfect

forecast line.

A quantitative measure of the correspondence between observed and

simulated values was provided by Theil's inequality coefficient [24,

p. 28]. Of the several versions of the coefficient, the one used in


A detailed discussion of the prediction-realization diagram is
given in [24, pp. 19-26].































25
10C
45"


P
(hundred
thousands)


yc,
4:'cc
'Cs'i
CC


Figure 13. Prediction-realization
of mature productive orange trees.


A
I I (hundred
25 50 75 thousands)
















diagram for changes in numbers


A = a -aP = -p
t t t-l t t t-l










this study was defined as follows:

E (a Pt)2
S t t 1/2
U= E (at at-1) 2





where at represents the observed or actual value at time t and pt repre-

sents the simulated or predicted value. In the case of perfect fore-

casts, Theil's coefficient takes on the value zero. The value of one

indicates that predictions are no better than those that would have

been made with the model pt = at-,. For the tree numbers data, the

coefficient was equal to .5513 indicating that the root mean square

prediction error was 55 percent of the root mean square error that would

have been realized had predictions been made with the model pt = at-l.


Crop Size

Figure 14 presents a comparison between simulated and observed crop

size data. In general, the path of the simulated variable corresponded

fairly closely with observed behavior; however, noticeable disparities

existed in 1963-64 and after the 1967-68 crop season. After 1967-68,

estimates made by the model overstated crop size and the magnitude of

the overstatement increased each season. The prediction-realization

diagram, Figure 15, indicated that of the nine changes generated, the

model overestimated five and underestimated the remainder. Theil's

coefficient, equal to .98, indicated that predictions were slightly

better than those that would have been realized with the no-change model.


On-Tree Price

A comparison of observed and simulated on-tree prices of Florida

oranges is presented in Figure 16. Again, the general behavior of the



















Crop size (millions of boxes)


200


150- / actual








100- y



\ /
\ /

\ /



50
1961-62 1963-64 1965-66 1967-68 1969-70 1971-72


Figure 14. Simulated and actual crop size, 1961-62 through
1971-72 seasons.

Source: [3, 1971-72 season] and simulated.































o 10
Ze4
aCj~i


A
"I I (millions
10 20 30 of boxes)


0 0
4 *
^'t~
w


Figure 15. Prediction-realization diagram for changes in Florida
orange production.


At = at-at-


t = t t-1


Source: [3, 1971-72 season] and simulated.














































































































u' o u o

CN C' r-


CN C d

I Vo


0' 01
r-


0



r--i t




I d








.10
0
10


0.











-4
D C


I 0



























,4
-C
41



0,
-C
'o CO







I U
(-I


<4








\D l0











, I








CO
C' C
so ,-


O 0

cn W o

CO CO


1 *4 0 4
0 C-0 O
o 0o.-'.0










simulated variable corresponded with observed data. Restricted supplies

following the 1962 freeze led to increased prices; whereas, the large

crop of 1966-67 caused a sharp price dip. A relatively small crop in

1967-68 was again associated with increased prices. The prediction-

realization diagram, Figure 17, indicated that the model underestimated

the magnitude of four changes, overestimated three and made two turning

point errors--one between the 1963-64 and 1964-65 seasons and another

between 1969-70 and 1970-71. The Theil coefficient equaled .67.


Market Proportions

As mentioned in Chapter IV, in order to maximize net returns,

processors as a group should attempt to allocate oranges so as to equate

marginal net revenues among product markets. Table 16 shows proportioned

allocations of the orange crop as observed during the 1963-64, 1964-65

and 1965-66 seasons and as performed by the model during the validation

period.3 As can be seen from the data, the proportion of the orange

crop allocated into a given product-market varied somewhat from season

to season. This variance, however, was relatively insignificant compared

to differences between simulated and observed allocations. Relative to

observed, the model allocated fewer oranges to each retail product and

more to each institutional product.

The allocation performed by the model, though somewhat different

from the observed, followed directly from the derived marginal net

revenue equations (equations 129 135). The demand equations used in

the derivations were obtained from several sources and most included

variables exogenous to the simulator. Since the model was designed to


Simulated figures corresponded to the end of each season; however,
there was little variation within seasons.




















1.50


.0 .50
0 0


P
(dollars
per box)


per box)


el
Q

00


Figure 17. Prediction-realization diagram for changes in on-tree
price.
At = at-at-1 t = P t-i

Source: [3, 1968-69 season, p. 95, and 1971-72 season, p. 104] and
simulated.










Table 16. Observed and simulated fruit usage, by product-market.


Season Product-Marketa
1 2 3 4 5 6 7

(percent)

Observed
1963-64 41.6 7.3 4.2 33.5b 5.5 4.4 3.5
1964-65 44.7 7.0 3.6 27.8b 6.3 7.5 3.1
1965-66 41.9 8.0 4.2 26.2b 5.3 11.5 2.9

Average
1963-66 42.8 7.5 4.0 28.7b 5.7 8.2 3.1
1- -- ^ - I -
83 17

Simulatedc
1961-62 22.6 4.7 2.3 31.0 7.8 12.9 18.7
1962-63 25.7 3.9 1.7 29.8 7.8 15.1 16.0
1963-64 26.5 3.9 1.7 28.6 7.8 15.6 15.9
1964-65 27.7 3.8 1.6 26.8 8.0 16.4 15.8
1965-66 25.1 4.5 2.2 27.3 8.1 14.5 18.3
1966-67 24.8 6.0 3.2 18.4 9.4 13.9 24.3
1967-68 24.2 4.8 2.4 27.0 8.3 13.8 19.5
1968-69 23.3 5.6 2.9 24.3 8.7 13.1 22.2
1969-70 22.8 5.6 3.0 24.7 8.7 12.8 22.4
1970-71 23.3 5.9 3.1 22.7 9.0 13.0 23.1
1971-72 23.5 5.8 3.0 22.9 8.9 13.2 22.6
1972-73 23.5 5.9 3.0 22.5 9.0 13.1 23.0

Average
1961-73 24.1 5.3 2.7 24.9 8.6 13.7 20.9

57 43


Source: [25, Appendix C] and simulated.

aRows may not add to one hundred due to rounding.

Assumes 12,000 fresh oranges equals 396.75 gallons single strength
equivalent.

CSimulated figures were at the end of each season; however, within
season variation was minor.










operate in a recursive fashion, the coefficients of these variables were

removed from the equation by incorporating them into the intercept. The

resulting equations, along with cost and margin information, were used

to derive marginal net revenue equations for each product-market. An

examination of these relationships revealed that several cross-product

coefficients had signs different from those expected and in some cases

the cross-price effect outweighted the own-price effect. Further examina-

tion indicated that these coefficients could lead to results inconsistent

with economic theory, e.g.,when all prices increase, total quantity

demanded increased. In order to prevent this problem cross-product

coefficients were incorporated into intercept terms. The loss of these

coefficients resulted in relatively naive demand equations. A different

set of equations might have led to results more consistent with the

observed data.


Conclusion


The obvious implication of the preceding comparisons is that there

exists room for improvement in the predictive accuracy of the DYNAMO

model. However, a definite similarity existed between real world and

model behavior especially with regard to turning points and it was

believed that the model captured the dynamics of the orange subsector.

















CHAPTER VI

POLICY ANALYSIS


The term "policy" as used in this chapter refers to changes in

either the model's operating rules or its structure. Most policies

were implemented by parameter changes in functions discussed in Chapter

IV. These changes altered the operating rules of the model and affected

performance by reducing orange supplies, increasing desired carry-overs,

and by modifying pricing and advertising schemes.

A set of five runs, each covering a twenty-five year period, was

made to provide a base with which to compare policy results. This base

was an attempt to characterize the orange subsector as it is currently

structured. Ten policies were then examined. Each run started with a

set of initial conditions based on the 1961-62 crop season and was

associated with weather effects computed by the stochastic procedure.

The weather effects used for the base run were also used for each policy

and provided comparable results for a variety of weather conditions.1

Policies were replicated five times--once with each of the weather sets

presented in Table 17. The weather effect for each season was greater

than, equal to, or less than one and denoted better than average,

average or poorer than average weather conditions, respectively.

1
DYNAMO contains a function which generates "pseudo random numbers"
that satisfy all of the statistical tests for randomness. However, each
number is calculated from the previous one by a fixed procedure. Thus,
a given noise seed always generates the same sequence of numbers. In the
normal distribution mode, the DYNAMO procedure does not perfectly repro-
duce a normal distribution in that no number can diverge from the mean by
more than 2.4 standard deviations. For more information, see Pugh [20].
84










Table 17. Weather conditions used
policy.


in the five simulation runs for each


a
Season Weather sets
Season
1 2 3 4 5


2b 1.14 1.01 1.07 1.07 1.10
3 1.01 .92 .89 .99 1.03
4 1.11 .95 1.01 .92 1.06
5 .95 .95 .99 .98 .97
6 1.08 1.11 .99 .96 .89
7 1.00 1.06 1.00 1.08 1.08
8 .98 1.00 1.05 1.02 .87
9 .94 .98 .95 1.01 1.02
10 1.11 1.08 1.03 1.03 .99
11 1.00 .97 .98 .98 1.01
12 .93 .91 1.05 1.01 1.04
13 1.00 -88 1.07 .96 .98
14 .97 .98 .97 1.03 1.02
15 1.06 1.06 .96 1.04 1.01
16 1.05 .96 .94 .95 .99
17 1.07 1.07 .94 .96 .97
18 1.05 .97 1.06 1.01 1.06
19 1.00 .99 1.06 1.04 1.03
20 .99 .98 1.01 1.04 .96
21 1.00 1.00 1.04 .90 .96
22 1.04 1.00 .92 .92 .97
23 .92 .95 1.08 1.01 1.01
24 1.03 1.03 1.08 1.03 .98
25 .97 .97 1.00 1.02 1.04

a
Weather conditions are based on an index (average weather = 100).
The larger (smaller) the index the more favorable (unfavorable) the
weather. The noise seeds used to generate weather sets 2 through 5 were
943805, 7641403, 10861407 and 86451509, respectively. The seed for
weather set 1 was already in the noise function.


Initial values were used for the first season.


1










Policies


The policies examined in this study are briefly described as

follows:

1. Restricted tree planting. A restriction was placed on new

tree planting whenever average grower profits rose above

specified levels. Three levels were considered in the study,

$1.25, $1.50 and $1.75 per box. When the policy was opera-

tive, tree planting was permitted or not permitted depending

on whether grower profits were below or above the level

specified. On first glance, this restriction may seem in

conflict with logical decision making since high profits would

be expected to call forth increased supplies. However, in

the orange subsector, growers have tended to react to high

profits as if a permanent shift in marketing structure has

occurred in spite of the fact that high grower profits have

normally been associated with a freeze. Consequently, they

tend to overinvest in new orange groves. It takes several

years for these groves to become fully productive, after which

the additional supplies have precipitated periods of relatively

low returns and low grove investment. These reactions have

caused the subsector to be characterized by production and

price cycles and it was believed that a restriction on tree

plantings during periods of high grower profits might exert a

stabilizing influence on the system.

2. Tree abandonment. The tree abandonment policy, when operative,

removed fully productive trees from the system whenever grower




Full Text

PAGE 1

A MODEL FOR EVALUATING ALTERNATIVE POLICY DECISIONS FOR THE FLORIDA ORANGE SUBSECTOR OF THE FOOD INDUSTRY By CHARLES EVERITT POWE A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1973

PAGE 2

UNIVERSITY OF FLORIDA 3 1262 08666 445 4

PAGE 3

ACKNOWLEDGMENTS The author would like to express his deepest gratitude for the direction and friendship extended by his chairman, Dr. Max R. Langham. He is also grateful to Dr. Lester H. Myers for sometimes acting as his sounding board and for providing many helpful suggestions. In addition, appreciation is extended to Dr. B. R. Eddleman, Dr. Leo Polopolus, Dr. David L. Schulze and Dr. J. M. Perry for their services on his graduate committee, and to Dr. James A. Niles for reading the final draft of the manuscript and offering many helpful suggestions. Many others have aided and befriended the author during his graduate studies. Special appreciation is extended to Dr. K. R. Tefertiller, who served as chairman of the Food and Resource Economics Department during most of the author's graduate program. The author would like to thank the Economic Research Service and the Florida Agricultural Experiment Stations for the much appreciated financial assistance which supported the study. Acknowledgment is made of the support and services of the Northeast Regional Data Processing Center of the State University System of Florida. The author is indebted to those who helped in the physical production of the thesis. Much of the early typing was done by Mrs. LeAnne van Elburg who also drew the large diagram of the model. Some of the figures were drawn by Miss Jan McCartan and the final manuscript was typed by Mrs. Phyllis Childress. Miss Sandra Claybrook proofread parts of the manuscript.

PAGE 4

TABLE OF CONTENTS ACKNOWLEDGMENTES i LIST OF TABLES iv LIST OF FIGURES vi ABSTRACT viii CHAPTER I. INTRODUCTION 1 The Problem 1 Objectives 2 Previous Work 3 II. STRUCTURE OF THE FLORIDA ORANGE SUBSECTOR 6 General Description 6 Production 7 Dynamics of the Florida Orange Subsector 9 III. CHARACTERISTICS OF DYNAMO II 15 Special Features 15 Time Notation 16 Type of Variables and Computational Sequence ... 17 IV. THE MODEL 19 Tree Nimibers Sector 21 Weather Effects Sector 29 Crop Size Sector 32 Grower Profit Sector 34 Processor Disappearance Sector 35 Advertising Sector 37 FOB Price Sector 42 Retail and Institutional Inventory and Sales Sector 53 Retail and Institutional Price Sector 57 Demand Sector 60 Initial Conditions 63

PAGE 5

V. VALIDATION 68 Long-run Stability 69 Retrospective Comparison 72 Conclusion 83 VI. POLICY ANALYSIS 84 Policies 86 Measures of Performance 91 Analysis of Alternative Policies 95 VII. SUMMARY AND CONCLUSION 110 Limitations 114 Implications for Future Research 116 APPENDICES Appendix A Alphabetized List of Variable Names 117 Appendix B The Computer Program 126 Appendix C Derivation of Marginal Net Revenue Relationships . 142 Appendix D DYNAMO Equations for the Alternative Advertising Policy 147 Appendix E Miscellaneous Data 152 Appendix F A Note on the Calculation of Present Values and the Variance of Present Values 160 BIBLIOGRAPHY 163 BIOGRAPHICAL SKETCH 166

PAGE 6

LIST OF TABLES Table Page 1 Acreage of bearing and nonbearing orange groves by Florida counties as of December 1969 8 2 Organizational structure for DYNAMO II equations 18 3 Estimated mature productive orange tree equivalents, movement of orange trees from Florida nurseries to Florida destinations, and returns above operating costs for groves averaging over ten years of age, 1955-56 through 1970-71 seasons .... 26 4 Yield loss, tree loss and hatrack loss factors, 1962-63 through 1972-73 seasons 31 5 Conversion factors for major orange products 37 6 Advertising tax rates for Florida oranges by type of use, 1962-63 through 1970-71 seasons 38 7 Relationship between per capita quantity of an orange product that would be demanded by retail and institutional consimiers given adequate time for system adjustment and the FOB price of the product 44 8 Mean values associated with estimated demand relationships 45 9 Base data periods associated with estimated demand relationships 46 10 "Normal" retail inventories of major orange products. . . 54 11 Retail and institutional demand relationships for Florida orange products 61 12 Mean values associated with estimated demand relationships 62 13 Estimated fruit usage rate by product type, 1961-62 season '65

PAGE 7

14 Net marginal revenues used to initialize model 66 15 FOB prices used to initialize model 67 16 Observed and simulated fruit usage, by product -market . . 82 17 Weather conditions used in the five simulation runs for each policy 85 18 Discounted values of two hypothetical streams of income received over a five-year period 93 19 Alphanumeric names used to identify simulation runs ... 96 20 The level and standard deviation of the present value of grower profits, average FOB price and crop size for twelve sets of simulations 98 21 Relative value of the level and standard deviation of the present value of grower profit, average FOB price and crop size for policies comparable with the base (B) run 99 22 Size and discounted costs of the carry-overs associated with alternative policies 100 23 Estimated costs and returns to orange processors, 1961-62 through 1970-71 seasons 103 24 A classification of nonadvertising policies by preference category relative to the base (B) by group of participants 107

PAGE 8

LIST OF FIGURES Figure Page 1 Simplified flow diagram of the orange subsector 10 2 Block diagram of major components of the Florida orange subsector 13 3 Size of the orange crop and per box return above operating costs received by growers for Florida oranges, 1961-62 through 1968-69 crop seasons .... 14 4 Per box return above operating costs received by growers for Florida oranges and orange tree movements from Florida nurseries, 1961-62 through 1965-66 14 5 Time notation for DYNAMO II 16 6 Flow diagram of the DYNAMO model of the Florida orange subsector 20 7 Comparison of output from exponential delay and empirical yield estimates 22 8 Relationship between per box returns above operating costs and movement of orange trees from Florida nurseries before and after the 1957-58 and 1962-63 freezes 25 9 Seasonal pattern of generic advertising and promotional expenditures for Florida oranges 40 10 Relative price adjustment for three product case 48 11 Simulated time path of selected variables 70 12 Simulated and actual numbers of mature productive orange trees, 1961-62 through 1972-73 seasons .... 73 13 Prediction-realization diagram for changes in numbers of mature productive orange trees 75 14 Simulated and actual crop size, 1961-62 through 1971-72 seasons 77 vi

PAGE 9

15 Prediction-realization diagram for changes in Florida orange production 78 16 Simulated and actual on-tree price, 1961-62 through 1970-71 seasons 79 17 Prediction-realization diagram for changes in on-tree price • • . 81 18 Advertising collections and expenditures for the alternative advertising policy and base runs, weather set 1 106

PAGE 10

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 A MODEL FOR EVALUATING ALTERNATIVE POLICY DECISIONS FOR THE FLORIDA ORANGE SUBSECTOR OF THE FOOD INDUSTRY By Charles Everitt Powe December, 1973 Chairman: Max R. Langham Major Department: Food and Resource Economics A third generation quantitative economic model of the Florida orange subsector was developed and then used to evaluate the effects on subsector performance of alternative inventory, pricing, advertising and supply control policies. The model was composed of ten interrelated sectors, extending from tree planting through consumer demand, and was written in the DYNAMO simulation language. The internal consistency of the model was examined. The model was then validated on the basis of its ability, when given empirical estimates of weather conditions, to reproduce the behavior of the orange subsector over the 1961-71 period. Theil's inequality coefficients were used to measure the correspondence between simulated and empirical data. Calculated values of the coefficients ranged from .55 to .98 and indicated that predictions were better than those that would have been realized with the model p = a , where a and p represent actual and predicted values at time t. After the model had been accepted as an adequate representation of the structure of the orange subsector, a set of simulations was made to establish a base with which to compare the ten policies considered in

PAGE 11

the study. Comparable results for a variety of conditions were obtained by replicating each simulation with five randomly selected weather patterns. Simulations were started with initial values corresponding to conditions that existed at the beginning of the 1961-62 season and covered a twenty-five-year period. Results were examined from the viewpoints of three major groups of subsector participants: orange producers, processors and distributors, and consumers. It was assumed that the interests of these groups could be evaluated on the basis of the present value and variance of grower profits, crop size, and average FOB price, respectively. These values were computed from model output with the aid of a FORTRAN computer program and along with estimated storage costs provided the information used in policy evaluation. Policies that reduced long-run supplies of orange products caused substantially higher grower profits, lower storage costs and higher retail prices. They also reduced risks for orange producers, but not for other subsector participants. Small gains from policies that failed to alter the long-run behavior of the subsector were partially or completely offset by increased storage costs associated with them. Given the advertising response functions in the model, the alternative advertising proposal, which increased average advertising expenditures from $11.9 million to $19.8 million per season, did not prove to be profitable. However, the study did not confront the question of whether or not one method of collecting and expending advertising funds was superior to the other. The characteristic which dominated policy analysis was the presence of conflicts of interests among subsector participants. In almost every instance, in order for one group of participants to gain, another was

PAGE 12

placed in a less desirable position. For the policies considered in the study, results provided insights into costs and returns and their distribution among subsector participants. With periodic updating, the model can provide an ex ante method of evaluating future decisions as policy questions develop in the Florida orange subsector.

