• TABLE OF CONTENTS
HIDE
 Front Cover
 Half Title
 Title Page
 Table of Contents
 List of tables
 List of Figures
 Acknowledgement
 Abstract
 Introduction
 Previous work
 Major forces in the Florida orange...
 The model
 Validation
 Policy analysis
 Limitations
 Summary
 Appendices
 Bibliography
 Back Cover
 Historic note






Group Title: Bulletin - University of Florida. Agricultural Experiment Station ; 815 (technical)
Title: Toward a policy testing model for the Florida orange industry
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 Material Information
Title: Toward a policy testing model for the Florida orange industry
Series Title: Bulletin - University of Florida. Agricultural Experiment Station ; 815 (technical)
Physical Description: Book
Creator: Powe, Charles E.
Langham, Max R.
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
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Bibliographic ID: UF00027482
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Front Cover
        Page i
    Half Title
        Page i-a
        Page ii
    Title Page
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
    List of tables
        Page vii
        Page viii
    List of Figures
        Page ix
        Page x
    Acknowledgement
        Page xi
    Abstract
        Page xii
    Introduction
        Page 1
    Previous work
        Page 2
        Page 3
    Major forces in the Florida orange industry
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
    The model
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 37a
        Page 38
    Validation
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
    Policy analysis
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
    Limitations
        Page 70
    Summary
        Page 71
        Page 72
        Page 73
        Page 74
    Appendices
        Page 75
        Page 76
        Appendix A. Alphabetized list of variable names
            Page 77
            Page 78
            Page 79
            Page 80
            Page 81
            Page 82
            Page 83
        Appendix B. List of model equations
            Page 84
            Page 85
            Page 86
            Page 87
            Page 88
            Page 89
            Page 90
            Page 91
            Page 92
            Page 93
            Page 94
            Page 95
            Page 96
        Appendix C. Supplementary equations
            Page 97
            Page 98
            Page 99
            Page 100
            Page 101
            Page 102
        Appendix D. Derivation of marginal net revenue relationships
            Page 103
            Page 104
            Page 105
        Appendix E. Calculation of present values and the variance of present values
            Page 106
            Page 107
        Appendix F. Miscellaneous data
            Page 108
            Page 109
            Page 110
            Page 111
            Page 112
            Page 113
            Page 114
            Page 115
            Page 116
    Bibliography
        Page 117
        Page 118
        Page 119
    Back Cover
        Page 120
    Historic note
        Page 121
Full Text




Bulletin 815 (technical)


Toward a Policy Testing Model for the
Florida Orange Industry

Charles E. Powe and Max R. Langham










: SEP 2G1980

L.Fi. Uniiv. of F1ri i









Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
LF. A. Wood, Dean for Research


s


V- --..q


-q%


10"ay 1980


i


r











Toward a Policy Testing Model for the
Florida Orange Industry


















































This public document was promulgated at an annual cost of $6,413
or a cost of $3.67 per copy to provide information on the dynamics
of the Florida citrus industry and to evaluate the effects of varying
institutional policies on growers, handlers, and consumers.













Toward a Policy Testing Model for the

Florida Orange Industry



Charles E. Powe and Max R. Langham




















AUTHORS
Charles E. Powe is Assistant Professor of Agricultural Economics, Missis-
sippi State University. He was formerly a research associate, University of
Florida. This report is based on his Ph.D. dissertation (22).
Max R. Langham is Professor of Food and Resource Economics, Univer-
sity of Florida.

EDITOR: Mary L..Cilley, Associate Professor, Editorial Department, Institute
of Food and Agricultural Sciences, University of Florida.