PAGE 13

CHAPTER I INTRODUCTION The Florida orange subsector has been characterized by large variation in orange production and crop value. Production during the past fifteen years (1958-72) has ranged from a high of 142,3 million boxes during the 1970-71 crop season to a low of 54.9 million boxes during the 1963-64 season. The on-tree value of the orange crop was 208.2 million dollars in 1970-71 as compared to a value of 241.3 million dollars for the smaller 1963-64 crop. Much of the short-run variation in crop size and value can be attributed to freeze damage. Freezes during the 1957-58 and 1962-63 seasons reduced orange supplies and caused large profits for some growers. These large profits were followed by new investments in orange groves which after a few years increased production and caused a period of low aggregate grower profits. During periods of low profits, grove establishment decreases; however, since existing orange groves produce over a long period of time, short-run supplies do not readily respond to low prices. The Problem Participants within the orange subsector have been concerned with the large variations in orange prices and supplies. Individual producers The "Florida orange subsector" is defined in a broad sense starting with the establishment of orange groves and extending through processing, marketing and final consumption of oranges and orange products.

PAGE 14

have sometimes benefited from short supplies and high prices; however, high prices allow the introduction of competitive products such as synthetic orange beverages and induce the establishment of new orange groves which increase supplies and reduce profits in future periods [17, p. 1]. The instability of the orange subsector may be detrimental to the longrun interests of all subsector participants. Supply stabilization would allow processors to eliminate excess processing capacity and reduce costs. Consumer interests may also be best served by stable prices. Little is known about the effects of alternative industry policies on the system as a whole and on various subsector participants. The dynamic and interdependent economic mechanisms operating within the Florida orange subsector may dampen or amplify the effectiveness of a policy more than static partial analysis and intuitive judgment would indicate. Computer simulation provides a method of studying the effectiveness of policy decisions within the dynamic environment of an abstract model without the risk of experimentation on the actual system. Objectives The objective of this study was to develop a third generation, multiproduct, multimarket model of the orange subsector and to test policies designed to improve the performance of the orange subsector. More specific objectives were to: 1. Identify the system structure underlying the orange subsector 's dynamic behavior. 2. Construct a four-product, two-market model of the orange subsector.

PAGE 15

3. Delineate and/or develop measures of performance which reflect the interest of all participants in the subsector. 4. Use the model to evaluate the effects of policies designed to improve the performance of the orange subsector. These policies include: a. changes in the end of year carry-over of orange products. b. changes in the Florida citrus industry's generic advertising budget. c. alternative pricing strategies. d. alternative supply control policies, including: (1) elimination of fully productive trees if grower profits fall below specified levels. (2) curtailment of new tree plantings when grower profits are above specified levels. Previous Work In 1962, under a grant from the Minute Maid Corporation, Jarmain [9] developed a first generation industrial dynamics model of the Florida frozen concentrated orange juice (FCOJ) industry. Jarmain' s study indicated that a larger carry-over of FCOJ from one season to the next would reduce price variability and improve the grower's position. Raulerson [21] revised and expanded Jarmain' s work in a second generation model in order to appraise the effectiveness of alternative supply control policies in stabilizing and raising grower profits. Emphasis was placed on the lack of knowledge in the area of supply response of oranges--particularly during the periods of low prices. Both Jarmain and Raulerson used average grower profits as a basis for evaluating the

PAGE 16

performance of the frozen concentrated orange juice subsector. These studies provided a basis for the current study. Models of the type used in this study require large amounts of information and it is helpful when this infoimation is summarized in relatively efficient forms. Information for this model was available from several sources--the following studies were particularly useful. A study completed by Polopolus and Black [17] in 1966 concluded that shifts in the quality and supply of orange juice due to periodic freezes have fostered the entry and proliferation of synthetic and partially natural citrus flavored drinks. The Polopolus and Black study was followed by a study in which Myers [14] empirically estimated cross elasticities of demand for major orange juice products, orange drinks and synthetic orange flavored beverages. Frozen concentrate and chilled orange juice were found to be strong substitutes. Chilled and canned single strength orange juice appeared to be weak substitutes. No significant substitution relationship was found between frozen concentrate and canned single strength orange juice. Weisenborn [25] completed a study in 1968 in which he used time series data and least squares regression procedures to estimate pricequantity relationships for major Florida orange products at the FOB level of the marketing system. These estimates provided the information necessary for the construction of net marginal revenue functions which were used to optimally allocate oranges among product markets for various size crops. Results based upon the estimated relationships indicated that a 128 million box orange crop maximized industry net revenue at the processor level.

PAGE 17

Priscott [19] carried Weisenborn' s study of the export market a step further in a 1969 study of the European demand for processed citrus products. In general, the study indicated that the demand for citrus products in West Europe was elastic and showed development potential. McClelland, Polopolus, and Myers [12] used time series data to estimate the response of consumer sales with respect to changes in generic advertising expenditures. These estimates were used in conjunction with a quadratic programming model to measure possible gains from allocating advertising funds more efficiently. Information from this study provided a basis for specifying the influence of advertising on product demand. In a 1971 study. Hall [8] estimated consumer demand in retail grocery stores for frozen concentrated orange juice, chilled orange juice, canned single strength orange juice, and canned single strength grapefruit juice for ten geographic regions of the United States. The analysis indicated that consumer demand functions for these products differ by region. Regional price elasticity estimates for canned orange juice compared closely with Weisenborn' s national estimates. Estimates were lower for chilled orange juice and higher for frozen concentrate than those reported by Weisenborn. Parvin [16] used yield estimates and standard regression techniques to estimate weather effects on early-midseason and Valencia orange production for eighteen Florida counties. These estimates provided a basis for the construction of a weather index for total Florida orange production.

PAGE 18

CHAPTER II STRUCTURE OF THE FLORIDA ORANGE SUBSECTOR''" An understanding of the essential relationships which give rise to a dynamic system's behavior is a prerequisite to the construction of a simulation model. A verbal description of the system's structure helped establish this understanding and provided a basis for building a quantitative economic model. General Description The Florida orange subsector is composed of five major groups of participants: producers, processors and packers, wholesalers, retailers and consumers. Producers are those individuals and business organizations who are primarily concerned with the production and sale of whole oranges. Processors and packers are involved with the conversion of whole oranges into processed products or with the packaging and sale of fruit in fresh form. Wholesalers and retailers provide marketing services and are concerned with the movement of orange products from the producing and processing area into consumer markets. Consumers are those primarily involved in the consumption of orange products and are the most numerous subsector participants. For the purposes of this study, final purchasers of orange products have been classified into two general types: retail and institutional. Some of the material used in this chapter also appears in an article by the author £18] .

PAGE 19

Institutional purchasers are nontaxsupported institutions such as restaurants and drugstore fountains and tax-supported institutions such as military establishments, hospitals, and school lunch programs. Retail purchasers are those who buy orange products through retail grocery outlets. Production The production of oranges in a given season depends on the acreage, variety, age distribution and physical environment of bearing orange trees plus the cultural and weather conditions that exist prior to harvest [16], Weather is the most erratic factor affecting orange production. Rainfall, low temperatures, and hurrican winds can cause extensive damage to fruit and trees. Freezes have historically been the factor most feared by Florida orange producers. In addition to the short-term effects of weather on orange production, freezes affect tree condition and productivity over long periods. Freeze damage to orange trees can be roughly divided into two general types: (1) damage to secondary branches requiring extensive pruning (hatracking) or (2) damage so severe that the tree dies. Secondary damage to the tree affects productivity for only a few crop seasons. More extensive damage requires that the tree be replaced. Florida orange production is geographically distributed over the south and central portion of the Florida peninsula. However, following the 1962 freeze, there was some indication that the producing area was gradually moving farther south. As of December 1969, two-thirds of the nonbearing acreage was located in eight south Florida counties. In each of these counties, the ratio of nonbearing to bearing groves was in

PAGE 20

excess of one to five (Table 1) . These plantings occurred before the enactment of the Holland Amendment which was incorporated into The Tax Reform Bill of 1969 [23]. This amendment requires the capitalization of all citrus grove development costs and exempts from capitalization requirements any citrus grove (or part thereof) "replanted after having been lost or damaged (while in the hands of the taxpayer) , by reason of freeze, disease, drought, pest or casualty . . ." [23, p. 574]. Thus, it provides an incentive for citrus producers to concentrate on the improvement and maintenance of established groves rather than on new grove development. The location of the orange producing area is important from the standpoint of a model which estimates crop size. If the location of the production area is rapidly shifting over time, historical data cannot be used as an estimate of future weather effects on orange production unless adjustments are made. Since the enactment of the Holland Amendment, locational movement within the producing area seems to be abridged. Whether or not this is an effect of the amendment is unknown. Dynamics of the Florida Orange Subsector A simplified flow diagram of the subsector is presented in Figure 1. Whole oranges move from the growing activity into the processing-packing sector where they are converted into processed orange 2 products. From processed inventory, orange products move into wholesale or institutional inventories and eventually consumption. Dotted lines in the diagram represent information flows between various system 2 Processed products include fresh fruit ready for shipment.

PAGE 21

Table 1, Acreage of bearing and nonbearing orange groves by Florida counties as of December 1969.

PAGE 22

10

PAGE 23

II components. Information may be in the form of order rates or prices. Associated with information flows are various delay factors. These delays represent the time lags required for information to move through the system. Information passed through the marketing system is the basis for management decisions. Several allocation problems must be solved by the market mechanism. The rate at which fruit flows from the growing activity into the processing sector must be controlled. This control is recognized in Figure 1 by hourglass shaped symbols. The solid lines represent physical flows. Whole fruit must also be allocated among alternative product forms, markets and consumers. Given a competitive market system, economic theory indicates that the allocation of productive resources will be made on the basis of the value of the marginal product. The marginal increment of a productive resource will go to the usage where it has the greatest value. Products will be produced until that output is reached where the value of the marginal unit of product is equal to its cost of production. The price system will allocate products among competing customers according to their ability and willingness to pay. Since information must be collected, it is reasonable to expect adjustments after a time lag. The demand for orange products is derived from the utility function of the individual consimier and product allocation is accomplished through the interaction of buyers and sellers; however, the allocation process as visualized in Figure 1 shows the processor-packer sector as a major decision point. Processor -packers receive information concerning inventory levels and the rates of flow of various products from inventory. If inventories are larger than desired or if the demand for a particular

PAGE 24

12 product changes, processors adjust FOB prices. These price signals pass through the marketing system and eventually affect consumption rates. As consumption rates change, signals are passed back through the system in the form of orders. Processors receive information on the adjusted movement from inventories and evaluate the effects of their pricing policies. If the effects of the pricing policy are not those desired, a new FOB price will be forthcoming. An equilibrium price will probably never result from this process. Consumers react to new prices over a period of time and while decision makers are considering new pricing policies, consumers are still reacting to previous prices. The relationship between short-run supply and price fluctuations and long-run industry investment patterns is shown in the block diagram presented in Figure 2. Weather is shown as an exogenous variable which affects tree numbers and orange supplies. Assuming relatively stable demand relationships for orange products, restricted supplies following freeze damage reduce product inventories and increase the FOB prices of orange products. Historical data indicate a strong inverse relationship between crop size and the per box return above operating costs received by growers (Figure 3) . During freezes the orange crops of some producers may be severely damaged while other producers with relatively undamaged crops benefit from high prices and high grower profits. These growers, having found orange production profitable, tend to reinvest in new orange groves (Figure 4). Thus, the orange subsector is characterized by periods of restricted capacity followed by periods of large supplies and low prices,

PAGE 25

13 weather

PAGE 26

14 Crop size (million boxes) Per box returns (dollars/box) 61-62 62-63 63-64 64-65 65-66 66-67 67-68 68-69 Crop season Figure 3. Size of the orange crop and per box return above operating costs received by growers for Florida oranges, 1961-62 through 1968-69 crop seasons. Source: See Table 3, p. 26, for data on per box returns and [3, 1968-69 season, p. 1] for crop size data. Per box returns (dollars/box) Movement (million trees) Figure 4. Per box return above operating costs received by growers for Florida oranges and orange tree movements from Florida nurseries, 1961-62 through 1965-66. Source: See Table 3, p. 26.

PAGE 27

CHAPTER III CHARACTERISTICS OF DYNAMO II The subsector model was constructed to meet the design and notational 1 requirements of the DYNAMO II computer compiler. The DYNAMO II compiler is a set of computer instructions used to translate mathematical models into tabulated and plotted results. It was developed by the industrial dynamics group at the Massachusetts Institute of Technology. Special Features DYNAMO II has several special features that facilitate model construction. These features include the following: 1. The compiler will reorder equations within a variable type whenever necessary in order to perform computations. Reordering will continue until all calculations have been made or until the compiler has identified equations that depend on other equations which in turn depend upon the equation defined, in which case the system is simultaneous and DYNAMO II prints an error statement identifying the equations involved. Version four was used in this study. It runs on the IBM S/360 computing system operating under OS or CP/CMS and is distributed by Pugh-Roberts Associates, Inc., 179 Fifth Street, Cambridge, Mass. 02141. See Pugh [20] for detailed documentation. 2 The industrial dynamics approach to problem solving is discussed by Forrester [7] . 15

PAGE 28

16 2, System macros in DYNAMO II includes clipping and limiting functions, exponential delays, maximum, minimum, random numbers, pulse, ramp, sample, smooth, step, switch, table, and trigonometric. 3. The compiler contains a convenient method of specifying output, The output routine includes various scaling alternatives and provides output in tabulated and plotted form. Data is outputted chronologically with respect to simulated time and can be requested for each calculation interval or some multiple of it. Time Notation The time notation used in DYNAMO II is presented in Figure 5.

PAGE 29

17 the values associated with time K become associated with time J. In this recursive fashion, the computer moves through the calculation process and time in the simulation. Type of Variables and Computational Sequence The DYNAMO II compiler is designed to handle three principal types of variables: levels, auxiliaries and rates. A level is a variable whose value at time K depends upon its value at time J and on changes during the JK interval. Levels are usually defined by equations of the form: quantity at time K = quantity at time J + change during the JK interval. Rates correspond to flows over time and are calculated for the KL interval. They are defined by levels and auxiliaries from time K and sometimes by rates from the preceding time interval. Auxiliaries are values calculated at time K from levels at time K and from ataxiliaries previously calculated at time K. The computational sequence in DYNAMO II is levels, auxiliaries and rates. In order to assure that the model is recursive and that values will be available for calculations, equations must be consistent with the organizational system presented in Table 2. A detailed exposition of DYNAMO II is given by Pugh [ 20] .

PAGE 30

18 Table 2. Organizational structure for DYNAMO II equations, Variable on left of equation Time associated with variable on left Time associated with variables on right if variable is LARS C N L Level A Auxiliary R Rate S Supplementary C Constant N Initial Value K K KL K J J JK * none none K K JK * none none K K JK * none none K K JK K none none * * * * * * * * * * none none Source: [20, p. 24] * Not permitted.

PAGE 31

CHAPTER IV THE MODEL The model of the Florida orange subsector consists of a set of relationships between individual system components. These relationships together with initial starting values provided the information necessary to simulate system behavior. Much of the effort in this study was expended in the specification and estimation of model equations and to a large extent the validity of the study must be judged on the basis of the confidence placed in them. Some relationships are self-explanatory given the definitions of the variables involved, others require explanation and justification. The model presented in this chapter represents a mathematical formulation of the interrelationships that underlie the dynamic behavior of the orange subsector. It draws heavily on previous models constructed by Raulerson [21] and Jarmain [9]. No attempt has been made to acknowledge each duplication. A detailed flow diagram is presented in Figure 6. Appendix A contains an alphabetic list of variable names. The following symbols were used in the flow diagram: P>0 rates LJ policies I ' levels > material flows r^ auxiliaries ---> information flows constants 19

PAGE 32

20 PROCfSSOR OISAPK^MNC€ gV :::::::3^^^^'^ DEMAWD SECTOR 10 Figure 6. Flow diagram of the DYNAMO moJol of the Florida orange subsector.

PAGE 33

21 Tree Numbers Sector The number of productive trees was increased by trees becoming productive and decreased by productive trees lost (equation 1) . During an initial period after the start of the simulation, the number of trees becoming productive was expressed as a fraction of the number of productive trees in existence (equations 2 and 2A) . This procedure allowed trees planted but not productive at the start of the simulation to be inserted into the system. After the initial period, trees became productive as a result of increases in the productivity of young trees and the recovery of freeze damage (hatracked) trees (equation 2B) . The rate at which young trees became productive was expressed as a sixth order exponential delay (actually two cascaded third order delays) with an input equal to the number of new trees planted and a delay in trees 2 becoming fully productive of 13 years (equations 3 6). The exponential delay approximated the yield response of newly planted orange trees by allowing larger proportions of a newly planted tree to come into production over simulated time. In Figure 7, the output from the delay in response to a step input is compared with a weighted average of the yields estimated by Chern [2, p. 58]. L PT.K = FT. J + (DT)(TBP.JK FTL.JK) 1 {ZTBP.JK if TIME.K 156 or NTBP.JK if TIME.K < 156 2 R NTBP.KL = (.178) (PT.K) /WPY 2A R ZTBP.KL = YTBP.JK + HTBP.JK 2B [7] 2 See Forrester for detailed explanation of exponential delays

PAGE 34

22 100 90 .. Tree productivity (percent of 80 mature yield) 70 60 • 50 • 40 30 20 10 Step input exponential yield estimate of the model empirical estimate Figure 7. Comparison of output from exponential delay and empirical yield estimates. Source: Empirical estimates from [2, p. 58].

PAGE 35

23 R YTBP.KL = DELAYS (XTBP.JK, XDG) 3 R XTBP.KL = DELAY3(NTP.JK, XDG) 4 N XDG = DG/2 5 C DG = 676 weeks 6 PT productive trees (trees) TBP trees becoming productive (trees/week) PTL productive trees lost (trees/week) YTBP young trees becoming productive (trees/week) HIBP hatracked trees becoming productive (trees/week) NTBP initial trees becoming productive (trees/week) NTP new trees planted (trees/week) DG delay in growiig (weeks) 3 XTBP internal transfer variables (trees/week) XDG internal transfer variable (weeks) ZTBP trees becoming productive after initial period (trees/week) TIME simulated time (weeks) WPY weeks per year (weeks) The rate at which new tree plantings occurred was controlled by a clipping function which set the number of new trees planted equal to zero or XNTP depending on whether or not a restriction on new tree planting was in effect (equation 7) . The restriction on new tree plantings was effective when average grower profit was greater than the new tree planting restriction (equation 8) . The effect of the policy was to prevent new trees from being planted when average grower profits were high. The rate at which new 3 Internal transfer variables will be defined in the future only when their meaning is not readily apparent.

PAGE 36

24 tree plantings would have occurred without considering the restriction policy was expressed (equations 9, 11 and 12) as a fraction of the number of productive trees in existence and was dependent upon the level of average grower profits per 90 pound field box (hereafter box). Figure 8 presents the basis for the assumption concerning this dependency. Supporting data are presented in Table 3. fxNTP.JK if NTPR = AGP.K R NTP.KL = < or 7 1 if NTPR < AGP.K I 1.50 if the policy was to be operative C NTPR = < or 8 1 1,000.0 if the policy was to inoperative R XNTP.KL = (PT.K)(FA.K)/WPY^ 9 C WPY = 52 10 A FA.K= TABHL(FAT, AGP.K, 0, 3.00, .50) 11 C FAT* = .022/. 054/. 086/. 118/. 150/. 182/. 214 12 XNTP the rate at which new tree plantings would have occurred without the planting restriction (trees/week) NTPR the value above which the planting restriction became effective (dollars/box) FA fraction of new trees added Hatracked trees becoming productive were expressed as a ninth order delay with an input equal to the number of trees hatracked (equations 13 17). The number of trees hatracked was expressed as a fraction of the productive trees in existence (equation 18) . The output from this delay in response to a unit input was faster and the average delay time shorter than for the sixth order delay that controlled the rate at which 4 The division of WPY was necessary since XNTP was expressed as trees per week.

PAGE 37

25 25 + Tree movement (percent) 20 .. 15 10 -' 5 -• .50 H 1.00 -41.50 2.00 2.50 3.00 Returns above operating costs (dollars/box) Figure 8. Relationship between per box returns above operating costs and movement of orange trees from Florida nurseries before and after the 1957-58 and 1962-63 freezes. Source: Table 3. Movement as a percent of mature tree equivalents.

PAGE 38

26 •H C J-l

PAGE 39

27 newly planted trees became productive. This difference reflected the rapid increase in the productivity of hatracked trees. The length of the delay was equal to 208 weeks. The rate at which productive trees were lost depended on the stochastic impact of weather and the "normal" losses associated with the passage of time (equation 19) . Productive trees lost as a result of freeze damage was determined by fractions generated within the freeze effects sector of the model and by the number of productive trees in existence (equation 20) . The "normal" loss was expressed in a similar fashion (equation 21). R HIBP.KL = DELAY3(XHrBP.JK, XDP) 13 R XHTBP.KL = DELAY3(YHrBP.JK, XDP) 14 R YHIBP.KL = DELAY3(THR.JK, XDP) 15 N XDP = DP/3 16 C DP = 208 weeks 17 R THR.KL = (FHR.K)(PT.K) 18 R PTL.KL = PTLA.JK+ PTLF.K 19 A PTLF.K = (1/DT)((FTLF.K)(PT.K) + (FHR.K) (PT.K))^ 20 R PTLA.KL = (PT.K)(FL.K)/WPY 21 THR number of trees hatracked (trees/week) DP length of delay in recovery of hatracked trees (weeks) PTLA productive trees lost as a result of "normal" aging factors or tree abandonment (trees/week) PTLF productive trees lost as a result of freeze damage (trees) FTLF fraction of productive trees lost as a result of freeze damage FHR fraction of productive trees hatracked Division by DT is necessary as a result of the multiplication that occurs in equation 1.

PAGE 40

28 FL fraction of productive trees lost "noirmally" or as a result of tree abandonment The value of the "normal" fraction lost variable was controlled by a clipping function (equation 22) which set FL equal to a tabular value which reflected "normal" tree losses (equations 23 and 24) or to a value that simulated a consciously applied policy of tree abandonment on the part of orange producers. The tree abandonment restriction could be made inoperative by setting its value at a sufficiently low level (equation 25) . When the policy was effective, trees were removed from production whenever grower profit was less than $.15 per box. The rate at which trees were removed from production was positively related to crop size through the DD variable (equations 26 and 27) . {XFL.K if GP.K = TAR or 22 YFL.K if GP.K < TAR A XFL.K = TABHL(XFLT, AGP.K, -.50, 2.00, .50) 23 C XFLT* = .08/. 06/. 04/. 03/. 02/. 015 24 r. 15 if tree abandonment policy was operative C TAR = I or 25 1-1000.00 if the tree abandonment policy was inoperative A YFL.K = (t3D7k)(DD.K YDD) 26 C YDD = 2.012E6 27 XFL "normal" fraction of trees lost YFL fraction of trees lost when tree abandonment restriction was operative GP grower profit (dollars/box) TAR tree abandonment restriction (dollars/box) DD disappearance desired (boxes/week)

PAGE 41

29 YDD disappearance associated with grower profits of $1.00 6 per box (boxes /week) Weather Effects Sector Values which determined weather effects were obtained in one of two ways depending on whether historical data were needed (for model validation purposes) or whether values were to be generated stochastically. When historical values were desired, option I was used; otherwise, values were generated by option II. Weather effects were divided into three catagories: tree effect, hatracking effect and yield effect. In the model each effect was treated as a pulse input which occurred once each Q season (equations 28 30). A FTLF.K= PULSE (XFTLF.K, 52, 52) 28 A FHR.K= PULSE(XFHR.K, 52, 52) 29 A FYLF.K= PULSE (XFYLF.K, 52, 52) 30 Option I Option I allowed predetermined values which reflected historical weather conditions to be incorporated into the model. These values were expressed as table functions dependent on simulated time (equations 31 36). 6 A disappearance rate of 2.012 million boxes per week was associated with grower profits of $1.00 per box only when weather and inventories were normal, the demand shifter was equal to its mean value, advertising influences were equal to 1, U.S. population was 193.89 million and the yield of oranges was 4.9 single strength gallons per box. During initial stages of model validation it was desirable to control as many factors as possible and to observe model performance under relatively stable conditions. In order to partially accomplish this a third weather option was constructed. This option maintained "average" weather conditions. For details see Appendix B, p. 129. vJeather effects for the first season are reflected in initial values.

PAGE 42

30 A XFTLF.K =TABHL(XFTIiFT, TIME.K, 52, 572, 52) 31 C XFTLFT* = See Table 4. 32 A XFHR.K = TABHL(XFHRT, TIME.K, 52, 572, 52) 33 C XFHRT* = See Table 4. 34 A XFYLF.K = TABHL(XFYLFT, TIME.K, 52, 572, 52) 35 C XFYLFT* = See Table 4. 36 9 A WI.K = SWITCH(1, 1, TIME.K) 36A A WIY.K =CLIP(WI.K, 1, WI.K, 1) 36B Option II When option II was used, a weather influence was selected from a population that was normally distributed with mean one and standard deviation .06 (equation 37). The total effect of this distribution was consistent with the "weather index" estimated by Parvin [16]. The weather influence selected was subtracted from one to arrive at an adjusted weather influence (equation 38) . The yield effect was set equal to the adjusted weather influence when the value of the weather influence was less than one; otherwise, it was set equal to zero (equation 39). Good weather was accounted for through a weather influence which increased yield (equation 40) . Tree and hatracking effects were expressed as functions of the yield effect (equations 41 44). A WI.K = N0RMRN(1, .06) 37 A XAWI.K = 1 WI.K 38 A AWI.K = MIN(XAWI.K, 1) 38A 9 Equations 36A and 36B have only mechanical significance in option I. They set to constants variables determined stochastically under option II.

PAGE 43

Table 4. Yield loss, tree loss and hatrack loss factors, 1962-63 through 1972-73 seasons. 31 Season Tree Loss (proportion) Hatrack Yield Total 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68 1968-69 1969-70 1970-71 1971-72 1972-73 226

PAGE 44

32 if WI.K = 1 A XFYLF.K = < or 39 I AWI.K if WI.K < 1 fwi.K if WI.K = 1 A WIY.K = < or 40 I 1 if WI.K < 1 A XFTLF.K = TABHL(XFTLFT, XFYLF.K, 0, .35, .35) 41 C XFTLFT* = 0/.15 42 A XFHR.K = TABHL(XFHRT, XFYLF.K, 0, .35, .35) 43 C XFHRT* = 0/.35 44 WI weather influence AWI adjusted weather influence WIY weather influence on yield Crop Size Sector Crop size was equal to the quantity of fruit remaining plus the quantity of fruit used to date (equation 45) . The quantity of fruit remaining at time K was equal to the quantity remaining at time J plus fruit added minus fruit used or lost during the JK interval (equation 46) . Fruit usage was accumulated as a level which was cleared at the end of each season (equation 47) . This was accomplished through a fruit discarded pulse which occurred once each year (equation 48). The pulse that cleared the level equation was a function of the quantity of fruit used (equation 49) . A CS.K = CR.K + FUTD.K 45 n L CR.K = CR.J CLF.J + NCA.JK (DT) ( Z FU(I).JK) 46 1=1 n L FUTD.K = FUTD.J + (DT) ( ^ FU(I).JK FD.JK) 47 1=1 R FD.KL = PULSE (FDP.K, 52, 52) 48

PAGE 45

33 A FDP.K = FUTD.K/DT 49 CS crop size (boxes) CR crop remaining (boxes) FUTD fruit used to date (boxes) NCA new crop added (boxes /week) FU(I)fruit used in I product (I = 1, . . . , 7) (boxes/week) CLF crop lost as a result of freeze damage (boxes) FD fruit discarded (boxes/week) FDP fruit discarded pulse (boxes) N number of orange products considered in the model New crop added was a function of the new crop pulse which occurred at the beginning of each new crop season (equation 50). The size of the pulse depended on the number of productive trees, yield per tree and a stochastic weather influence on yield (equation 51) . Yield per tree was considered a function of (lagged) average grower profit and reflected the improved cultural practices provided by growers in response to higher prices (equations 52 and 53). R NCA.KL = PULSE(CSP.K, 52, 52) 50 A CSP.K = (PT.K)(BPT.K)(WIY.K) 51 A BPT.K = TABHL(BPTT, AGP.K, -.50, 2.00, .50) 52 The following numerical code was used to identify the I product. Market Product Retail Institutional (I*^'^ product) Frozen concentrated orange juice 1 5 Chilled orange juice 2 6 Canned single strength orange juice 3 7 Fresh oranges 4 * * Not included.

PAGE 46

33A ATTENTION! Error Note The influence of weather on grower costs (equation 60) was Intended to be determined once at the beginning of each season and then to be held constant until the start of the next crop year. During years when weather was favorable (WI>1) grower costs per box would be decreased. On the other hand, unfavorable weather (WI<1) would cause a cost increase. Due to an error in programming, this was not what actually occurred in the operation of the model. The weather influence was an auxiliary (equation 37) which, with DT specified as .5 , was calculated twice per week. This caused grower cost per box (equation 60) to be subject to a stochastic influence. The major effects of the error are the following. (1) On the average, grower profits were overstated (understated) during seasons of unfavorable (favorable) weather, (2) The rate at which new trees were planted was affected through average grower profits; however, since the averaging period was two years the stochastic effect was small. (3) When the tree abandonment policy was operative (equations 22 and 25), the rate of tree abandonment was influenced since it was based directly on the level of grower profits. Correction The problem may be corrected by changing equation 60 to A GC.K=CPB/XWI.K 60 and adding the following equations:

PAGE 47

33B {WI.K if WP.K>52 or LWI.K if WP.K<52 L LWI.K=XWI.J N LWI=1 60A 60B 60B Comparison A comparison of results from uncorrected and corrected versions of the model is presented below for two of the policies (B and TA2, see page 96) considered in the study.

PAGE 48

34 C BPTT* = 4.5/4.6/4.7/4.8/5.0/5.3 53 CSP crop size pulse (boxes) BPT yield per tree (boxes/tree) AGP average grower profit (dollars/box) The crop lost as a result of freeze damage was the sum of the loss from each of the three freeze effect catagories (equation 54) . Each of these losses was the product of the appropriate loss factor (from the freeze effects sector) and the crop size pulse (equations 55 57) . A CLF.K = TLOSS.K + HLOSS.K + YLOSS.K 54 A TLOSS.K = (FTLF.K) (CSP. K) 55 A HLOSS.K = (FHR.K) (CSP. K) 56 A YLOSS.K = (FYLF.K)(CSP.K) 57 TLOSS crop loss associated with tree kills (boxes) HLOSS crop loss associated with hatracking (boxes) YLOSS yield loss (boxes) Grower Profit Sector Grower profit per box was the difference in on-tree price per box and grower cost (equation 58). Grower cost was initially set at .85 dollars per box and remained at that level until option II was employed to generate a weather influence (equation 59). When option II was used, grower cost was influenced by weather conditions (equation 60). On-tree price was a function of the weighted average FOB price paid for orange products (equations 61 and 62) . Average grower profit was an exponentially smoothed function of grower profit (equations 63 and 64). Profit was calculated by multiplying profit per box times the number of boxes used (equation 65) . It was then accumulated for each year in a level equation (equations 66, 66A and 66B) .

PAGE 49

35 A GP.K = OTP.K GC.K 58 C CPB = .85 dollars per box 59 A GC.K = CPB/WI.K 60 A OTP.K = TABHL(OTFr, AFOB.K, .35, 1.25, .18) 61 C OTPT* = .03/1.00/1.96/2.94/3.90/4.86 62 L AGP.K = AGP. J + (DT)(^p|g^)(GP.J AGP. J) 63 C TAGP = 104 weeks 64 R PROFT.KL = (GP.K)(TFU.K) 65 L GP.K = CP.J + (DT)(PROFT.JK CPD.JK) 66 R CPD.KL = PULSE (CPDP.K, 52, 52) 66A A CPDP.K = CP.K/DT 66B DTP on-tree price (dollars/box) GC grower cost (dollars/box) CPB cost per box (dollars/box) AFOB weighted average FOB price of orange products (dollars/gallon single strength equivalent) TAGP time for averaging grower profits (weeks) PROFT profit (dollars/week) TFU total fruit usage per week (boxes) CP cumulative profit per year (dollars) CPD cumulative profits discarded (dollars) CPDP cumulative profit discard pulse (dollars) Processor Disappearance Sector Weeks of crop (supply) remaining was a function of crop remaining and average fruit usage (equation 67) . Average fruit usage was equal

PAGE 50

36 to fruit usage exponentially smoothed with a four week averaging period (equations 68 and 69). Fruit usage associated with the I product depended on the disappearance of product I and a conversion factor (equations70 76) . The constant portion of the conversion factor was based on yield figures for the 1969-70 and 1970-71 seasons (Table 5). The conversion factor remained at the constant level until the weather influence was generated. When the weather influence was available, yield was influenced by weather conditions (equations 77 90). Processor disappearance was a function of retail and institutional demand and processor availability (equations 91 97) . Processor availability was related to the number of weeks of crop remaining (equations 98 and 99). A WCR.K = CR.K/AFU.K 67 L AFU.K = AFU.J + (DT)(--^) E (FU(I) . JK AFU. J) 68 1 = 1 C TAFU = 4 weeks 69 R FU(I).KL = (PD(I).JK)(BPG(I).K) 70-76 n A TFU.K= E FU.JK 76A 1 = 1 ^ BPG(I).K= (GpB(i))(wi.K) ^^-^^ C GPB(I) = See Table 5. 84-90 R PD(I).KL= (D(I).JK)(PA.K) 91-97 A PA.K= TABHL(PAT, WCR.K, 0, 15, 5) 98 C PAT* = 0/. 84/. 97/1.0 99 WCR weeks of crop remaining (weeks) AFU average weekly fruit usage (boxes) TAFU time for averaging fruit usage (weeks)

PAGE 51

37 PD(I) processor disappearance product I (gallons single strength equivalent /week) BPG(I) conversion factor for product I (boxes/gallon single strength equivalent) GPB(I) conversion factor for product I (gallon single strength equivalent /box) D(I) order rate for the I product (gallons single strength equivalent /week) PA processor availability Table 5. Conversion factors for major orange products. Conversion factors Product Gallons single strength equivalent per 90 pound box 1 4.90 2 5.29 3 5.20 4 5.29 5 4.90 6 5.29 7 5.20 Source: Based on yield estimates for 1969-70 and 1970-71 seasons. Advertising Sector Advertising revenue was equal to fruit usage times the advertising tax less administrative and other nonadvertising costs (equation 100) . Administrative and other nonadvertising costs were assumed to be a constant $26,306 per week (equation 101). The advertising tax rate was based on actual values for the 1962-63 through 1970-71 seasons (Table 6). After the 1970-71 season, the tax was assimied constant at

PAGE 52

38 Table 6. Advertising tax rates for Florida oranges by type of use, 1962-63 through 1970-71 seasons. Season Advertising tax rate 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68 1968-69 1969-70 1970-71 Source: Personal interview with the Economic Research Department, Florida Department of Citrus. Fresh

PAGE 53

39 10 cents per box (equations 102 and 103) . Advertising tax revenue accumulated at time K was equal to revenue accumulated at time J plus revenue collected minus revenue spent during the JK interval (equation 104) . The weekly advertising expenditure was the product of revenue available for advertising and the fraction spent each week (equation 105). The fraction spent each week reflected the seasonal expenditure pattern presented in Figure 9 and was a function of the number of weeks remaining in the season (equation 106 and 107) . Trademark advertising was not considered in this study. n R ATR.KL = ( E FU(1) . JK) (AT.K) AC 100 1 = 1 C AC = 26,306 101 A AT.K= TABHL(ArT, TIME.K, 0, 416, 52) 102 C AIT* = .09/. 09/. 08/. 08/. 08/. 08/. 08/. 08/. 10 103 L ATRA.K= ATRA.J + (DT)(ATR,JKATS.JK) 104 R AIS.KL = (ArRA.K)(FSPW.K) 105 A FSPW.K= TABHL(FSPWT, WP.K, 1, 52, 1) 106 C FSPWT* = See Figure 9. 107 ATR advertising tax revenue (dollars/week) AC administrative cost (dollars/week) AT advertising tax (dollars/box) ATRA advertising tax revenue accumulated (dollars) ATS advertising tax spending (dollars/week) FSPW fraction spent per week WP weeks passed (weeks) Consumers were assumed to respond gradually to advertising expenditures in the model. The magnitude of their response at a given time was

PAGE 54

40 Weighting factor 160 120 • 80 40 • .02439 .02033^ ,02033 .00813 . Sept. 10 Dec. 10 Mar. 10 June 10 Months Figure 9. Seasonal pattern of generic advertising and promotional expenditures for Florida oranges. Source: Personal interview with the Economic Research Department, Florida Department of Citrus. Fraction of tax revenue spent per week.

PAGE 55

41 determined on the basis of the average advertising expenditure for the preceding two years (equations 108 117) . Since little data were available, advertising responses for institutional products were based on the assvmption that customer oriented institutional purchasers such as restaurants and drugstore fountains were affected by advertising programs in the same manner as retail consumers. Noncustomer oriented institutions such as hospital and military establishments were assumed to be unaffected by advertising programs (equations 118 123). -"-^ L AA.K = AA.J + (DT)(1/TAA)(ATS.JK AA.J) 108 C TAA = 104 weeks 109 A AIl.K = TABHL(AI1T, AA.K, .5E5, .3E6, .5E5) 110 C AIIT* = .96625/. 9810/. 9925/1. 0030/1. 0095/1. 015 111 A AI2.K = TABHL(AI2T, AA.K, .5E5, .3E6, .5E5) 112 C AI2T* = .9445/. 9720/. 9895/1. 0055/1. 0195/1. 027 113 A AI3.K = TABHL(AI3T, AA.K, .5E5, .3E6, .5E5) 114 C AI3T* = .9555/. 9920/. 9990/. 9990/. 9910/. 9840 115 A AI4.K = TABHL(AI4T, AA.K, .25E5, .225E6, .5E5) 116 C AI4T* = .74/. 92/1. 068/1. 116/1. 146 117 A AI5.K = TABHL(AI5T, AA.K, .5E5, .3E6, .5E5) 118 C AI5T* = .97604/. 98651/. 99468/1. 00213/1. 00675/1. 01065 119 A AI6.K = TABHL(AI6T, AA.K, .5E5, .3E6, .5E5) 120 C AI6T* = .96781/. 98376/. 99391/ -1.00319/1.01131/1.01566 121 A AI7.K = TABHL(AI7T, AA.K, .5E5, .3E6, .5E5) 122 C AI7T* = .97419/. 99536/. 99942/. 99942/. 99478/. 99072 123 For the data on which these relationships were based, see Appendix E ,

PAGE 56

42 AA average advertising (dollars/week) TAA time for averaging advertising (weeks) AI(I) advertising influence on demand for the I product FOB Price Sector The FOB price of orange products was the mechanism through which allocation was accomplished. Allocation occurred in a resursive fashion. A time lag existed during which the model waited for consumers to respond to the most recent price adjustment. When price adjustments did not produce the desired effect or when conditions changed, new prices would be forthcoming. In making price changes, the model considered the size of the orange crop, the time that remained in the marketing season, the rate at which fruit was being used and the relative profitability of orange products. When fruit usage was less than desired, the model attempted to increase consumption and order rates by reducing prices. When it appeared that shortages would occurs the model increased prices. Price adjustments designed to alter fruit usage were accompanied by adjustments in the relative price of orange products. The model adjusted relative price whenever the marginal net revenue from the sale of one product was different from another. For example, when the marginal net revenue from product I was greater than that from product J, the model increased the price of J, reduced the price of I, or both. Thus, the 12 model attempted to equate marginal net revenues among orange products. The marginal net revenue of product I at time K was specified as a function of the FOB price of the I product at time J (equations 124 12 Refer to pp. 47-49 for a discussion of the allocation problem. Net marginal revenue functions were derived from cost and revenue relationships. For details see Appendix C.