CONTENTS

Page
LIST OF TABLES ................................................ ......................... vii
LIST OF APPENDIX TABLES ......................................... ............. viii
LIST OF FIGURES .......................................................................... ix
ACKNOWLEDGMENTS ................................................................ xi
ABSTRACT ........................................................... ............................. xii
INTRODUCTION ................................................................................... 1
PREVIOUS WORK ...................................................... 2
MAJOR FORCES IN THE FLORIDA ORANGE INDUSTRY .......... 4
THE MODEL ............................................ ....................... 9
Tree Numbers Section ................................................................ 11
Weather Effects Section .................................................. 14
O option I ..................................... ........................................... 15
O option II ......................................... ....................... ...... ....... 15
Crop Size Section ................................. ........................................ 15
Grower Profit Section .................................. ... ............ 19
Processor Disappearance Section ........................ ............... 19
Advertising Section .............................. ........................... ............. 21
FOB Price Section .................................... .................................... 24
Retail and Institutional Inventory and Sales Section ................... 30
Retail and Institutional Price Section ................. .............. 32
D em and Section ..................................................... .... .. .......... 33
Initial Conditions .................................................... 36
VALIDATION ................................................... ...................... 39
Long-run Stability .............................................................................. 39
Retrospective Comparison ................................................ ...... 42
POLICY ANALYSIS ................................................................. 47
Policies ........................................ ............................ 47
Analysis .......................................................... ....................... 49
Restricted Tree Planting .......................................... .......... 60
Tree Abandonment ..................................... ....... ........... 61
Increasing Carryover ................................... .............. 61
Price Adjustment Restriction .................................. ..... 62
Price Floor ................................... ... ................. 63
Restricted Tree Planting and Price Floor ................................ 66
Alternative Advertising ................................... ............. 66
LIMITATIONS ................................................ ........... ......... 70
SU M M A RY ..................................................................... ..................... 71
APPENDICES
A ALPHABETIZED LIST OF VARIABLE NAMES .............. 77








B LIST OF MODEL EQUATIONS ......................................... 84
O ption I ........................................................................... 86
Option II ................................................. ................... 86
C SUPPLEMENTARY EQUATIONS ........................................ 97
Advertising Policy Option ................................................ 97
Initial Conditions .............................................................. 101
Average Weather Option .................................................. 102
D DERIVATION OF MARGINAL NET REVENUE
RELATIONSHIPS .................................................................... 103
E CALCULATION OF PRESENT VALUES AND THE
VARIANCE OF PRESENT VALUES .................................. 106
F MISCELLANEOUS DATA ..................................................... 108
BIBLIOG RAPH Y ................................................................................... 117









































vi














LIST OF TABLES

Table Page
1 Acreage of bearing and nonbearing orange groves by Florida
counties as of December 1969 ................................................... 5
2 Conversion factors for major orange products .............................. 21
3 Advertising tax rates for Florida oranges by type of use, 1962-70 .... 23
4 Relationships between quantity of orange products demanded by
retail and institutional consumers and FOB prices .......................... 27
5 Mean values associated with estimated demand relationships ......... 27
6 Base data periods associated with estimated demand relationships .... 29
7 "Normal" retail inventories of major orange products ...................... 32
8 Retail and institutional demand relationships for Florida
orange products ........................................................... .................. 36
9 Observed and simulated fruit usage, by product-market ............... 46
10 Discounted values of two hypothetical streams of income
received over a five-year period .................................. .......... ... 51
11 Weather conditions used in simulation runs ................. ............... .. 53
12 Alphanumeric names used to identify simulation runs ................... 54
13 Average simulated grower profits for the five sets of weather
conditions, by year and policy ..................................................... 55
14 Average simulated crop size for the five sets of weather
conditions, by year and policy ..................................................... 56
15 Average simulated FOB price for the five sets of weather
conditions, by year and policy ................................... .................. 57
16 The level and standard deviation of the present value of grower
profits, average FOB price and crop size for 12 sets of base and
policy simulations ......................................................................... 64
17 Relative value of the level and standard deviation of the present
value of grower profits, average FOB price and crop size for
policies comparable with the base (B) run ..................................... 65
18 Size and discounted costs of the carryovers associated with
alternative policies ................................................. ......... ........ 66
19 Estimated costs and returns to orange processors, 1961-70 .............. 67
20 Nonadvertising policies classified for major groups of participants
by preference category relative to the base (B) ................................ 69
















LIST OF APPENDIX TABLES

Table Page
1 Derived relationships between marginal net revenue
and FOB price ...................................................................................... 104
2 Derived relationships between FOB price and
m arginal net revenue ............................................................................ 105
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, 1955-70 ........................................ 109
4 Florida orange products: crop utilization, advertising tax
rates and estimates of receipts, administrative costs, and
advertising expenditures for generic advertising, 1962-70 .............. 110
5 Mean generic advertising expenditure levels during base data
periods associated with estimated demand relationships .................. 111
6 Proportional retail sales of processed orange products for
various generic advertising expenditure levels .................................. 111
7 Proportional retail sales of fresh Florida oranges for
various generic advertising expenditure levels .................................. 112
8 Total cost relationships for selected Florida orange products ......... 112
9 Percentage of processed Florida orange products allocated to
retail and institutional markets, average 1963-64 through
1965-66 seasons .................................................................................. 112
10 Movement of processed Florida orange products,
1970-71 season .................................................................................... 113
11 Institutional sales of Florida orange products by type
of outlet, 1970-71 season .................................................................. 113
12 Sale of Florida orange products by type institution as a
percent of total institutional sales .................................................... 113
13 Yield loss, tree loss, and hatrack loss factors, 1962-72 .................. 114
14 Estimated fruit usage rate by product type, 1961-62 season ............ 115
15 Net marginal revenue used to initialize model .................................. 116
16 FOB price used to initialize model .................................................... 116