PAGE 57

43 130). Marginal net revenues were weighted by the quantity of each product to arrive at a weighted average marginal net revenue per gallon single strength equivalent (equation 131). This weighted average was used to suggest an FOB price for each product (equations 132 138) . Suggested FOB prices along with demand equations and advertising influences on demand provided estimates of the monthly per capita quantity of product demanded (equations 139 145) . When multiplied times an estimate of U.S. population, summed and converted to boxes per week, these estimates suggested processor disappearance (equations 146 153) . Tables 7, 8 and 9 show the demand functions, mean values of variables and the data periods, respectively, for the demand relationships. L MNR(I).K = A1(I) + (A2(I))(F0B(I).J) + (A3(I)) (DS. J) 124130 n S (MNR(I).K)(XQD(I).K) mm K = 1=1 131 n E XQD(I).K I =1 XFB(I)S.K = A4(I) + (A5(I))(AMNR.K) + (A6(I)) (DS.K) 132138 n XPQS(I).K = (AI(I).K)(A7(I) + I ((A8(I)) (XFB(I) 1 = 1 S.K)) + (A9(I))(DS.K) 139-145 XQS(I).K = (XPQS(I).K)(P0P.K)/4 146-152 A PDS.K = E ((BPG(I).K)(XQS(I).K)) 153 1=1 MNR(I) marginal net revenue of I product (dollars/ gallon single strength equivalent)

PAGE 58

44 Table 7. Relationship between per capita quantity of an orange product that \i7ould be demanded by retail and institutional consumers given adequate time for system adjustment and the FOB price of the product. Quantity (gallons single strength equivalent per capita per month) Intercept FOB price (dollars/gallon single strength equivalent) Seasonal shifter^ TCOJ XOJ CSSOJ FO TCOJ COJ 145935

PAGE 59

45 Table 8. Mean values associated with estimated demand relationships. Product' FOB price (dollars /gallon single strength equivalent) Quantity (per capita gallons single strength equivalent /month) FCOJj^ COJr CSSOJp FCOJj. CO J J. CSSOJ, .5242 .5532 .5547 .7618 .7492 1.0600 .9043 .0867 .0085 .0084 .0364 .0113 .0162 .0062 The subscript refers to the retail or institutional market.

PAGE 60

46 Table 9. Base data periods associated with estimated demand relationships. Product Market Retail Institutional FCOJ COJ CSSOJ Fresh oranges January, 1968 April, 1971 January, 1968 April, 1971 January, 1968 April, 1971 August, 1962 July, 1963 December, 1963 November, 1966 December, 1963 November, 1966 December, 1963 November, 1966 ^ot applicable.

PAGE 61

47 f"h FOB (I) FOB price of I product (dollars/gallon single strength equivalent) AMNR weighted average marginal net revenue (dollars/ gallon single strength equivalent) 4-1XQD(I) quantity of the I product demanded at time J (gallons single strength equivalent /week) XFB(I)S suggested FOB price for product I (dollars/ gallon single strength equivalent) XPQS(I) monthly per capita consumption of product I suggested (gallons single strength equivalent per capita/month) POP U.S. population XQS(I) suggested consumption of I product (gallons single strength equivalent /week) PDS suggested processor disappearance (boxes/week) In order to maximize profits, economic theory indicates that a product should be allocated among markets so as to equate the marginal net revenue from the sale of the product in each market. The use of the average marginal net revenue to suggest new FOB prices insured that this condition was met. Perhaps this should be illustrated by an example. Assume that the FOB prices (P,, P2 and P ) of products 1, 2, 3 yield the marginal net revenues (MNR, , MNR^ and MNR„) shown in Figure 10. Further assume that the marginal net revenue of product 1 is less than the marginal net revenue of product 2 and greater than that of product 3. Since prices and marginal net revenues are positively related, profit maximization requires that the price of product 2 be reduced relative to product 1 while that of product 3 should be increased. A simple average

PAGE 62

48 CJ

PAGE 63

49 13 of the three marginal net revenues yields a value equal to AMNR. Prices suggested by this average value will be associated with equal marginal net revenues. In the example, the FOB price for product 1 would be unchanged while prices of products 2 and 3 would be reduced and increased, respectively. This technique adjusts relative prices; however, it does not consider adjustments in overall fruit usage relative to desired. In order to make this adjustment, it was necessary to com-, pare processor disappearance suggested with processor disappearance desired. Desired disappearance was a function of crop remaining, the number or weeks left in the marketing season, and the end of season carry-over (equation 154) . The carry-over was set equal to an eight week supply, except when an increased carry-over was operative in which case the desired carry-over increased to a 16 week supply (equation 155) . Weeks passed were accumulated by a level equation which was reset to zero at the beginning of each season (equations 156 158) . A DD.K = (CR.K)/(WPY WP.K + WCO) 154 xhe weighted average actually used in the model reduces the magnitudes of the fluctuations in aggregate fruit usage that result from relative price adjustments. 14 Bharat Jhunjhunwala has pointed out that an alternative approach would be to solve the constrained maximization problem and to use the resulting relationships as the basis for selecting the new price set. This method would allow the selection of prices that equate marginal net revenues while conforming to a quantity constraint. If the constraining quantity was set equal to desired disappearance, the movement suggested by the new price set would be that required to deplete available orange supplies (less carry-overs) . This method was not used since it was believed that the iterative technique provided a closer approximation of real world behavior and was computationally less demanding than a solution to the constrained maximization problem. The constrained maximization problem becomes computationally complex if the B matrix defined in Appendix C is nondiagonal .

PAGE 64

50 WCO = < 8 if the increased carry-over policy was inoperative or 155 16 if the increased carry-over policy was operative L WP.K = WP.J + (DT)(1 WD.JK) 156 R WD.KL = PULSE (WDP, 52, 52) 157 N WDP = (WPY/DT) 158 WCO weeks of carry-over (weeks) WD weeks discarded (weeks) WDP weeks discarded pulse (weeks) Processor disappearance relative to desired was the variable that determined whether an adjustment in product flow was necessary (equation 159) . When its value was not equal to one, an overall price adjustment was indicated; however, whether or not the adjustment was made depended on the value (either or 1) of R (equation 160) . The value of R depended on the value of V which in turn depended on the values of E, H and TIME (equations 161 165) . These equations allowed specification of a minimum time period during which price adjustments could not occur. A PDRD.K = PDS.K/DD.K 159 11 if V.K or 160 if V.K < A V.K = (TIME,K/H) E.K 161 L E.K = E.J + (DT)(Z.J) 162 15 The mechanics of the mechanism was as follows: no adjustment was allowed when R.K was equal to zero. R.K was equal to zero whenever V.K was negative. V.K was negative when the ratio TME.K/H was less than E.K. When the ratio was equal to E.K, V.K became zero and R.K was set equal to one allowing the adjustment to be made. In order to prevent continuous price adjustments beyond time H, the value of E.K was incremented by one. Then, the process was repeated.

PAGE 65

51 Z.K = R.K/DT 163 H ={ .5 if the price adjustment restriction was inoperative or 164 4 if the price adjustment restriction was operative N E = 1 165 PDRD processor disappearance relative to desired When adjustments were allowed, average marginal net revenue was adjusted and prices increased or decreased according to processor disappearance suggested relative to desired (equation 166) . When suggested disappearance was greater than desired, average marginal net revenue was adjusted upward. When suggested disappearance was less than desired, the average net marginal revenue was adjusted downward. The magnitude of the adjustment was increased by the Q variable as the disappearance ratio moved further from its equilibrium value (equations 167 and 168) . A policy option allowed the specification of a limit below which average marginal net revenue could not be adjusted (equations 168A and 168B) . Once the average marginal net revenue had been adjusted and new prices suggested they became the basis for new FOB prices (equations 169 189) . Thus, when the policy was effective lower limits were placed on the prices of the orange products. Finally weighted average FOB price was smoothed (equations 189B and 189C) . A ZAMNR.K= AMNR.K+ (R.K) (PDRD.K 1)(Q.K) 166 A Q.K= TABHL(QT, PDRD.K, .94, 1.06, .01) 167 C QT* = 20/18/16/14/12/10/1/10/12/14/16/18/20 168 A XAMNR.K= MAX (FLOOR, ZAMNR. K) 168A f-.20 if lower limit on XAMNR was operative or 168B -1000 if lower limit on XAMNR was inoperative

PAGE 66

52 A FOB(I)S.K = A2(I) + (B2(I)) (XAMNR.K) + (B4(I)) (DS.K) 169-175 A AQS(I).K= (P0P.K)(AI(I).K)(A3(I) + (B3(I)) (FOB(I)S.K) + (B4(I))(DS.K)) 175A-175G n A AQS.K = E (AQS(I).K)(BPG(I).K) 175H 1 = 1 L FOBd.K = FOB (I). J + (DT) (^^^ ) (FOB(I)S. J FOB(I).J) 176-182 C TCFP(I) = 4 weeks 183-189 n E (FU(I).JK)(FOB(I).K) A AFOB.K = i-^-i 189A TFU.K L SFOB.K = SFOB.J + (DT) (— |— ) (AFOB. J SFOB.J) 189B C TSFOB = 12 weeks 189C ZAMNR average marginal net revenue before considering the policy limit FLOOR lower limit on XAMNR XAMNR average marginal net revenue after the overall adjustment (dollars/gallon single strength equivalent) FOB(I)S FOB price of I product suggested after the overall adjustment (dollars/gallon single strength equivalent) AQS(I) quantity of the I product suggested after price adjustment (gallon single strength equivalent /week) AQS total quantity suggested after the price adjustment (boxes /week) TCFP(I) smoothing period used in determining FOB price for I product (weeks)

PAGE 67

53 SFOB smoothed weighted average FOB price (dollars/box) TSFOB time for smoothing weighted average FOB price (weeks) Retail and Institutional Inventory and Sales Sector Sales of orange products were equal to the product consumers demanded as long as adequate supplies were available at the consumer level (equations 190 196). The model's ability to satisfy consumer demand depended on the nxnnber of weeks of product inventory on hand relative to "normal." Data collected by the A. C. Nielsen Company and a priori knowledge provided a basis for estimating "normal" inventory levels for orange products (Table 10), When inventories dropped below "normal," a portion of consumer demand went unsatisfied (equations 197 210). The number of weeks of product inventory on hand was calculated by dividing the inventory level by average consumer demand (equations 211 217) . Inventories were increased by processor disappearance and decreased by product sales (equations 218 224) . R S(I).KL = (QD(I).K)(IA(I).K) 190-196 A lAl.K = TABHL(IA1T, WIAl.K, 0, 1.5, .5) 197 C lAlT* = 0/. 85/. 98/1.0 198 A IA2.K = TABHL(IA2T, WIA2.K, 0, 1.5, .5) 199 C IA2T* = 0/. 85/. 98/1.0 200 A IA3.K = TABHL(IA3T, WIA3.K, 0, 4, 2) 201 C IA3T* = 0/. 85/1.0 202 A IA4.K = TABHL(IA4T, WIA4.K, 0, .6, .2) 203 C IA4T* = 0/. 85/. 98/1.0 204

PAGE 68

54 Table 10. "Normal" retail inventories of major orange products. Product Inventory level (C(I)) ^Or (weeks) FCOJ„ , 1.3 R and I CO J , 1.2 R and I CSSOJ , 3.7 R and I Source: The estimate for fresh oranges was based on a priori knowledge. Estimates for processed products were based on data collected by the A. C. Nielsen Company.

PAGE 69

55 A IA5.K = TABHL(IA5T, WIA5.K, 0, 1.5, .5) 205 C IA5T* = 0/. 85/. 98/1.0 206 A IA6.K = TABHL(IA6T, WIA6.K, 0, 1.5, .5) 207 C IA6T* = 0/. 85/. 98/1.0 208 A IA7.K = TABHL(IA7T, WIA7.K, 0, 4, 2) 209 C IA7T* = 0/. 85/1.0 210 A WIA(I).K = I(I).K/AQD(I).K 211-217 L 1(1). K = 1(1). J + (DT)(PD(I).JK S(I).JK) 218-224 S(I) sales of the I product (gallons single strength equivalent /week) IA(I) influence of product availability on sales of the I product QD(I) quantity of the I product demanded (gallons single strength equivalent/week) WIA(I) number of weeks of inventory available (weeks) 1(1) inventory level (gallons single strength equivalent) AQD(I) average quantity of I product demanded (gallons single strength equivalent/week) Retail and institutional order rates depended on the level of average consumer demand, the inventory level relative to "normal" and a competitive influence which was associated with future price expectations (equations 225 231). When inventories were below "normal" regular order rates were increased in an effort to rebuild inventories, while above "normal" inventories caused a reduction in orders (equations 232 245). The competitive influence was expressed as a function of processor disappearance relative to desired and reflected the influence of price expectations on current order rates (equations 246 247) .

PAGE 70

56 When the ratio of suggested and desired processor disappearance was larger than unity, a price increase was expected at the FOB level and retail and institutional purchasers increased their orders in an attempt to take advantage of the lowest possible price. Similarly, when processor disappearance relative to desired was less than unity, order rates were reduced in anticipation of lower FOB prices. R D(I).KL = (AQD(I).K)(II(I).K)(CI.K) 225-231 A IIl.K = TABHL(II1T, WIAl.K, .3, 2.8, .5) 232 C HIT* = 2. 2/1. 4/1.0/. 9/. 85/. 82 233 A 112. K = TABHL(II2T, WIA2.K, .2, 2.7, .5) 234 C II2T* = 2. 2/1. 4/1.0/. 9/. 85/. 82 235 A 113. K = TABHL(II3T, WIA3.K, .7, 6.7, 1.5) 236 C II3T* = 1.5/1. 2/1.0/. 9/. 85 237 A II4.K = TABHL(II4T, WIA4.K, .1, .9, .2) 238 C II4T* = 3. 0/2. 4/1.0/. 81/. 72 239 A 115. K = TABHL(II5T, WIA5.K, .3, 2.8, .5) 240 C II5T* = 2. 2/1. 4/1.0/. 9/. 85/. 82 241 A 1X6. K= TABHL(II6T, WIA6.K, .2, 2.7, .5) 242 C II6T* = 2. 2/1. 4/1.0/. 9/. 85/. 82 243 A 117. K= TABHL(II7T, WIA7.K, .7, 6.7, 1.5) 244 C II7T* = 1.5/1. 2/1.0/. 9/. 85 245 A CI.K= TABHL(CIT, PDRD.K, .6, 1.4, .2) 246 C CIT* = .9/. 97/1. 0/1. 03/1.1 247 II (I) inventory influence associated with I product CI competitive influence

PAGE 71

57 Retail and Institutional Price Sector Retail prices of orange products normally adjust to levels suggested by FOB prices. The length of the adjustment period and the degree to which retail prices respond to changes at the FOB level depend on several factors, among these is the price protection policy of processors. At the time of this study, price protection was offered for processed products for a two week period. No protection was offered for fresh oranges. Factors such as the magnitude of the FOB price adjustment, the rate of product sales, and the level of inventories probably influence the length of the adjustment period. For this study, the time to correct the retail price of each product was assumed constant. Once the FOB price of a product was known, it was used to suggest a price which exponentially smoothed over an adjustment period determined the retail price of the product (equations 248 263) . These retail prices were averaged and used as inputs to the consvaner demand sector (equations 264 268). A XFOBl.K = (2.2501) (FOBl.K) 248 A XF0B2.K = (3)(FOB2.K) 249 A XF0B3.K = (4.3119)(FOB3.K) 250 A XF0B4.K = (2.645) (F0B4.K) 251 A RPSl.K =4.60 + (8. 3333) (XFOBl.K) 252 A RPS2.K = 16.91 + (8.3333) (XF0B2.K) 253 A RPS3.K = 12.38 + (8.3333) (XF0B3.K) 254 A RPS4.K = 2.34 + (4.0) (XF0B4.K) 255 L RP(I).K = RP(I).J + (DT)(^^^|^)(RPS(I).J RP(I).J) (E = 1, 2, 3, 4) 256-259

PAGE 72

58 C TCRPl = 2 weeks 260 C TCRP2 = 2 weeks 261 C TCRP3 = 4 weeks 262 C TCRP4 = .5 weeks 263 L ARP(I).K = ARP(I).J + (DT)(^^)(RP(I).J ARP(I).J) (I = 1, 2, 3, 4) 264-267 C TARP = 2 weeks 268 XFOBl FOB price of frozen concentrated orange juice (dollars/dozen 6 ounce cans) XF0B2 FOB price of chilled orange juice (dollars/dozen quarts) XF0B3 FOB price of canned single strength orange juice (dollars/dozen 46 ounce cans) XF0B4 FOB price of fresh oranges (dollars/45 pound carton) RPSl retail price suggested for frozen concentrated orange juice (cents/6 ounce can) RPS2 retail price suggested for chilled orange juice (cents/quart) RPS3 retail price suggested for canned single strength orange juice (cents/46 ounce can) RPS4 retail price suggested for fresh oranges (cents/pound) RP(I) retail price of the I product (same units as retail price suggested) TCRP(I) time for correcting the retail price of the I product (weeks)

PAGE 73

59 f~Vi ARP(I) average retail price of the I product (same units as retail price suggested) TARP time for averaging retail price (weeks) The heterogeneity of the institutional market makes data collection and analysis at the consumer level difficult and costly. The difficulty is further complicated by the fact that many institutional outlets purchase orange products through retail stores. For example, restaurant sales accounted for the consumption of about 88 million gallons of orange juice during 1971 [1]. Of this, 19 percent was reported to have been purchased by restaurants through retail outlets. The total institutional consumption of orange products during 1971 was estimated to be 196 million single strength gallons. This represented about 28 percent of total 1971 orange juice consumption. Demand estimates for institutional products at the FOB level were available from a study by Weisenborn [25]. This information was used as the basis for predicting consumption in the institutional market. It should be noted that the model estimates neither wholesale nor consumer prices for orange products sold through institutional outlets. The FOB prices of institutional products were converted to units consistent with Weisenborn' s equations (equations 269 271). They were then exponentially smoothed and used as inputs to the demand sector (equations 272 275). A XFGB5.K = (12)(FOB5.K) 269 A XF0B6.K = (3)(FOB6.K) 270 A XF0B7.K = (4.3125) (F0B7.K) 271 L IP(I).K= IP(I).J+ (DT)(— i-)(XFOB(I).J IP(I).J) 272TGIP 274 (I = 5, 6, 7)

PAGE 74

60 C TCIP = 2 weeks 275 XF0B5 FOB price of FCOJ (dollars/dozen 32 ounce cans) XF0B6 FOB price of COJ (dollars/dozen quarts) XF0B7 FOB price of CSSOJ (dollars/dozen 46 ounce cans) IP (I) smoothed institutional FOB price of the I product; (1=5, 6, 7) (same units as XFOB prices) TCIP time for correcting institutional price (weeks) Demand Sector Relationships used to estimate product comsumption are presented in Table 11 and the mean values for prices and quantities are given in Table 12. Advertising and price information (inputs to the sector) were used in conjunction with the demand equations to predict the quantity of each product demanded (equations 276 282) . Estimates were made on a monthly per capita basis. These estimates, converted to weekly per capita quantities and multiplied times projected U.S. population, provided an estimate of the total weekly consumption of each product (equations 283 290) . Population was accumulated in a level equation and was dependent on a growth rate which was related to time (equations 291 293). Average quantity demanded was an input to the retail and institutional inventory and sales sector (equations 294 301) . 4 A PQD(I).K = (AI(I).K)[A(I) + H (B(I)) (ARP(I) .K) + 1=1 (B8)(DS.K)] (I = 1, 2, 3, 4) 276-279 7 A PQD(I).K = (AI(I).K)[A(I) + E (B(I)) (IP(I)) .K] 1=5 (I = 5, 6, 7) 280-282

PAGE 75

61 Table 11. Retail and institutional demand relationships for Florida orange products. Quantity (gallons single strength equivalent per capita) Intercept Pricing Unit Retail or institutional price coefficient Seasonal shifter^ .R FCOJ R COJ R CSSOJ R FO I FCOJ I COJ I CSSOJ ,171943 cents/6 ounce -.005654 -.009218 ,067536 cents/quart -.001916 -.000294 ,033276 cents/46 ounce -.000771 .000131 ,152239 cents /pound .011138 052886

PAGE 76

62 Table 12. Mean values associated with estimated demand relationships. Product ' Price/Unit Quantity (per capita gallon single strength equivalent) FCOJ R 14.43 cents/6 ounce .0867 COJ, 30.74 cents/quart .0085 CSSOJ R FO. FCOJ, 32.31 cents/46 ounce 10.40 cents/pound $8.99/dozen 32 ounce .0084 .0364 .0113 CO J, $3.18/dozen 32 ounce .0162 CSSOJ, $3.90/dozen 46 ounce .0062 The subscript refers to the retail or institutional market.