LIST OF FIGURES

Figure Page
1 Simplified flow diagram of the orange industry ................................ 6
2 Block diagram of major components of the Florida orange industry 8
3 Flow diagram of section 1 (tree numbers of the model) ................ 12
4 Comparison of output from exponential delay and empirical
yield estim ates ....................................................... ....................... 13
5 Flow diagram of section 2 (weather effects) of the model .............. 16
6 Flow diagram of section 3 (crop size) of the model ..................... 17
7 Flow diagram of section 4 (grower profit) of the model ............. 18
8 Flow diagram of section 5 (processor disappearance) of the model .. 20
9 Flow diagram of section 6 (advertising) of the model ................. 22
10 Seasonal pattern of generic advertising and promotional
expenditures for Florida oranges .................................... ........... 23
11 Flow diagram of section 7 (FOB price) of the model ................... 26
12 Relative price adjustment for three product case ........................... 28
13 Flow diagram of section 8 (retail and institutional inventory
and sales) of the model ............................................................... 31
14 Flow diagram of section 9 (retail and institutional price)
of the m odel .................................................. ............................. 34
15 Flow diagram of section 10 (demand) of the model ........................ 35
16 Flow diagram of the DYNAMO model of the Florida orange
industry ........................................................... ............................. 37
17 Simulated time path of selected variables ........................................ 40
18 Simulated and actual numbers of mature productive orange
trees, 1961-62 through 1972-73 seasons .......................................... 43
19 Simulated and actual crop size, 1961-71 ........................................ 44
20 Simulated and actual on-tree price, 1961-62 through 1970-71
seasons ............................................................. ............................. 45
21 Average simulated grower profits for the five sets of weather
conditions for planting restriction policies 1, 2, 3, and base,
by year ............................................................ .............................. 58
22 Average simulated crop size for the five sets of weather
conditions for planting restriction policies 1, 2, 3, and
base, by year ...................................................... .......................... 59
23 Average simulated FOB price for the five sets of weather
conditions for planting restriction policies 1, 2, 3, and
base, by year ........................................................ ........................ 60








24 Average simulated grower profits for the five sets of weather
conditions for tree abandonment policies 1, 2, and base, by
year ............................................................... ............................... 61
25 Average simulated crop size for the five sets of weather
conditions for tree abandonment policies 1, 2, and base,
by year .............................................................. ............................ 62
26 Average simulated FOB price for the five sets of weather
conditions for tree abandonment policies 1, 2, and base,
by year ............................................................. ............................. 63
27 Collections and expenditures of advertising tax revenues for
the alternative advertising policy (ADV) and base (B) runs,
weather set 1 ....................................................... ......................... 68
28 Crop size, weather set 1 ............................................................. 68















ACKNOWLEDGMENTS

The authors would like to express appreciation to Drs. B. R. Eddleman,
R. D. Emerson, Lester H. Myers, James A. Niles, Leo Polopolus, T. H.
Spreen, D. S. Tilley, and three anonymous reviewers for reading drafts of
the manuscript and offering many helpful suggestions. Special appreciation is
extended to Dr. K. R. Tefertiller for his support and encouragement.
The authors would like to thank the Florida Agricultural Experiment Sta-
tions and the Economic Research Service, United States Department of Agri-
culture, for support. The support of Farmer Cooperative Service, USDA,
during manuscript revision is appreciated.
Acknowledgment is made for the support and service of the Northeast
Regional Data Processing Center of the State University System of Florida
and the Washington Computer Center. The authors appreciate the computer
programming assistance of Mr. Stewart A. Monplaisir and Mr. Dennis Egan.
Much of the early typing was done by Mrs. LeAnne van Elburg, who also
drew Figure 16, and by Mrs. Phyllis Childress. This assistance is much ap-
preciated. Appreciation is also expressed to Mrs. Louise B. Griffith and Mrs.
Beverly L. Rotan, ESCS; to Mrs. Elizabeth G. Roebuck and Mrs. Bonnie J.
Morgan; and to Mrs. Maureen Adams. Finally the authors wish to thank
Miss Christine Regan for drawing many of the diagrams and Mrs. Patricia
F. Smart for typing the final draft.