PAGE 77

63 A DS.K = CLIP(1, 0, WP.K, 30.3) 283 A QD(I).K = (PQD(I).K)(P0P.K)/4 (I = 1, . . . , 7) 284-290 L XQD(I).K = QD(I),J 290A-290G L POP.K = POP. J + (DTXPG.JK) 291 R PG.KL = (.01) (PGR.K) (POP.K) 292 A PGR.K = .0232 + (.0462/TM.K) 293 A TM.K=MAX(4, TIME.K) 293A L AQD(I).K = AQD(I).J + (DT) (^^^^^ (QD(I) . J AQD(I).J) (I = 1, . . . , 7) 294-300 C TAQD = 2 weeks 301 PQD(I) per capita quantity of the I product demanded (gallons single strength equivalent /month) DS demand shifter = /? ^^P^" ^^^1 1 Apr . Aug . PG U.S. population growth (people/week) PGR weekly U.S. population growth rate (percent) TM TIME proxy (TM 4) TAQD time for averaging quantity demanded (weeks) Initial Conditions In order to start the computation process, a requirement of computer simulation is that initial conditions be specified. The values specified in this section roughly approximate subsector conditions at the beginning of the 1961-62 season. Once the starting conditions were specified, the DYNAMO compiler had the information required to compute initial values for level equations. These values were then available for the solution of auxiliary and rate equations. Within the computing

PAGE 78

64 sequence (levels, auxiliary, rates), the DYNAMO compiler rearranges the solution order of equations when necessary. Initialization for N

PAGE 79

65 cS 3 3 3 u

PAGE 80

66 Table 14. Net marginal revenues used to initialize model, Product Market Retail Institutional FCOJ COJ CSSOJ FO (dollars/gallon single strength equivalent) .105654 ,410560 ,145009 ,560814 .516743 1.043205 .523586 Source: Calculated. TTot applicable.

PAGE 81

Table 15. FOB prices used to initialize model, 67 Product Market Retail Institutional FCOJ COJ CSSOJ FO (dollars/gallon single strength equivalent) .862362 .660564 .688240 .911312 .856507 1.278780 . 918408 Source: Calculated. Not applicable.

PAGE 82

CHAPTER V VALIDATION The usefulness of the model presented in the preceding chapter depends upon its ability to characterize the response of the Florida orange subsector to changes in economic conditions. If the model is a "good predictor" of subsector response, it should be useful as a tool for policy analysis. If not, its value for studying economic policies may be limited. The predictive ability of a model can be evaluated on the basis of a set of criteria established for this purpose. However, the choice of criteria is a subjective process. The model can also be evaluated from the standpoint of the reasonableness of the estimates and assumptions presented in Chapter IV. The purpose of this chapter is to provide insight into the model's ability to predict. In his book. Computer Simulation Experiments with Models of Economic Systems , Naylor makes the following statement: In general, two tests seem appropriate for validating simulation models. First, how well do the simulated values of the endogenous or output variables compare with known historical data, if historical data are available? Second, how accurate are the simulation model's predictions of the behavior of the actual system in future time periods? [15, p. 21] In this study, a simulation was made to determine whether or not the model would converge when run for a long period of time with weather conditions held constant. The model was then evaluated on the basis of its ability, when given empirical weather data, to reproduce the behavior of the orange subsector during the 1961-71 period. 68

PAGE 83

69 Long-run Stability The model was intitialized to reflect, as nearly as possible, conditions that existed in the orange subsector at the beginning of the 1961-62 crop season. During the run stochastic weather generation was suppressed and weather effects were set equal to constants that reflected average weather conditions. With 1961-62 initial conditions, there was reason to expect the model to start from a disequilibrium position. However, a run period of one hundred years was believed long enough to allow the model to overcome initial disequilibrium and to provide an opportunity for observing whether the model, if left undisturbed, would come to a stable position. Partial results of this run are presented in Figure 11. In Figure 11 variables were plotted against time and the appropriate vertical scale. The vertical scales are identified by groups of numbers. Each number is associated with a respective variable identified by letter. The number of mature productive orange tree equivalents, represented by T, was initialized at 18.7 million. After the start of the simulation this figure increased at a rapid but decreasing rate for approximately sixteen years. After this period, tree numbers remained relatively stable within the 40-41 million range for about six years, before taking a slight dip and beginning a substained increase that lasted the remainder of the run. At the end of the simulation the number of mature productive orange trees stood at 94.7 million and had been increasing by 1.2 million trees per year. This behavior may be compared to the behavior of average grower profit during the same period. At the beginning of the run, prices were initialized at levels which yielded an average grower profit of $1.99 per box. The fact that this

PAGE 84

70 c

PAGE 85

71 figure was immediately adjusted downward by the model seemed consistent with the behavior that would have been expected from the orange subsector, if rather than having experienced the 1962-63 freeze, "normal" weather conditions had been encountered. The absence of freeze damage would have resulted in an estimated 42-44 million additional boxes of fruit during the 1962-63 season and would have prevented the temporary or permanent loss of approximately 13.5 million trees. In the simulation, average grower profit ranged from $1.99 to $.09 per box. Compared to a realized range during the 1961-70 period of $2,52 to $.21 per box, the simulated range seemed reasonable, particularly considering that the model, operating with "normal" weather conditions generated larger supplies than those experienced by the orange subsector. Other variables in Figure 11 follow similar patterns. Average marginal net revenue stabilized at a negative 16 cents per box. This behavior seemed inconsistent with the behavior required to maximize long-run net revenue at the FOB level and reflected a tendency of the model to overplant trees even under "normal" weather conditions. This overplanting tendency may represent a hedge against recurring crop damage. At any rate, it resulted from the specification of new tree plantings relative to average grower profits. As specified in Chapter IV (equations 11 and 12), the response table required that new tree plantings occur at the minimum rate of 2.2 percent of productive orange trees even when average grower profit was zero or negative. An earlier simulation, which used a response function that allowed new tree plantings to fall to zero, reached a stable position after approximately the same number of years with an average marginal net revenue of $-.03 per box. Differences between the two runs indicate behavior of the model is sensitive to changes in this relationship.

PAGE 86

72 The purpose of this run was to determine whether the model would stay within reasonable ranges and exhibit relatively stable behavior or whether it would explode if given time to overcome its initial disequilibrium. Results of the run seemed to affirm reasonable behavior, i.e., the model converged. Retrospective Comparison A simulation was made with initial values corresponding to conditions that existed at the beginning of the 1961-62 season and with weather effects specified to replicate as nearly as possible those that occurred during the 1961-62 through 1971-72 period. Results were compared with empirical data reflecting the behavior of the Florida orange subsector during the same period. Tree Nimibers Figure 12 presents a comparison of simulated and observed numbers of mature productive orange tree equivalents during the 1961-62 through 1971-72 period. In the simulation, the tree numbers variable was initialized at 18.7 million and had increased to 22 million trees by the end of the 1961-62 crop season. As a result of the freeze which occurred in the simulation at the beginning of the 1962-63 season, tree numbers were reduced to 16.9 million by mid-season. Carry-over effects of the freeze also caused a reduction in productive trees during 1963-64During this period, an almost identical pattern of change was reflected Initialization of tree numbers at 18.7 million probably overstated the number of trees in existence at the beginning of the 1961-62 season. Reflection indicated that this figure was more nearly associated with the end than with the beginning of the season.

PAGE 87

73 J3 00 o u trt

PAGE 88

74 in the observed data; however, levels of observed tree numbers were approximately ten percent lower than those generated by the model. Following the 1963-64 season, the combined effect of new trees becoming productive and damaged tree recovery produced a sharp increase in tree numbers. This increase was particularly evident in the time path of the observed variable and may have partially resulted from the reassessment of freeze damage. At any rate, there were 3.5 million more trees observed than simulated in 1964-65. Further comparison of the time paths revealed high correspondence between observed and simulated tree numbers during the 1966-67 and 1968-69 seasons. However, after the 1968-69 season, simulated tree numbers increased at a rate faster than the rate based on the observed data point. A summary of observed versus simulated changes in tree numbers is 2 presented in Figure 13. In this diagram, completely accurate predictions fall on the line of perfect forecasts. As points move away from this line, predictive accuracy decreases. The second and fourth quadrants of the diagram map turning point errors, i.e., the prediction of a change in direction when no change occurred or a change in direction not predicted. For the six points for which comparable tree numbers data were available, the model overestimated realized changes three times, underestimated once and predicted one point on the perfect forecast line. A quantitative measure of the correspondence between observed and simulated values was provided by Theil's inequality coefficient [24, p. 28]. Of the several versions of the coefficient, the one used in 2 A detailed discussion of the prediction-realization diagram is given in [24, pp. 19-26].

PAGE 89

75 75 •(hundred . qO thousands) ^ A (hundred thousands) Figure 13. Prediction-realization diagram for changes in numbers of mature productive orange trees. A = a -a t t t-1 P = p -p t t '^t-l

PAGE 90

76 this study was defined as follows: 2 (a,. P^.)' U = ^ (^ \-l^' 111 where a represents the observed or actual value at time t and p represents the simulated or predicted value. In the case of perfect forecasts, Theil's coefficient takes on the value zero. The value of one indicates that predictions are no better than those that would have been made with the model p = a^_, . For the tree numbers data, the coefficient was equal to .5513 indicating that the root mean square prediction error was 55 percent of the root mean square error that would have been realized had predictions been made with the model p. = 3l^_-iCrop Size Figure 14 presents a comparison between simulated and observed crop size data. In general, the path of the simulated variable corresponded fairly closely with observed behavior; however, noticeable disparities existed in 1963-64 and after the 1967-68 crop season. After 1967-68, estimates made by the model overstated crop size and the magnitude of the overstatement increased each season. The prediction-realization diagram. Figure 15, indicated that of the nine changes generated, the model overestimated five and underestimated the remainder. Theil's coefficient, equal to .98, indicated that predictions were slightly better than those that would have been realized with the no-change model. On-Tree Price A comparison of observed and simulated on-tree prices of Florida oranges is presented in Figure 16. Again, the general behavior of the

PAGE 91

77 Crop size (millions of boxes) 200 -150 -• 100 50 simulated ^*' *"*•»»•' 1961-62 1963-64 1965-66 1967-68 1969-70 1971-72 Figure 14. Simulated and actual crop size, 1961-62 through 1971-72 seasons. Source: [3, 1971-72 season] and simulated.

PAGE 92

78 (millions <\ • o of boxes) O' -* (millions 30 of boxes) Figure 15. Prediction-realization diagram for changes in Florida orange production. A = a -a ' t t t-1 P = p -p , t '^t ^t-1 Source: [3, 1971-72 season] and simulated.

PAGE 93

79

PAGE 94

80 simulated variable corresponded with observed data. Restricted supplies following the 1962 freeze led to increased prices; whereas, the large crop of 1966-67 caused a sharp price dip, A relatively small crop in 1967-68 was again associated with increased prices. The predictionrealization diagram. Figure 17, indicated that the model underestimated the magnitude of four changes, overestimated three and made two turning point errors — one between the 1963-64 and 1964-65 seasons and another between 1969-70 and 1970-71. The Theil coefficient equaled .67. Market Proportions As mentioned in Chapter IV, in order to maximize net returns, processors as a group should attempt to allocate oranges so as to equate marginal net revenues among product markets. Table 16 shows proportioned allocations of the orange crop as observed during the 1963-64, 1964-65 and 1965-66 seasons and as performed by the model during the validation 3 period. As can be seen from the data, the proportion of the orange crop allocated into a given product -market varied somewhat from season to season. This variance, however, was relatively insignificant compared to differences between simulated and observed allocations. Relative to observed, the model allocated fewer oranges to each retail product and more to each institutional product. The allocation performed by the model, though somewhat different from the observed, followed directly from the derived marginal net revenue equations (equations 129 135) . The demand equations used in the derivations were obtained from several sources and most included variables exogenous to the simulator. Since the model was designed to 3 Simulated figures corresponded to the end of each season; however, there was little variation within seasons.

PAGE 95

81 P (dollars per box) "• (dollars ^•50 per box) Figure 17. Prediction-realization diagram for changes in on-tree price. \ = \-\-l ^t = Pt-Pt-1 Source: [3, 1968-69 season, p. 95, and 1971-72 season, p. 104] and simulated.

PAGE 96

Table 16. Observed and simulated fruit usage, by product -market, 82 Season Product -Market' 1

PAGE 97

83 operate in a recursive fashion, the coefficients of these variables were removed from the equation by incorporating them into the intercept. The resulting equations, along with cost and margin information, were used to derive marginal net revenue equations for each product -market . An examination of these relationships revealed that several cross-product coefficients had signs different from those expected and in some cases the cross-price effect outweighted the own-price effect. Further examination indicated that these coefficients could lead to results inconsistent with economic theory, e.g., when all prices increase, total quantity demanded increased. In order to prevent this problem cross-product coefficients were incorporated into intercept terms. The loss of these coefficients resulted in relatively naive demand equations. A different set of equations might have led to results more consistent with the observed data. Conclusion The obvious implication of the preceding comparisons is that there exists room for improvement in the predictive accuracy of the DYNAMO model. However, a definite similarity existed between real world and model behavior especially with regard to turning points and it was believed that the model captured the dynamics of the orange subsector.

PAGE 98

CHAPTER VI POLICY ANALYSIS The term "policy" as used in this chapter refers to changes in either the model's operating rules or its structure. Most policies were implemented by parameter changes in functions discussed in Chapter IV. These changes altered the operating rules of the model and affected performance by reducing orange supplies, increasing desired carry-overs, and by modifying pricing and advertising schemes. A set of five runs, each covering a twenty-five year period, was made to provide a base with which to compare policy results. This base was an attempt to characterize the orange subsector as it is currently structured. Ten policies were then examined. Each run started with a set of initial conditions based on the 1961-62 crop season and was associated with weather effects computed by the stochastic procedure. The weather effects used for the base run were also used for each policy and provided comparable results for a variety of weather conditions. Policies were replicated five times--once with each of the weather sets presented in Table 17. The weather effect for each season was greater than, equal to, or less than one and denoted better than average, average or poorer than average weather conditions, respectively. DYNAMO contains a function which generates "pseudo random numbers" that satisfy all of the statistical tests for randomness. However, each nvimber is calculated from the previous one by a fixed procedure. Thus, a given noise seed always generates the same sequence of numbers. In the normal distribution mode, the DYNAMO procedure does not perfectly reproduce a normal distribution in that no number can diverge from the mean by more than 2.4 standard deviations. For more information, see Pugh [20]. 84

PAGE 99

85 Table 17. Weather conditions used in the five simulation runs for each policy. Season Weather sets' 2 1.14 1.01 1.07 1.07 1.10 3 1.01 .92 .89 .99 1.03 4 1.11 .95 1.01 .92 1.06 5 .95 .95 .99 .98 .97 6 1.08 1.11 .99 .96 .89 7 1.00 1.06 1.00 1.08 1.08 8 .98 1.00 1.05 1.02 .87 9 .94 .98 .95 1.01 1.02 10 1.11 1.08 1,03 1.03 .99 11 1.00 .97 .98 .98 1.01 12 .93 .91 1.05 1.01 1.04 13 1.00 .-88 1.07 .96 .98 14 .97 .98 .97 1.03 1.02 15 1.06 1.06 .96 1.04 1.01 16 1.05 .96 .94 .95 .99 17 1.07 1.07 .94 .96 .97 18 1.05 .97 1.06 1.01 1.06 19 1.00 .99 1.06 1,04 1.03 20 .99 .98 1.01 1.04 .96 21 1.00 1.00 1.04 .90 .96 22 1.04 1.00 .92 .92 .97 23 .92 .95 1.08 1.01 1.01 24 1.03 1.03 1.08 1.03 .98 25 .97 .97 1.00 1.02 1.04 a Weather conditions are based on an index (average weather = 100) . The larger (smaller) the index the more favorable (unfavorable) the weather. The noise seeds used to generate weather sets 2 through 5 were 943805, 7641403, 10861407 and 86451509, respectively. The seed for weather set 1 was already in the noise function. b Initial values were used for the first season.

PAGE 100

86 Policies The policies examined in this study are briefly described as follows: 1. Restricted tree planting. A restriction was placed on new tree planting whenever average grower profits rose above specified levels. Three levels were considered in the study, $1.25, $1.50 and $1.75 per box. When the policy was operative, tree planting was permitted or not permitted depending on whether grower profits were below or above the level specified. On first glance, this restriction may seem in conflict with logical decision making since high profits would be expected to call forth increased supplies. However, in the orange subsector, growers have tended to react to high profits as if a permanent shift in marketing structure has occurred in spite of the fact that high grower profits have normally been associated with a freeze. Consequently, they tend to overinvest in new orange groves. It takes several years for these groves to become fully productive, after which the additional supplies have precipitated periods of relatively low returns and low grove investment. These reactions have caused the subsector to be characterized by production and price cycles and it was believed that a restriction on tree plantings during periods of high grower profits might exert a stabilizing influence on the system. 2. Tree abandonment. The tree abandonment policy, when operative, removed fully productive trees from the system whenever grower

PAGE 101

87 profits fell below $.15 or $.25 per box, depending on which level had been specified in a particular run. The effect of the policy, by immediately reducing tree numbers, was similar to the sale of grove acreage for nonagricultural purposes. 3. Increased carry-over. A policy which increased the end of season carry-over of orange supplies from 8 to 16 weeks of average consumer demand was implemented. The purpose of this policy was to determine if increased carry-overs would improve system performance by providing buffer inventories. Carryovers were specified as a constant multiple of average consumer demand. Thus, when large supplies remained at the end of the season, price would be low, the level of average consumer demand high and a relatively large inventory would be carried over. This inventory would be available the next season and would tend to stabilize prices and retail inventories in case of a small crop. On the other hand, if a large crop occurred, the increased carry-over could contribute to even lower prices. An increase in carry-over from 8 to 16 weeks provided an opportunity to evaluate the model's reaction to changes in carry-over while other components of the model were the same. 4. Price adjustment restriction. A policy which altered the time that must elapse following a price adjustment before another adjustment could be made was incorporated into the model. In the base model, pricing was continuous and price adjustments could be made as often as twice each week. This is more often than price adjustments occur in the orange industry. When the price adjustment restriction was in effect, price could be

PAGE 102

altered only twice each month. In reality, the citrus industry does not adjust price even this often and in the past has extended two week price protection to wholesalers in the case of a price decrease. However, decision rules within the model were not as flexible as those used by the industry and it was felt that a two week restriction would provide a test of the model's sensitivity to changes in the price response relationship without preventing the model from reacting for a long period when conditions indicated that a price change was necessary. The system could become more or less stable as this response function was changed. Price floor. Implementation of this policy, by placing a lower limit on the average marginal net revenue of orange products, effectively set lower limits on FOB and retail prices. In the base run, the model was allowed to reduce prices to the levels required to sell the desired quantities of orange products. When the price floor was effective, prices were not allowed to fall below the level set by the floor. Supplies which could not be sold without causing unacceptably low prices were carried over to periods of higher prices, normally coincident with a freeze. When the price floor was operative it set a lower limit on average marginal net revenue of $-.20 per gallon single strength. The prices associated with this marginal net revenue allowed a large proportion of the oranges to be sold, yet exerted a stabilizing effect on the system by not allowing extremely low prices.

PAGE 103

89 2 6. Alternative advertising. An alternative method of determining advertising revenues and expenditures was adapted from a pro3 posal by Myers [13]. In his report, Dr. Myers suggested a procedure for funding the Florida Department of Citrus that related revenue collection to a five year moving average of citrus production rather than the yearly production level. This procedure was designed to change the incidence of the tax by causing a larger tax per box to be collected during periods of small crops which are generally associated with high per box prices. Revenue collection based upon the procedure were expected to be more stable than if they were collected by the method currently used in the industry. Expenditures, on the other hand, allowed more to be spent on advertising when there was a large crop to be sold. The DYNAMO equations used to construct this policy are listed in Appendix D. The general procedure used to calculate revenues and expenditures was as follows: Total revenue was determined by the formula: YP TR = (2.6E6)(1.05) + a(ACS) + b(SACS) + c 2 Two changes were made in the structure of the base model before running the advertising policy. Advertising costs were made variable and added to grower costs rather than being deducted from on-tree price per box (a change in equations 59, 60 and 62 in Chapter IV) and administrative and other costs were allowed to increase over time (a change in equation 100 in Chapter IV) . A new base was then generated in order to be comparable with the advertising policy. Specific changes in the model are presented in Appendix D. For a more detailed discussion see footnote 6. There are differences between the procedure presented here and the one proposed by Dr. Myers. The most important being that Myers' proposal based revenue collection and expenditure on a standardized production level that included grapefruit, while the procedure used in the simulation was based only on oranges.

PAGE 104

90 .06

PAGE 105

91 Crop size Value of the nimerical coefficients (million boxes) "d" "e" "f" 0-77 .06 -.0001 78-230 .11 -.00007 231 or more .05 .00003 6.9E6 Administrative costs were deducted from total receipts and expenditures before determining the advertising influence on consumer demand. The initial amount deducted was $26,306 per week. And since costs and revenues increased over time in the total receipt and expenditure equations, the amount deducted was also increased. 7. Restricted tree planting and price floor. The final policy considered in this study consisted of a combination of restrictions that limited increases in productive capacity in response to high grower profits and at the same time set a limit which prevented extremely low prices following a succession of large crops. It was felt that these restrictions might, by leveling out "ups and downs," improve the performance of the orange subsector. The policy prevented tree planting when grower profit was above $1.50 per box and placed a lower limit of $T.20 per box on average marginal net revenue. Measures of Performance In theory, for a given set of alternatives, it is possible for the participants in a subsector to bargain with each other until they arrive at a preferred position. This implies that for a given set of policies, one which is Pareto optimal will be chosen. In practice and particularly in the short-run, it is difficult to arrive at such a position since

PAGE 106

92 participants must be able to determine the relevant factors on which to base their decisions and obtain the information necessary to evaluate 4 the effect of the dynamics of the system. This analysis examined two factors believed to be of major importance for each major interest group participating in the orange subsector. No attempt was made to define the tradeoffs between subsector participants. Policies were examined from the viewpoints of three major groups of subsector participants: the producers, processors and distributors, and consumers of orange products. The assumption was made that the interests of participants within each of these groups were homogeneous enough to be represented by a variable selected from the mathematical model. This is, of course, an oversimplification of the real world and ignores many conflicts of interest within each group. However, it was believed that the present values of three representative variables and the variances associated with those values provided a reasonable basis for comparing alternative policies. Present values were used in the analysis since it was believed that participants within the orange subsector view costs and returns from a point in time and base their decisions on discounted values. For example, consider the two hypothetical streams of income presented in Table 18 and assume that t denotes the present and t + 1, t + 2, t + 3 and t + 4 the next four years. The total value of each income stream is equal to five hundred dollars and assuming that no time preference exists and that both streams 4 For a theoretical discussion see Langham [11] . The term "present value" as used in this study refers to the value of the variable discounted to the beginning of the simulation run. A note on the calculation of these values is presented in Appendix F.

PAGE 107

93 a Table 18. Discounted values of two hypothetical streams of income received over a five-year period. -r ^ Discounted value Income stream Year — : z — at tim e t A B — ; B t $120.00 $ 80.00 $120.00 $ 80.00 t + 1 110.00 90.00 102.80 84.11 t + 2 100.00 100.00 87.34 87.34 t + 3 90.00 110.00 73.47 89.79 t + 4 80.00 120.00 61.03 91.55 Total $500.00 $500.00 $444.64 $432.79 "Discounted to time t at the rate of seven percent per year.

PAGE 108

94 will occur with a probability of one, they would be equally preferred. However, if a time preference equivalent to a seven percent discount rate is assumed, policy A would be the more attractive since it has the higher present value. This comparison, based only on present values, ignores the fact that income streams may be associated with different levels of risk. For example, one policy may be relatively insensitive to weather conditions and the income stream it generates may have a small variance compared to other policies. It was believed that most men are risk averters and, therefore, prefer to minimize risk for a given level of income. The variances of present values over the five weather replications were, therefore, considered to be important in the decisionmaker's utility function. Grower profit was selected as the variable which best represented the interests of orange producers. The premise underlying this assumption was that the utility of producers was directly related to the present value of grower profits and inversely related to the variance of grower profits. Processors and distributors were also assumed to be interested in the return on their investment; however, this return was believed to be related to the volume of oranges moving through the marketing system. Processors and distributors tend to formulate prices on the basis of cost plus a constant markup per unit of output. Thus, their interest is closely associated with crop size which was chosen to reflect their preference. In order to account for time and risk, the size of the orange crop was discounted in the same manner and at the same rate as grower profit and the variances associated with present values calculated.

PAGE 109

ATTENTION! See error note on pages 33A and 33B.

PAGE 110

95 Consumers were assumed to prefer the lowest possible prices and since, in general, prices were inversely related to crop size, their interests seemed somewhat parallel to those of processors and distributors. A stream of retail prices was generated for each of the seven orange products considered in the model; however, the variable which seemed to best summarize consumer interests was the average price of single strength orange juice at the FOB level. This variable was related to each of the retail prices and provided a less complex and computationally more efficient basis for evaluating consumer interests than could be obtained by considering all of the retail prices directly. Like other participants in the orange subsector, consumers were assumed to base their decisions on present values, except in their case, they preferred the policy which provided the lowest present value of the price stream, ceteris paribus. Consumers were also considered to be risk averters and their utility was believed to increase with a decrease in either the level or variance of the present value of average FOB price. Analysis of Alternative Policies The alphanumeric names used to identify the simulation runs are presented in Table 19. Fifty of the runs were for the ten policies described in this chapter and the remainder for two slightly different versions of the base model. The results of policy analysis emphasized 6 In the base (except for advertising) model, the cost of administering the Florida Department of Citrus was deducted at a constant rate of $26,306 per week; however, when modeling the alternative advertising policy, administrative costs were compounded at the rate of five percent per year. This was a change in structure which needed to be and was reflected in the base (for advertising) model. A problem resulted from the ability of advertising queues in the

PAGE 111

96 c to Xi a. in m m

PAGE 112

97 that tradeoffs exist between subsector participants. Discounted values of the averages of the variables over the five weather replications are presented in Table 20. In the base (B) , the discounted values of grower profits, average FOB price and crop size were $1,000.98 million, $7.16 and 1,746.39 million boxes, respectively. Policies that reduced orange supplies either by a restriction on tree planting or by tree abandonment or removal caused corresponding increases in the discounted values of FOB prices and grower profits. A comparison, with base values equal to 100, is presented for the nonadvertising policies in Table 21. Each of the three planting restrictions considered in the study increased the present value of grower profits by at least fifty percent indicating that orange producers would benefit from the policy. Each of the restrictions also reduced crop size by as much as 28.5 percent and caused an increase in the prices paid by consumers by as much as 19 percent. The variance of grower profits decreased but remained unchanged or increased for the other variables. Estimates of the cost of storing the end of season carry-overs associated with the alternative policies are presented in Table 22. For the planting restrictions (PRl, PR2 and PR3), reductions in storange costs ranged from 11.3 to 13.4 million dollars. These reductions were base (for advertising) and advertising policy to accumulate different levels of unspent advertising revenue. To the extent that this occurred, grower profits net of advertising tax collections would have reflected the costs of advertising without the benefits, and the policy which accxmiulated the largest unspent revenue would have been unfairly penalized in the comparison. A change in the model which made grower profits net of advertising expenditures rather than receipts partially corrected the problem in that accumulated advertising funds were no longer deducted from grower profits; however, some discrepancy remained because the potential gain from the use of these funds was ignored.

PAGE 113

ATTENTION! See error note on pages 33A and 33B.

PAGE 114

98 M O 0) M trt

PAGE 115

99 3 CO 0) x: g o

PAGE 116

100 Table 22. Size and discounted costs of the carry-overs associated with alternative policies. Policy Average carry-over Cost of storage Relative cost (million gallons concentrate) B

PAGE 117

101 directly associated with the reduced crop size and inversely related to the changes in grower profits. The increase in grower profits ranged from 505 to 523.8 million dollars (Table 20). Tree abandonment policies (TAl and TA2) , while not as successful at increasing grower profits as the planting restrictions, were the most successful of the policies at reducing the variance associated with FOB price and crop size. In other respects, the effects of tree abandonment were similar to those obtained with planting restrictions. The present value of grower profits increased by eight and one-half million dollars as a result of increasing carry-overs (CO) from eight to sixteen weeks of average consumer demand. There was also a slight increase in the discounted value of FOB prices, crop size and the variances of grower profits and crop size. From the standpoint of orange producers, the policy seemed desirable; however, assuming "normal" returns, the additional storage costs of 47 million dollars more than offset the benefits of the policy from the viewpoint of processors. The price adjustment restriction (PA), partially implemented to test the sensitivity of the model to changes in the adjustment mechanism, reduced grower profits and at the same time caused an increase in average FOB price and crop size. Taking the price restriction as the norm of present operations, the simulation indicated that producers and consumers would benefit from increased price responsiveness and that processors would benefit from reduced storage costs with only a small sacrifice in crop size. This, of course, ignores other efficiencies associated with stable prices that were beyond the scope of this study and which may be substantial.

PAGE 118

102 Advantages of the price floor (F) were offset by an increase in storage costs to $79.88 million from the base of $50.08 million. This cost increase, even after deducting the $16.4 million increase in grower profits, would have required a return above variable costs (excluding storage) of $1.55 per box on the increased volume handled by processors in order to break even. And, if processors had been required to bear the total cost increase, the break even return would have been $3.46 per box on the increased volume handled. The cost and return estimates presented in Table 23 indicated that during the 1961-71 period fixed costs would have had to represent a very high proportion of total costs in order to have justified the price floor policy. For example, assuming that half the total cost (excluding storage) was fixed, returns above variable costs (excluding storage) during the 1961-71 period never exceeded $2.11 per box and was greater than $1.55 only in 1962-63 and 1968-69. Thus, the policy did not seem to be justified by the increased volume. The price floor in conjunction with the planting restriction (PR2 + F) performed somewhat better than the price floor alone, probably because with reduced supplies, storage time was shorter and costs did not accumulate over several seasons. At any rate, the increase in grower profits exceeded additional storage costs by $1.94 million. The policy had little effect on FOB price and crop size, except for a slight increase in the variance of the latter and would probably benefit the orange subsector based on the criterion used here. However, the administrative costs of maintaining a price floor might well outweigh the small gains.

PAGE 119

103 Table 23. Estimated costs and returns to orange processors, 1961-62 through 1970-71 seasons.^ Season Total cost

PAGE 120

104 Implementation of the alternative advertising policy (ADV) caused an increase in the level of advertising expenditures. Expenditures increased from a season average (across weather replications) of $11.9 million for the base (B2) to $19.8 million for the alternative policy, or by 66 percent. Given the advertising response functions of the model, the additional advertising was not profitable, as indicated by the present values presented in Table 20. With increased advertising and higher taxes, the present value of grower profits decreased from $1026.10 to $989.16 million, or by 3.6 percent. Smaller grower profits led to a reduction in the present value of crop size which in turn was associated with an increase in FOB prices. Thus, from the standpoint of all three groups of subsector participants, the policy seemed undesirable. However, these results hold only for the specific formulation of the policy used in this study which does not confront the question of whether or not one method of collection or expenditure is superior to the other. The results also rest heavily upon the advertising response functions used in the model. These functions were based on a limited analysis of data from a study by McClelland which basically reflected conditions during the 1960-67 period [12]. As the functions were specified in Chapter IV, advertising reached a saturation point when expenditures were $300,000 per week and additional advertising did not increase consumer purchases. Thus, the average expenditure of $19.8 million involved considerable waste, at least $105 million over the twentyfive years of the simulation and probably considerably more. The decrease in grower profits (without discounting) was $89 million; thus, had the expenditure level been lower, performance would have improved.

PAGE 121

105 Figure 18 shows simulated tax collections, expenditures and crop sizes associated with weather set 1. Tax collections in the base simulation (B2) followed the same pattern as crop size. Expenditures, on the other hand, were somewhat more stable than the crop. The pattern was reversed with the ADV policy, expenditures were based on crop size and tax collections were more stable except when reserves fell below the $3.8 million minimum and the additional two-cent tax was collected. The latter method has the most intuitive appeal since it advertised more during seasons of large crops and it would have been interesting to compare the two procedures with average advertising at the same levels. Perhaps the most consistent characteristic of the results was the presence of conflicts of interests. As can be seen from the summary presented in Table 24, none of the nonadvertising policies were clearly preferred by all three groups of subsector participants. If CO and F are eliminated on the basis of increased storage costs, TAl and TA2 are left or the only policies which might have been preferred by all participants. Whether either TAl or TA2 were preferred would depend on how consumers and processors and distributors view tradeoffs between present values and variance in their respective decision variables. The remaining policies were preferred by some participants but not by others. The fact that none of the policies were clearly preferred to the base by all participants would support the supposition that the base was Pareto optimal. A subsector characterized by perfect competition would In order to make such a comparison, a series of simulations with incremental changes in the parameters of the total revenue and expenditure functions would be needed. Then, the run with an average advertising expenditure of about $12 million per season could be compared with the base. Further investigation of consumer response to advertising would increase the confidence placed in the results of the analysis.

PAGE 122

&.

PAGE 123

107 Table 24. A classification of nonadvertising policies by preference category relative to the base (B) by group of participants. a Participant Policy T, J r. Processors and Producers Consumers distributors PRl X PR2 X PR3 X TAl X TA2 X co'' PR PR2 + F X a The letter X indicates that the policy was clearly preferred to the base. A indicates that the base was clearly preferred to the policy. The space was left blank when the preference was not clear. This classification does not consider changes in storage costs. It is based on the present values and variances of the policies. The increase in storage cost was believed sufficient to eliminate the policy.

PAGE 124

108 be expected to organize itself in a Pareto optimal fashion; and, in fact, perfect competition in the absence of external economics and diseconomies is a sufficient condition for Pareto optimality. Hov/ever, other forms of market organization can also lead to positions that are Pareto optimal. Thus, one cannot conclude from these results that the orange subsector is competitive. In summary, policies that reduced orange supplies led to substantially higher grower profits, lower storage costs and higher retail prices. Supply restrictions also reduced risks for orange producers, but not necessarily for other subsector participants, tree abandonment being the only policy that consistently reduced the variance of the discounted values for all variables. The increased carry-over and price floor policies caused increases in the present value of grower profits and crop size. They also increased storage costs and FOB prices, probably enough to offset their positive effects. When the alternative advertising policy was simulated, expenditures were 66 percent higher than in the base simulation and, given the response functions in the model, were not profitable. A lower average expenditure would have improved the performance of the advertising policy since advertising was often above the level required to maximize retail sales. Restricting price adjustments to every two weeks, reduced the present value of grower profits by $38 million and increased FOB prices. Taking price stability as the norm, the subsector would benefit from increased price responsiveness. However, these benefits might be offset by externalities associated with frequent price changes. The policy which came closest to being acceptable on the basis of all performance criteria was the price floor operating in conjunction with the planting restriction when compared to

PAGE 125

109 the planting restriction alone. However, gains from the floor were small and the policy would be justified only if administrative costs were low. In addition to economic feasibility, there are other factors that should be considered in the selection of a policy. In many cases, legal mechanisms have been established in order to provide the means for adopting and implementing specific policies which otherwise might be considered illegal, and a major consideration for any policy should be legal requirements. Also, popular support is usually necessary in order for a policy to be effective and policies that are easily understood and intuitively appealing often succeed where more complex policies fail. Undoubtedly, there are additional factors that should be considered in formulating alternative policies. This study provides an example of simulation as an ex ante method of policy investigation and, for the policies examined in this chapter, results provide some insights into potential costs and returns and their distribution among subsector participants.

PAGE 126

CHAPTER VII SUMMARY AND CONCLUSIONS The Florida orange subsector has been characterized by shifts in production and crop value and subsector participants--particularly growers and processors — have been interested in evaluating the effects of alternative policies on subsector performance. Computer simulation provided a method of studying the effectiveness of alternative policies within the dynamic environment of an abstract model without the risks of experimentation on the actual system. Objectives in the study were (1) to identify the structure underlying the subsector 's dynamic behavior, (2) to construct a quantitative model which captured the essential characteristics of this structure, and (3) to use the model to evaluate the effects on subsector performance of alternative inventory, pricing advertising and supply control policies. A verbal description of the structure of the subsector provided an understanding of the system's dynamic behavior and formed the basis for building the model. The model was a third generation effort drawing from previous work by Jarmain [9] and Raulerson [21]. It was composed of ten sectors and was written in the DYNAMO simulation language. Validation was on the basis of the model's ability, when given empirical estimates of weather conditions, to reproduce the behavior of the subsector over the 1961-71 period. A quantitative measure of the correspondence between simulated and empirical data was provided by 110

PAGE 127

Ill Theil's inequality coefficient, values of which ranged from .55 to .98, indicating that predictions were better than those that would have been realized with the model p = a. _, , where a^ and p^. represent actual and predicted values at time t. To verify that the model was internally stable, a simulation was made for a long period of time with weather conditions held constant. After the model was accepted as an adequate representation of the status quo, a set of simulations was made to establish a base with which to compare the ten policies considered in the study. Comparable results for a variety of conditions were obtained by replicating each simulation with five randomly selected weather patterns. Simulations were started with initial values corresponding to conditions that existed at the beginning of the 1961-62 season and covered a twenty-five year period. The results were examined from the viewpoints of three major groups of subsector participants: orange producers, processors and distributors, and consumers. It was assumed that the interests of these groups could be evaluated on the basis of the present value and variance of grower profits, crop size and average FOB price, respectively. These items were computed with the aid of a FORTRAN computer program and along with estimated storage costs provided the information used in policy evaluation. The first policy examined was one where restrictions were placed on new tree plantings whenever grower profits exceeded specified levels. Three levels were examined in the study--$1.25, $1.50 and $1.75 per box. In the simulations, these restrictions increased the present value of Two bases were actually used in the study, one for advertising and the other for nonadvertising policies.

PAGE 128

112 grower profits. They also reduced crop size and caused an increase in the prices paid by consumers. The associated changes in the variance of the decision variables affected participants in a similar fashion. Consequently, the restrictions were beneficial from the viewpoint of orange producers but not from the viewpoints of processors and distributors or consumers. Policies that abandoned fully productive orange trees whenever grower profits fell below $.15 or $.25 per box were also examined. Like the restrictions on tree plantings, the tree abandonment policies caused an increase in grower profits; however, they reduced the variance of FOB price and crop size. Thus, it was possible that these policies were beneficial from the viewpoint of all three groups of subsector participants. Whether this result would be true, however, would depend on how processors and consumers made tradeoffs between the present value and variance of their respective decision variables. Three policies were examined which, respectively, increased carryovers from 8 to 16 weeks of average consumer demand, restricted price adjustments to twice each month (rather than twice each week), and placed a lower limit on average marginal net revenue which, in effect, placed a floor on prices. Results indicated that the orange subsector would receive some benefits from more flexible prices; however, these benefits might be offset by additional costs associated with frequent price changes. Gains from the larger carry-overs and the price floor were offset by increased storage costs. A policy consisting of a combination of restrictions that limited increases in productive capacity whenever grower profits were above $1.50 per box and also placed a lower limit on average marginal net

PAGE 129

113 revenue was examined. The small gains from this policy, when compared to the planting restriction alone, probably would not justify the administrative costs of the price floor. Finally, a policy which altered the collection and expenditure of advertising funds was considered. In the base model, advertising was funded by a constant tax per box of oranges. In the alternative policy, the tax per box increased with a decrease in crop size. A small crop was normally associated with high prices. Also, the procedure allowed a large proportion of advertising funds to be spent when there was a large crop to be sold. The policy increased average advertising from $11.9 million to $19.8 million per season, or by 66 percent. Given the advertising response functions in the model, this much additional advertising was unprofitable. Thus, the policy was undesirable from the viewpoints of all three groups of subsector participants. No attempt was made in the study to determine the most profitable level of advertising or whether or not one procedure was preferable to the other. However, had the level of advertising been lower in the simulations, the performance of the policy would have improved. In conclusion, policies that reduced orange supplies caused substantially higher grower profits, lower storage costs and higher retail prices. They also reduced risks for orange producers, but not necessarily for other subsector participants. The alternative advertising proposal did not prove to be profitable, given the advertising response functions in the model. Small gains from policies that failed to alter the long-run behavior of the subsector were partially or completely offset by increased storage costs. The characteristic which dominated policy analysis was the presence of conflicts of interests

PAGE 130

114 among subsector participants. In almost every instance, in order for one group to gain, another was placed in a less desirable position. For the policies considered in the study, results provided insights into costs and returns and their distribution among subsector participants. The model has potential usefulness in the continuing evaluation of alternative policies; since, as specific proposals develop in the orange subsector, the model provides a means of studying their effectiveness and obtaining insights into potential problems. The model's usefulness will depend upon the ingenuity of the user and upon the particular policies 2 to be studied. Limitations Several model relationships were estimated on the basis of inadequate information. One of these was the relationship between grower profits and future orange supplies. As orange producers have become more sophisticated in their decision making, they have altered their response to changes in grower profits. Also, real estate values within the orange producing area have increased rapidly with unclear effects on long-run supplies. In estimating the response relationship, the effect of these changes was not completely understood. Two other areas of the model were bothersome. Several demand equations had coefficients with signs differing from theoretical expectations and cross-product terms that outweighted the ownprice effect. 2 Large models such as the one discussed in this study have two offsetting characteristics — as the model becomes larger and more detailed, additional linkage points exist and it becomes easier to build in alternative policies. On the other hand, the model becomes more difficult to comprehend and there is greater opportunity for estimation errors in the simulations. Also, the resources required to update the model increase along with the complexity of policy evaluation.