ABSTRACT

A quantitative economic model of the Florida orange industry was
developed and used to simulate the effects on industry 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.
Policy simulation results were examined from the viewpoints of pro-
ducers, handlers, and consumers. Policies that reduced long-run supplies
of orange products caused substantially higher aggregate grower profits,
lower storage costs, and higher retail prices. They also reduced risks for
orange producers, but not for handlers and consumers.
The characteristic which dominated policy analysis was the presence
of conflicts of interest among growers, handlers, and consumers. In al-
most every instance, in order for one group of participants to gain, an-
other was placed in a less desirable position.
KEY WORDS: Computer simulation, recursive model, Florida orange
industry, industrial dynamics, industry stabilization, policy analysis.













INTRODUCTION


The Florida orange industry' has been characterized by large varia-
tion in orange production and crop value. Production during the past 19
years (1958-76) has ranged from a high of 181.2 million boxes during
the 1975-76 crop season to a low of 54.9 million boxes during the
1963-64 season. The on-tree value of the orange crop was $379.7
million ($2.10 per box) in 1975-76 as compared to a value of $241.3
million ($4.40 per box) 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 has
decreased; however, since existing orange groves produce over a long
period of time, short-run supplies have not readily responded to low
prices.
Participants within the orange industry have been concerned with the
large variations in orange prices and supplies. Individual producers have
sometimes benefited from short supplies and high prices; however, high
prices encourage 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 (20,
p.1).
The instability of the orange industry may be detrimental to the
long-run interests of all participants. Supply stabilization would intro-
duce greater certainty into the decision environment of producers and
handlers. Consumer interests may also be best served by stable prices.
The effects of alternative industry policies on the system as a whole
and on the grower, handler, and consumer components merit investiga-
tion. The dynamic and interdependent economic mechanism operating
within the Florida orange industry may dampen or amplify the effective-
ness of policy decisions within an environment generated by a computer.

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






Experiments conducted on the model provide guidance to decision mak-
ers without the cost and risk of policy changes in the industry.
The specific objectives of the study were to:
1. Identify the structure underlying the orange industry's dynamic
behavior.
2. Construct a quantitative economic model of the orange industry.
3. Develop measures of performance which reflect the interest of
growers, processors, and consumers.
4. Evaluate the effects on the three major industry groups (grow-
er, handler, consumer) of policies designed to improve the per-
formance of the orange industry. These policies which are
discussed later (pp. 47-49) include:
a. Supply control policies:
i. Curtailment of new tree planting whenever grower profits
were above specified levels.
ii. Elimination of fully productive trees whenever grower profits
were below specified levels.
b. Changes in the end-of-year carryover of orange products.
c. Alternative pricing strategies.
d. Changes in the Florida citrus industry's generic advertising
budget.