PAGE 131

115 These equations, along with cost functions, formed the basis for product allocation and in the simulations a smaller proportion of the product was channeled through the frozen concentrate retail market and a larger proportion through institutional product markets than was observed in empirical data. This discrepancy was believed indicative of problems with cost and demand relationships. Estimates of consimier response to advertising were also bothersome. The response relationships developed by McClelland could not be accommodated in the DYNAMO model without making alterations in structure. Thus, advertising functions were based upon a simplified adaptation of his results. These estimates had an important effect on the evaluation of the advertising policy. Mention should be made of the model's overemphasis of the discontinuity between crop seasons. When the end of a season drew near, the model had less time to adjust to specified end of season conditions and made changes more rapidly than would occur in the orange subsector. This characteristic was dampened by averaging and by making operating rules dependent upon conditions that changed as the end of season approached. However, the model overstated the end of season discontinuity of the orange subsector. Finally, answers provided by the model for particular policies need to be carefully evaluated. Also, questions for which the model is being used need to be evaluated. It may be that other approaches are more suitable for studying a particular question. Sometimes partial analysis will be a more reliable and a less expensive approach. More aggregate econometric type models have advantages for structural estimation.

PAGE 132

116 Implications for Future Research If the results of current and future research are to be used to improve the model, considerable effort will be required to make results compatible with model structure. In this respect, efforts should come from two direct ions--from that of researchers involved in studies with relatively specific objectives and from that of the researcher attempting to improve the model. Both will have to be willing to place themselves in the other's position and expend time and energy in understanding the reasons for a particular specification and each will have to compromise in order to make their work compatible. The tendency seems to be for the researcher studying a relatively specific problem, in his search for accuracy, to become involved in more detail than can be accommodated in the model, whereas, on the other hand, the model builder, from his viewpoint of a large and necessarily more abstract model, may tend to gloss over important details. In order to obtain complementary results, both researchers will have to make a conscientious effort to accommodate the other's purpose.

PAGE 133

APPENDIX A Alphabetized List of Variable Names

PAGE 134

ALPHABETIZED LIST OF VARIABLE NAMES Defined by equation(s) AA average advertising (dollars /week) 108 AC administrative cost (dollars/week) 101 AFOB weighted average FOB price of orange products (dollars/gallon single strength equivalent) 189A AFU average weekly fruit usage (boxes) 68 AGP average grower profit (dollars/box) 63 th AI(I) advertising influence on demand for the I product 110-123 AMNR weighted average marginal net revenue (dollars/ gallon single strength equivalent) 131 4.1AQD(I) average quantity of I product demanded (gallons single strength equivalent /week) 294-300 AQS total quantity suggested after the price adjustment (boxes/week) 175H AQS (I) quantity of the I product suggested after price adjustment (gallon single strength equivalent /week) 175A-175G ARPl average retail price of frozen concentrated orange juice (cents/6 ounce can) 264 1 "Box" when used in a definition refers to a 90 pound field box. 118

PAGE 135

119 ARP2 average retail price of chilled orange juice (cents/quart) ARP3 average retail price of canned single strength orange juice (cents/42 ounce can) ARP4 average retail price of fresh oranges (cents/ pound) AT advertising tax (dollars/box) ATR advertising tax revenue (dollars/week) ATRA advertising tax revenue accumulated (dollars) ATS advertising tax spending (dollars/week) AWI adjusted weather influence (AWI ^l) BPG(I) conversion factor for product I (boxes/gallon single strength equivalent) BPT yield per tree (boxes/tree) CI competitive influence (.9 £ CI _< 1.1) CLF crop lost as a result of freeze damage (boxes) CP cumulative profit per year (dollars) CPB cost per box (dollars/box) CPD cumulative profits discarded (dollars) CPDP cumulative profit discard pulse (dollars) CR crop remaining (boxes) CS crop size (boxes) CSP crop size pulse (boxes) th D(I) order rate for the I product (gallons single strength equivalent /week) Defined by equation(s) 265 266 267 102 100 104 105 38A 77-83 52 246 54 66 59 66A 66B 46 45 51 225-231

PAGE 136

120 DD desired disappearance (boxes/week) DG delay in growing (weeks) DP length of delay in recovery of hatracked trees (weeks) DS demand shifter = J ? ^ept. Mar. ^ 1 Apr. Aug. FA fraction of new trees added FD fruit discarded (boxes/week) FDP fruit discarded pulse (boxes) FHR fraction of productive trees hatracked FL fraction of productive trees lost "normally" or as result of tree abandonment FLOOR lower limit on XAMNR FOB (I) FOB price of the I product (dollars/gallon single strength equivalent) FOB(I)S FOB price of I product suggested after the overall adjustment (dollars/gallon single strength equivalent) FSPW fraction spent per week FTLF fraction of productive trees lost as a result of freeze damage FU(I) fruit used in I product; (1=1, (boxes/weeks) FUTD fruit used to date (boxes) GC grower cost (dollars/box) GP grower profit (dollars/box) 7) Defined by equationps) 154 17 283 11 48 49 29 22 168B 176-182 169-175 106 28 70-76 47 60 58

PAGE 137

121 Defined by equation(s) GPB(I) conversion factor for product I (gallons single strength equivalent /box) 84-90 HLOSS crop loss associated with hatracking (boxes) 56 HIBP hatracked trees becoming productive (trees/week) 13 1(1) inventory level (gallons single strength equivalent) 218-224 IA(I) influence of product availability on sales of the I product 197-210 th II (I) inventory influence associated with I product 232-245 IP5 smoothed institutional FOB price of frozen concentrated orange juice (dollars/dozen 32 ounce cans) 272 IP6 smoothed institutional FOB price of chilled orange juice (dollars/dozen quarts) 273 IP7 smoothed institutional FOB price of canned single strength orange juice (dollars/dozen 46 ounce cans) 274 MNR(I) marginal net revenue of the X product (dollars/gallon single strength equivalent) 124-130 N number of orange products considered in the model NCA new crop added (boxes/week) 50 NTBP initial trees becoming productive (trees/week) 2A NTP new trees planted (trees/week) 7 NTPR the value above which the planting restriction became effective (dollars/box) 8

PAGE 138

122 OTP PA PD(I) PDRD PDS PG PGR POP PQD(I) PROFT PT PTL PTLA PTLF QD(I) RPl RP2 RP3 on-tree price (dollars/box) processor availability processor disappearance of product I (gallons single strength equivalent /week) processor disappearance relative to desired suggested processor disappearance (boxes /week) U.S. population growth (people/week) weekly U.S. population growth rate (percent) U.S. population per capita quantity of the I product demanded (gallons single strength equivalent /month) profit (do liars /week) productive trees (trees) productive trees lost (trees/week) productive trees lost as a result of "normal" aging factors or tree abandonment (trees/week) productive trees lost as a result of freeze damage (trees) quantity of the I product demanded (gallons single strength equivalent /week) retail price of frozen concentrated orange juice (cents/6 ounce can) retail price of chilled orange juice (cents/ quart) retail price of canned single strength orange juice (cents/46 ounce can) Defined by equation(s) 61 98 91-97 159 153 292 293 291 276-279 65 1 19 21 20 284-290 256 257 258

PAGE 139

123 RP4 retail price of fresh oranges (cents/pound) t'Vi RPS(I) retail price suggested for the I product (same units as retail prices above) S(I) sales of the I product (gallons single strength equivalent/week) SFOB smoothed weighted average FOB price (dollars/ box) TAA time for averaging advertising (weeks) TAFU time for averaging fruit usage (weeks) TAGP time for averaging grower profits (weeks) TAQD time for averaging quantity demanded (weeks) TAR tree abandonment restriction (dollars/box) TARP time for averaging retail price (weeks) TBP trees becoming productive (trees/week) TCFP(I) smoothing period for FOB price of I product (weeks) TCIP time for correcting institutional prices (weeks) th TCRP(I) time for correcting the retail price of the I product (weeks) TFU total fruit usage per week (boxes) THR number of trees hatracked (trees/week) TIME simulated time (weeks) TLOSS crop loss associated with tree kills (boxes) TM time proxy (TM >^ 4) TSFOB time for smoothing weighted average FOB price (weeks) Defined by equation(s) 259 252-255 190-196 189B 109 69 64 301 25 268 2 183-189 275 260-263 76A 18 55 293A 189C

PAGE 140

124 WCO WCR WD WDP WI WIA(I) WIY WP WPY XAMNR XDG XFB(I)S XFL XFOBl XF0B2 XF0B3 XF0B4 XF0B5 Defined by equation(s) 155 67 157 158 37 211-217 40 156 10 weeks of carry-over (weeks) weeks of crop remaining (weeks) weeks discarded (weeks) weeks discarded pulse (weeks) weather influence number of weeks of inventory available (weeks) weather influence on yield weeks passed (weeks) weeks per year (weeks) average marginal net revenue after the overall adjustment (dollars/gallon single strength equivalent) 168A internal transfer variable (weeks) 5 suggested FOB price for product I (dollars/ gallon single strength equivalent) 132-138 "normal" fraction of trees lost 23 FOB price of frozen concentrated orange juice (dollars/dozen 6 ounce cans) 248 FOB price of chilled orange juice (dollars/dozen quarts) 249 FOB price of canned single strength orange juice (dollars/dozen 46 ounce cans) 250 FOB price of fresh oranges (dollars/45 pound carton) 251 FOB price of frozen concentrated orange juice (dollars/dozen 32 ounce cans) 269

PAGE 141

125 Defined by equation(s) XF0B6 FOB price of chilled orange juice (dollars/ dozen quarts) 270 XF0B7 FOB price of canned single strength orange juice (dollars/dozen 46 ounce cans) 271 XNTP the rate at which new tree plantings would have occurred without the planting restriction (trees/ week) 9 XPQS(I) per capita monthly consumption of product I suggested (gallons single strength equivalent/ week) 139-145 th XQD(I) quantity of the I product demanded at time J (gallons single strength equivalent /week) 290A-290G th XQS(I) suggested consumption of I product (gallons single strength equivalent/week) 146-152 XTBP internal transfer variable (trees/week) 4 YDD disappearance associated with profits of $1.00 per box (boxes /week) 27 YFL fraction of trees lost when tree abandonment restriction was operative 26 YLOSS yield loss (boxes) 57 YTBP young trees becoming productive (trees/week) 3 ZAMNR average marginal net revenue before considering whether or not the policy limit was effective 166 ZTBP trees becoming productive after initial period (trees /week) 2B

PAGE 142

APPENDIX B The Computer Program

PAGE 143

< CO < CO FHCM<*-iAvO

PAGE 144

128 oo o
PAGE 145

129 in -J =) • + => ^ u. -> + • iC •* -> rj • a. >n + 3 ^ u. 2 < lU — T. i£ •-4 t • U. 5i ~ -J • )-«>•-« »U. 3 iii X » • • ii »-« H— • TE U. •-« 1-4 ft _J 3 • UL ^ + 3 ^ U. -» + CM n rs • •• => !K! U. -S + • ^ U. (M + I • 04 (*\ >£ » ii: < » -4 • • i<: » •-< o • •H ^ as •— •-• — • < Q. 'X X *-« X »-< w o 2 -' u a K I 2U -• •-• ,^ •_! II _| 3E II Z ^ U (/) ^ II • II II • iCUL 3£ ^ t-< • _i • • a: t-« > >Ol (-4 < 3 U. M X 3 X < X 2 Z o a. o oc LU X »< of X u. X in — »-• _j in • X fO «>^ GO • o < V « »o « II II »:^ * u. • H_i QC of tX X u. u. u. XXX Of o u lU «/» UJ ISl < — o — Z tsd • Q • -5 -» a • -f »u. -> 3 ~i • U. O — Q f I ^ K i£ "9 -» 3 • t • u. >> Of a: fte II ^ o u 3 s«: -5 II II LL • • s<: 5«: + Q Q • • :^ H> u. CO oc -> 3 I u o • u. ^ ex. Iao UJ • I/) o -I Io. u. II II -I ^ :i^ • • Q. O Q U. UL O — in — s<: • rM • I >n > • • »-> i£ eg 3 • in — a • — o ^ ^ < • • •• a K t(/) o. to CO a. ---. to UJ — — . 00 ^ .-I -J • X 3h03 CL CL < II —I-J II II ^ ^ ^ • • • < Q. >o . -~ >^ + v: 00 ^ • • • Q. •4«/) to WO O hO — • _j -« ^ X :m! ^ + • O ^ U. • • ^ ^ U) hV O Ui in O — • -J II * hi^ II n • * :^ CO I• CO ^ U. o a. -J _j CD O hSi • • a. Q, CO CO O U w — s«i )< • « u. Oi _i X > u. u. II II CO CO t/i CO o o u. o a: a. aiuj uiujujujuj ujujuj t1--•--I»-»-»oo ooooo ^ -4 ooo ZZ<<<<<<0<02ZZZZ<_JX-JXQC
PAGE 146

130 coo«ai-<(Mm<«-tr\o>n h-~>ooo«Oi-4«Mro>t'ir»%OvOf».ooo»o o •^o>or>»^-N•^"^-^-^-r^^-^-^>•oo

PAGE 147

131 oococoaocoaoaoaoaoo>c^o«c^o<'0^c^oo«o^ — -'-^— — — -~i^ •^ >£!!/. a i£ -^ >£ • • ••tt*tQ£0 <<<<<<oo«ooaaaaaoxoo • ••••• II II II II II H II < >. intntn£ :ic :tie :^ ^ II ii or* • • • • • • "i^* a3(OoocacDao^Okiro<4'inor> •»o.aouaaaooooaQO<< oooooocLCLa.a.Q.CLa.aLOu o o o o o F^ ,-4 lo-o r-

PAGE 148

132 • o >* >. (M m o O f« • • o >» V. PJ fO O Ct -* ro • 00 **• V. o esi fo o O fO • • o >. V. f\J fO (> o ^ fO • 00 * >* o » CM fO C> O »H CO • flO ^ *% o CM f*> O O fO • • O *s, •^ Csl m o^ o ^ CO • 00 «4>* O (Nj m o O CO • • o>» «v CM • 00 «t V. o fM ro o o o • • o >» V «M fO o> o ^ fO • 00 ^ •«* o fVJ fO o O f*^ • • O >k •V cyj ro o> o m fO • o ^» *v fSJ fM en o O fO • • O "V >» CM rr> <^ o fO fO • o >1>» . CM «^ r»ooa«o^(Mm<^m%or»> OOOr>lf-4t-l>-4)»4>-lf-ti>4 CO cf' a r-t pii i*\ 1-4 f-4 CVJ <\i Oi (Ni )-< t>4 CM O O f• • o »-t iH 0» "s. >» 0< oo o — o «n • tu •s. — in m -? • t-4 • •> 00 • •-it/) lU 00 htX\ O 4 • O w • • — :^ "^ < • m < < f-i »< CO N. • o '* o — • "^ >» »CO fO Q Si£ tn o> — o in o uj • tn o o fO UJ O (f\ o • '* m >. lU in in csi • > o^ » • • o < •-I • 00 hO* «M • 1-4 N. < tn ~> ca _i « X o CO o» < • »II II * ^ in -~ <> in i-« tu o in in lu tn CO o • o •> • tn •H tJU *v tn in • o» • 00 m: <^ • • < •s. < O ft CM I• < tn -I * I •t CO 00 -f lU o -J a: o • • «:<: II •^tf• 00 •<.^,HCM(MrO o < < O < III II O «4-* 00 tn a> ai • tn "V • O ft ^ 0 >. CM ^t O • -* O^ ft • o» to <-• (7> UJ s» • in >o •< CM r-« O • .^ 0« ft • CJ« ^ r-l . • < CO V, < « • < CM N. w (> in -J • tn I >» tn CO ^ o < r^ • I• II II II * ^ * I• H(*» J" >io o in -• in UJ "^ UJ in CO in • t-«^ • ft CM ft ^0 O «0 UJ o UJ c*> • c<> • «^ • ft ""S ft tn 00 in UJ «o UJ in «t tn • <> • ft 0> ft 2i^ • ^ • V • < »^ < < U^ < ft >0 ft I00 »in o o l>4 • •-• < N» < w ,t w ^ o ^ I « X (n r» CO < CJ» < >• hII II II -* oo O •* • -. 0» fH tn o^ >« UJ • c> in >» •-4 • CM fO ft sf o >o <^ o lu <^ • m (^ .-I tn O UJ cri in <^ • <> ft • ^ «0 < r< (f\ ft 00 »CD -J hX >o 00 c^ <»-XrO s: — + 2 • Q CO C2r Q X Of— . X — »» • • ot fO z of s: '-. z — St: s: + • w ^ h. + id a — • c» ^ * 00 CM c^ fO r«o ^ -d00 vO o o o o t o • + — T -? — -» -^ -? -1 -n oo CM a 00 u. o CO 4OQ CO o o IJL U. in o '4' CO f-4 O en <0 CJH 1-4 r-« ^o •>« CM CM f-c tn en t o« • • • • • X in fO • of O oc ar X z w + 2: + X <<<<<<<<<<<<< tn tn «o >o r oo »-i a < u» I I II II X X • • .-4 CM Q£ OC z z X X • • z z I I I II H II XXX • • t in >o rQC ccoc zzz s: s: £ w X CM H • O X ^ O • Q X oc a + Z X X SE — • < — r-C tiJ tXI UJ lU HIHhO O O O cMm.*in aooo xxxx-iu
PAGE 149

133

PAGE 150

134 <0Q QLUU-ta— X VO to t/5 Q O Q o o o o a o o o • C3 m a. 13 CO a. — aa — w a,: liMf ^ ^ ^ !i^ ha. • o >. z O .-< ho; o a ^t o •* o o o «/> t/) O O u. u. U) to sf vn 00 CO a o u. u. v; ^ ^ h> • ••(/) «/)«/) fo a >o hto 4 o3 eo Of — a o < + u. u. — -r. -5 -1 -> -n -> n -J in -c f-i o o o O «n ^ 00 O O

PAGE 151

135 ^ •

PAGE 152

136 -H (vj m ,*• lA ^o^-ooo»o-•{Mm<^m«o^•oDC^Ol-ljrkir\i(\irNtr>jiNiN(si ^ «. (n »n in •-•mm • • • t-4 (Ni • • i-H 00 o 00 I I ^ ^ ^ -5 -5 -J • • • m <*• «n (/)«/) t/) t I I I I (M0MrMfM>O • (M(\|rsl<,*>k« »ii4»M»-it-ti>>t»-4H4 »tf> B.tf\ otft ^>^• •Un •if> •> OOOOUOO!i^00<>^00b^00^ •^0Oy!0O^ s^siii;s^:«Jii^* "v "s. Q v: ^ b^ »• • • • + in «o h«. -5 lot l-^ 1-4 • II II II •-• ^ ^ ^ ^H • • • It in >o h^ < < < tMrr>^inoh-'-»njf>»*in>or-3c«s3cv.ie QQQOOQ»-«»-<»- 3: 3 3 3 3 2 3 l-l-t-KHl-i^^siais*:^ www««ww.Hni(n«i-in«o 4> + + + + 4000000 "i-i-i'n-i-iaiaaiaaia • • • • • t <. *t t 3 >». 3 • O • K• Iin •o tii^ ^ i-< «^ t-« •V 3 O X a CO It II -I i£ ^ • O >-i ^ I CM CO • < CM tII II CM 00 • < CM III II i-« -J CM N. X -S. in CO o • < • »-« ^ m II II II « ^ « ro ><• «* I >* I oo
PAGE 153

137 »f\ vO f» ^ «d^ OJ (M OJ .4^^nlfvlf^lnlnln^r^^r^l/^lf>•o^oo^oJCM(MrM<\J{\J fSI (M rsl«M (-4 ^ i^ "V o> • fO • o o ^oc • o o •-• • a N. * -J o* Ift I • • CO >k fH < o* II t• * II II -•o o < z o •-4 3 CO CO — o ^ u. • •-• fM — CO o» O-^ U. ^ CM m •* CM fO 03 CO o o u. u. X X — 5^ ai • tvj m <-« CO OQ 00 o o O u. u. — • U. X X s<: X «-*^ — m f*> 00 o ro ro O fO (*> r«^ IL CO CO <*> *» fO • • — • CO 00 lf> 00 «— * — + + • rs o fo (M «o • • w • « fM II ^^ r-« f-4 ^ II II II • i£ i£ ^ <^ • • • 00 p^ (M O I/) «/> 00 IL CL 0. CL X OC OC QC -^ -9 T -> • • • • <-• tM ro >!• a. O. CL Q. o£ q£ oj oe I I I I ^ (M m -^ to t/) ql a. a. a. etccce.ee. • •-! CM fO 4" ^ Q. o. ol a. CO oe a: a: a: o u o o o U. tItH" X "V -V N» -5 -> -> • • • • tH <\J fO >t 0.0.0.0. ee et eC K T -? • • • • fH ca ro >* o. o. o. o. ce. cc ce cc o. o. o. o. OLCCCCCC <.<.<.<. O O Q Q + + • c-l (M Q. a o. ce.ce.cc + + -J "5 • • O. Q. II II • • o. a ce. QC CO «/> i^ v: UJ UJ UJ UJ 3e 3 CVJ (M II II •-I rsl o. & oe ce o o 00 •iCUi • UJ UJ 1-4 UJ 3 O. 3 ce. m < >»• • II II II ^1^ f^ •* • O. O. r-4 OC OC o. O O QC tt< • + + -J -J -5 • • • (M fO ^ O. O. Qu CCCCCC < < -4 I I • • in o CO 00 a a u. u. X X :^ o. a. OD HH— O "s. >. i<£ U. 1-1 t-« • •M «^ o — — -« CO in hhO rsi O Q u. .-• w •_ *fO + 4-» • -5 -? fO * • • w w irv vO II II o. a 5(j b^ *^ *-< • • II II <© r5^ i£ 00 OO • • O o in vO u. u. a o. X X •-< H^ UJ tU UJ UJ UJ o o o o o ^<.Li :z.'z zzz<<<<<<<<_j_i -J.^UOOO^-l-i-JO<<4_J~J

PAGE 154

138 fM Pkl ^-h-N-N-eOCDOOOOeOOOOOtOOOQOO^O^O^OO^O^O^O^O^OO^O^O* tMPJ
PAGE 155

139 tn >o fo CO (^ o 1-4

PAGE 156

140 CO «C00OOUJU. pi4^f-i>>«r^r^t-4>ii4i-«r^(Nlca(Ni(Ni(Nir\i(\t(\i(NJ(NJru(Nj(Nir\ir\irg(\ii\i(\i(Nj(si(NirMCJ ^•^"^"^~f^^~^*•^^*^flOoocoooflOooooo*o*ffo «o ^ r^ o ho arooQOoar in minrsifomoo^ <<or«tn co^-'->m(Mr»(/)(/)(/)a.a,Q.Q.oooooaooa • • • • • •>! •< • • tin • • •a.Q.a.Q.ococecocu.u.u.ooaiaiaiai n II II II II 11 II II II t-« t-« m •f-tr-^ayococoeccn ii n ii x x x ii ii ii ii ii ii f*-o<-««Mfn'tm>Oh-co — — www*-w|| II II n r-t (\t rt\ ^ H ii ii.-irsjfO«^in«o Qfiiaaeaaacocacocoaii ii ii ii ii ii iif-irMro<^Q.CLa.Q.tnor>-aooooa z:a.ooooooou.f-«(Mm<4-in>ot»a.a.aaciCa:a:aeaQ.aoararoc7ar 2:3u.u.u-u.u»u.u.t/5t-i«-«.-.«h-«t-»i-
PAGE 157

141 ta

PAGE 158

APPENDIX C Derivation of Marginal Net Revenue Relationships

PAGE 159

DERIVATION OF MARGINAL NET REVENUE RELATIONSHIPS The keystone of the allocation procedure was the ability of processors to evaluate the marginal net revenues of orange products and adjust prices. Given retail demand equations, retail-wholesale price margins, conversion factors and cost functions, it was possible to derive the marginal net revenue of each product as a function of FOB prices and other variables. Comparison of the marginal net revenue estimates generated with these functions provided a basis for relative price adjustments among product -markets. Demand relationships implicit in the model were expressed in matrix notation as follows: Q = ZA [DE + BP] where: Q denotes a vector of quantities demanded Z denotes a scalar equal to U.S. population A denotes a diagonal matrix of advertising influences D denotes a matrix of demand intercepts and coefficients E denotes a vector which includes a seasonal demand shifter B denotes a matrix of FOB price coefficients P denotes a vector of FOB prices Total revenue to the processor group was expressed as: R = P'Q Defining A = ZA and assuming I AB I ^ 0, total revenue becomes: R = Q'(a"-'-)'(b"''")'Q E'D'(b"''')'Q 143

PAGE 160

144 Marginal revenue was: II = 2(a"S'(b"S'Q b'^DE Assuming linear total cost functions (see Table E-5), total variable cost was expressed as follows: C = KQ where: C denotes a vector of total variable costs, and K denotes a vector of cost coefficients. Marginal cost was equal to the derivative of total cost with respect to quantity: Net marginal revenue was equal to marginal revenue less marginal cost: M = 2(a" ) ' (b" ) 'Q b" DE K' where: M denotes a vector of marginal net revenues. Solving for net marginal revenue in terms of price, the relationship becomes: M = 2(a"-'')'(b"-'-)'ADE + 2(a"''")'(b"-'-)'ABP b"''"DE K' -1 -1 -1 If A and B are diagonal, (A ) ' (B ) ' A = B and the expression reduces to: M = b' DE K' + 2P The derived relationships are presented in Table C-1. Solution in terms of price yields: P = .5 (K' b' DE + M) If the demand equations include cross price-quantity relationships among orange products, the B matrix will be nondiagonal. In the initial calculation of marginal net revenue relationships, cross product terms were present in some equations. However, once marginal net revenue relationships had been derived, weaknesses in the empirical demand equations became apparent and the decision was made to remove cross product terms and adjust intercepts to reflect mean values.

PAGE 161

145 See Table C-2 for the derived relationships.

PAGE 162

146 Table C-1. Derived relationships between marginal net revenue and FOB price. a Relationship MNRl

PAGE 163

APPENDIX D DYNAMO Equations for the Alternative Advertising Policy

PAGE 164

DYNAMO EQUATIONS FOR THE ALTERNATIVE ADVERTISING POLICY The model with the alternative advertising option included may be reconstructed by replacing equations 59, 60, 62, 100 and 105 from Appendix B with the equations listed below. When AP is set equal to zero, the alternative advertising proposal is operative. When AP is nonzero, the structure of the advertising sector is the same as presented in Chapter IV except that advertising costs are variable and accounted for in grower costs rather than on-tree prices (equations 59, 60, and 62) and administrative costs are compounded at five percent per year (equation lOOC) . A GC.K = (.85/WI.K) + VC.K 59 L VC.K = ATR.JK/TFU.J 60 C OTPT* = .13/1.10/2.06/3.04/4.00/4.96 62 XATR.JK if AP = R ATR.KL = < or YATR.JK if AP ^ AP = < if the alternative advertising proposal is operative or 1 if the alternative advertising proposal is inoperative YATR.KL = (FUl.JK + FU2.JK + FU3.JK + FU4.JK + FU5.JK + FU6.JK + FU7 . JK) (AT . K) (AC)(CE.K) XATR.KL = [(TR.K + ARA.K)/52] (AC)(CE.K) r TRl.K if ACS.K ^ 230E6 TR.K = ^ or TR2.K if ACS.K < 230E6 100 lOOA lOOB lOOC lOOD 148

PAGE 165

149 A TRl.K = (2.6E6)(CE.K) + (.05)(ACS.K) + (.00003) (SACS.K) + 6.9E6 lOOE rTR3.K if ACS.K 77E6 A TR2.K =< or lOOF 1tr4.K if ACS.K < 77E6 A TR3.K = (2.6E6)(CE.K) + (.11)(ACS.K) (.00007) (SACS.K) lOOG A TR4.K = (2.6E6)(CE.K) + (.06)(ACS.K) (.0001) (SACS.K) lOOH r YARA.K if A.K = A ARA.K = < or 1001 1 XARA.K if A.K ^ L A.K = YPP.JK lOOJ L YARA.K = ARA.J lOOK fo if ATRA.K 3.8E6 A XARA.K = .^ or lOOL 1 RA.K if ATRA.K < 3.8E6 A RA.K = (.02)(CS.K) lOQM A ACS.K = (CSl.K + CS2.K + CS3.K + CS4.K + CS5.K)/5 lOON A SACS.K = t (CSl.K) (CSl.K) + (CS2.K) (CS2.K) + (CS3.K)(CS3.K) + (CS4.K)(CS4.K) + (CS5.K)(CS5.K)]/5E6 1000 fxCSLK if A.K = A CSl.K = < or lOOP [ CS.K if A.K ^ L XCSl.K = CSl.J lOOQ rxCS2.K if A.K = A CS2.K = < or lOOR 1 XCSl.K if A.K ^ L XCS2.K = CS2.J lOOS {XCS3.K if A.K = or lOOT XCS2.K if A.K ^ L XCS3.K = CS3.J lOOU rxCS4.K if A.K = lOOV A CS4.K = < or XCS3.K if A.K f'

PAGE 166

150 L XCS4.K = CS4.J fxCSS.K if A.K = A CS5.K = < or [XCS4.K if A.K ?* L XCS5.K = CS5.J L CATR.K = CATR.J + (DTXATR.JK ATRD.J) A XATRD.K = PULSE (CATR.K, 52, 52) A ATRD.K = XAIRD.K/DT A CE.K = EXP(LCE.K) A LCE.K = (YP.K)LOGN(1.05) L YP.K = YP.J + YPP.JK R YPP.KL = PULSE (1, 52, 52) R YATS.KL = (AIRA.K)(FSPW.K) R XATS.KL =MAX(ZATS.K, 0) A ZATS.K = [(TE.K)(SA.K)/52] (AC)(CE.K) A SA.K = TABHL(SAT, WP.K, 1, 52, 1) C SAT* = 1.1112/ . . . /I. 1112/1. 3332/ . . . / 1.3332/1.1112/ . . . /I. 1112/. 4444/ . . . /.4444 (where I ... I represents 11 elements with the value indicated) {TEl.K if CS.K 230E6 or TE2.K if CS.K < 230E6 A TEl.K = (2.6E6)(CE.K) + (.05) (CS.K) + [(.00003) (CS.K) (CS.K) /1E6] rTE3.K if CS.K 77E6 A TE2.K = I or 1 TE4.K if CS.K < 77E6 A TE3.K = (2.6E6)(CE.K) + (.11)(CS.K) [(.00007) (CS.K) (CS.K) /1E6] A TE4.K = (2.6E6)(CE.K) + (.06) (CS.K) [(.0001) (CS.K) (CS.K) /1E6] lOOW lOOX lOOY lOOZ AlOOZ BIOOZ lOlA lOlB lOlC lOlD 105A 105B 105C 105D 105E 105F 105G 105H 1051 105 J

PAGE 167

151 L CATS.K = CATS. J + (DT)(AIS.JK ATSD.J) A XATSD.K = PULSE (CATS.K, 52, 52) A ATSD.K = XATSD.K/DT 107A 107B 107C Initial Conditions

PAGE 168

APPENDIX E Miscellaneous Data

PAGE 169

U 00 •rl o to

PAGE 170

154 Table E-2. Mean generic advertising expenditure levels during base data periods associated with estimated demand relationships. Product Market Retail Institutional (thousand dollars per year) FCOJ 9,424 5,590 COJ 9,424 5,590 CSSOJ 9,424 5,590 Fresh oranges 5,546 a Source: Calculated from estimates of generic advertising expenditures. a Not applicable.

PAGE 171

155 Table B-3. Proportional retail sales of processed orange products for various generic advertising expenditure levels. Advertising Proportional retail sales ^ FCOJ COJ CSSOJ (do liars /week) 45,127 68,324 97,140 115,988 181,231 188,843 225,633 264,597 291,601 Source: Based upon relationships derived from information obtained from [12], Sales are proportional to what they were when average advertising .965

PAGE 172

156 Table E-4. Proportional^ retail sales of fresh Florida oranges for various generic advertising expenditure levels." Advertising Proportional retail sales (dollars/week) 23,037 .712 24,424 .733 26,237 .754 31,996 .782 52,794 .870 101,641 .991 106,654 1.000 154,222 1.082 201,576 1.136 Source: Based upon relationships derived from information obtained from [12]. Sales are proportional to what they were when average advertising expenditures were $106,654 per week. b The relationship assumes the advertising expenditure was optimally allocated among advertising media.

PAGE 173

157 Table E-5. Total cost relationships for selected Florida orange products. Product Relationships FCOJ COJ CSSOJ FO C^ = 119.210220 + .242545 q^ C^ = 23.649570 + .17704 Q2 C„ = 25.302520 + .37488 Q 3 ^3 C^ = 53.076980 + .19107 Q^ Source: [25, p. 103] a th C = total cost of the I product (million dollars) Qj = millions of gallons single strength equivalent of the I product th Table E-6. Percentage of processed Florida orange products going to retail and institutional markets, average 1963-64 through 1965-66 seasons. Product Market Retail

PAGE 174

158. Table E-7. Movement of processed Florida orange products, 1970-71 season. Product Quantity (million gallons single strength equivalent) FCOJ 402.9 COJ 110.1 CSSOJ 38.4 Source: Based on movement figures obtained from [3, 1970-71 season, pp. 30, 46, 47]. Table E-8. Institutional sales of Florida orange products by type of outlet, 1970-71 season. Outlet Product Commercial Other Total restaurants (million gallons single strength equivalent) FCOJ 29.72 COJ 31.59 CSSOJ 10.53 Source: Commercial restaurant sales were obtained from [1]. Total institutional sales of FCOJ were obtained from [3, 1970-71 season, p. 30]. Total institutional sales of COJ and CSSOJ were estimated by multiplying movement from Table E-7 by the percentage of product going to institutional markets from Table E-6. 12.18

PAGE 175

159 Table E-9. Sales of Florida orange products by type institution as a percent of total institutional sales. Product Type institution Customer oriented Noncustomer oriented FCOJ COJ CSSOJ (percent) 71 29 58 42 58 42 Source: Table E-8.

PAGE 176

APPENDIX F A Note on the Calculation of Present Values and the Variance of Present Values

PAGE 177

A NOTE ON THE CALCULATION OF PRESENT VALUES AND THE VARIANCE OF PRESENT VALUES A FORTRAN program was used to perform these calculations. This program read edited output from the DYNAMO model, formed arrays and made calculations for each of the three variables considered in the policy analysis. Average values for the five weather replications were computed with the equation S = B A where: S a 1 X 25 vector of means. B a 1 X 5 vector with each element equal to .20. A a 5 X 25 matrix containing values for one of the three variables used in the policy analysis. The FORTRAN program formed three separate A matrices, one each for grower profit, average FOB price and crop size. Each matrix contained 125 elements (A..'s), where i = 1, . • . , 5 represented the five weather replications and j = 1, . . . ,25 represented the twentyfive years of the simulation. Present values of S and A were computed with equations E = S R D = A R where: E a scalar representing the present value of S. 161

PAGE 178

162 R a 25 X 1 column vector of discount values (7%). The t element of the vector r> = 1 t aTTToTF D a 5 X 1 column vector of present values for each weather replication. The variances of the present values were computed as follows: 1 , , A'ZZ'A , w = ^TTT [A'A -j;— ] V = R' W R n = 5, representing the number of weather replications. Z a 5 X 1 sum vector. W a 25 X 25 variance covariance matrix. V a scalar representing the variance of E.

PAGE 179

BIBLIOGRAPHY [ 1] Audits and Surveys, Inc., National Sample Census of Product Usage in Commercial Restaurants , New York, 1971. [2] Chern, Wen-Shyong, "Determination of the Optimum Number, Size and Location of Orange Packing and Processing Plants in Florida,'' Master's thesis. University of Florida, 1969. [ 3] Florida Citrus Mutual, Annual Statistical Report , Lakeland, 1962-63 through 1971-72 annual reports. [ 4] Florida Crop and Livestock Reporting Service, Florida Agricultural Statistics; Citrus Summary , Orlando, 1965 through 1968 annual reports. [5] , Florida Agricultural Statistics: Commercial Citrus Inventory , Orlando, December 1970. [ 6] Florida Department of Citrus, Statement of Receipts and Expenditures , Lakeland, 1962-63 through 1970-71 annual reports. [7] Forrester, Jay, Industrial Dynamics , Cambridge, Massachusetts Institute of Technology Press, 1965. [ 8] Hall, L. W., "An Analysis of the U.S. Regional Demands and Marketing Costs for Selected Florida Processed Citrus Products," Master's thesis. University of Florida, 1971. [ 9] Jarmain, W. E. C, "Dynamics of the Florida Frozen Orange Concentrate Industry," Master's thesis, Massachusetts Institute of Technology, September 1962. [10] Langham, Max R., "On-Tree and In-Store Citrus Price Relationships," Proceedings of the Second Annual Citrus Business Conference , Florida Citrus Commission, Lakeland, November 1965. [11 ] , "Toward Improving Performance of a System Through Participatory Decisions," unpublished paper. University of Florida, 1969. [12] McClelland, E. L., Leo Polopolus and Lester H. Myers, Optimal Allocation of the Florida Citrus Industry's Generic Advertising Budget , Agricultural Economics Report 20, Florida Agricultural Experiment Stations, University of Florida, April 1971. 163

PAGE 180

164 [13] Myers, Lester H., Proposal for Funding the State of Florida Department of Citrus , Florida Department of Citrus, Gainesville, November 1969. [14] , The Consumer Demand for Orange Beverages , Florida Citrus Commission Report No. FCC-ERD-69-1, Lakeland, August 1969. [15] Naylor, Thomas H. , Computer Simulation Experiments with Models of Economic Systems , New York, John Wiley and Sons, Inc., 1971. [16] Parvin, E. W., Jr., "Effects of Weather on Orange Supplies," Ph.D. dissertation. University of Florida, 1970. [17] Polopolus, Leo, and W. E. Black, Synthetics and Substitutes and the Florida Citrus Industry , Florida Citrus Commission Report No. FCC-ERD-66-4, Lakeland, April 1966. [18] Powe, C. E., "A Model for Evaluating Alternative Policy Decisions for the Florida Orange Subsector of the Food Industry," The American Economist , 16:66-75, Fall 1972. [19] Priscott, R. H., "Demand for Citrus Products in the European Market," Master's thesis. University of Florida, 1969. [20] Pugh, Alexander L., Ill, DYNAMO II User's Manual , Cambridge, Massachusetts Institute of Technology Press, 1970. [21] Raulerson, Richard C, "A Study of Supply-Oriented Marketing Policies for Frozen Concentrated Orange Juice: An Application of Dynamo Simulation," Master's thesis, University of Florida, June 1967. [22] Spurlock, A. H., Costs of Processing, Warehousing and Selling Florida Citrus Products , Agricultural Economics Mimeo Report, Florida Agricultural Experiment Stations, University of Florida, 1962-63 through 1971-72 annual reports. [23] Tax Reform Act of 1969 . P. L. 91-172, Sec. 216, 83 U.S Statute, December 1969, p. 487. [24] Theil, H., Applied Economic Forecasting , Amsterdam, North Holland Publishing Co., 1966. [25] Weisenborn, D. E., "Market Allocation of Florida Orange Production for Maximization of Net Revenue," Ph.D. dissertation. University of Florida, 1968. [26] Weisenborn, D. E., W. W. McPherson and Leo Polopolus, Demand for Florida Orange Products in Foodstore, Institutional, and Export Market Channels , Florida Agricultural Experiment Stations Bull. 737, University of Florida, May 1970.

PAGE 181

165 [27] , Market Allocation of Florida Orange Production for Maximum Net Returns , Florida Agricultural Experiment Stations Bull. 736, University of Florida, March 1970.

PAGE 182

BIOGRAPHICAL SKETCH Charles Everitt Powe was born December 29, 1942, in Waynesboro, Mississippi. He attended the public schools of Wayne County, Mississippi, and graduated from Waynesboro High School in May, 1960. Shortly thereafter, he entered Mississippi State University, and received the degree Bachelor of Science, with honors, in June, 1964. From September, 1964, until June, 1966, he attended the graduate school of Mississippi State University, where he earned the degree Master of Science. In September, 1966, he enrolled in the graduate school of the University of Florida. Since that time, he has pursued a program of work toward the degree Doctor of Philosophy. He is a member of the Southern Agricultural Economics Association and the American Agricultural Economics Association. 166

PAGE 183

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. Max R. Langham, Chaipffian 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. Leo Polopolus 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. £.R^ £JAjL^ Bobby R. Eddleman 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. David L. Assistant Professor of Econc

PAGE 184

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, 1973