PREVIOUS WORK

In 1962, under a grant from the Minute Maid Corporation, Jarmain
(10) developed a first generation industrial dynamics model of the Flor-
ida orange industry. Jarmain's study indicated that a larger processor
carryover of frozen concentrated orange juice (FCOJ) from one season
to the next would reduce price variability and improve the grower's posi-
tion. Raulerson (25) 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 periods of low prices. Both Jarmain and
Raulerson used average grower profits as a basis for evaluating the per-
formance of the industry. These studies by Jarmain and Raulerson pro-
vided a basis for the study reported here.
Models of the type used in the study reported here require large
amounts of information, and it is helpful when this information is sum-
marized 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 (20) 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 par-
tially natural citrus flavored drinks.
Weisenborn (34) completed a study in 1968 in which he estimated
price-quantity relationships for major Florida orange products at the
FOB level. These estimates were then used to construct net marginal
revenue functions which could be used to optimally allocate oranges
among product markets for various size crops.
Priscott (23) carried Weisenbom's study of the export market a step
further in a 1969 study of the European demand for processed citrus
products. Results of the study indicated that the demand for citrus
products in West Europe was elastic and showed development potential.
Since the analysis in this study, Tilley and Lee (30) and Tilley (29)
have estimated that the elasticity of demand of FCOJ with respect to
its price is more elastic in Canada than in the U. S. This result suggests
that net revenues to the industry could potentially be increased by ex-
ploiting export markets further.
McClelland, Polopolus, and Myers (14) used time series data to esti-
mate the response of consumer sales to changes in generic advertising
expenditures. They then used these estimates to estimate an optimal
allocation of advertising funds. Considerable work (9, 13, 31, 32, 33)
has been done on the effects of advertising in the citrus industry since
the analysis in the present study. Some work by Ward (31, 32) sug-
gested that the full impact of citrus advertising is realized within four
to five quarters. Later work by Ward and Myers (33), using a model
which permits coefficients to vary over time, suggests that it takes long-
er than five quarters to realize the full impact of advertising. This
work also suggests that advertising is becoming more effective over
time.
In 1971, Hall (8) [Also see Myers and Hall (16)] 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.
Myers and Liverpool (17) in 1972 empirically estimated cross elas-
ticities of demand for major orange juice products, orange drinks, and
synthetic orange flavored beverages. The demand equations for frozen
concentrated orange juice, chilled orange juice, and canned single
strength orange juice for the retail market used in this report were de-
veloped from estimates by Myers. Recent work by Tilley (29) suggests
that the demand for FCOJ is more elastic and demand for chilled
orange juice (COJ) less elastic than was assumed in this study. Tilley's
estimates would lead to somewhat more of the crop being allocated to
FCOJ and less to COJ.
Parvin (19) used yield estimates and standard regression techniques
to estimate weather effects on early-midseason and Valencia orange
production for 18 Florida counties. Parvin's estimates provided a basis
for the construction of the weather index for total Florida orange pro-
duction presented in this report.








A major part of the research on the model was conducted during the
period 1970-73 using research results from the late Sixties and early
Seventies. However, the major supply and demand forces in the industry
which the model attempts to capture remain operational today. This is
not to say that some structural shifts have not occurred in the industry.



MAJOR FORCES IN THE FLORIDA
ORANGE INDUSTRY

The Florida orange industry is composed of five major groups of par-
ticipants: producers, processors and packers, wholesalers, retailers, and
consumers.2 Producers are those individuals and business organizations
who are primarily concerned with the production and sale of whole or-
anges. 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 to consumer mar-
kets. Consumers are final purchasers of orange products and comprise
the largest group of industry participants. For the purposes of this study,
final purchasers of orange products have been classified into two general
types: retail and institutional. Retail purchasers are those who buy or-
ange products through retail grocery outlets. Institutional purchasers are
businesses such as restaurants and drugstore fountains and tax-supported
institutions such as military establishments, hospitals, and school lunch
programs.
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
(19). Weather is the most erratic factor affecting orange production.
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 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 (hatrack-
ing) 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.

2. Some of the introductory material in this section appears in a previous
article (21).









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 south. As of December 1969, two-thirds of the non-
bearing acreage was located in eight south Florida counties. In each of
these counties, the nonbearing was at least 20 percent of the bearing
acreage (Table 1). These plantings occurred before the enactment of the
Holland Amendment which was incorporated into The Tax Reform Act

TABLE 1. Acreage of bearing and nonbearing orange groves by Florida
counties as of December 1969.a
Acreage
Acreage Nonbearing as
County Bearing Nonbearing percentage of bearing
(acres) (percent)
Brevard 6,930 755 10.9
Broward 3,327 125 3.8
Charlotte 3,109 645 20.7
Collier 1,817 637 35.1
De Soto 10,763 2,407 22.4
Hardee 18,221 432 2.4
Hendry 8,094 1,765 21.8
Hernando 2,887 34 1.2
Highlands 20,456 613 3.0
Hillsboro 19,342 483 2.5
Indian River 12,436 2,237 18.0
Lake 48,638 685 1.4
Lee 3,539 2,666 75.3
Manatee 5,994 167 / 2.8
Marion 1,652 5 .3
Martin 18,714 6,778 36.2
Okeechobee 1,465 500 34.1
Orange 21,933 299 1.4
Osceola 6,746 93 1.4
Palm Beach 3,972 1,781 44.8
Pasco 16,560 463 2.8
Pinellas 1,980 87 4.4
Polk 59,527 1,232 2.1
St. Lucie 24,123 2,574 10.7
Seminole 2,536 18 .7
Volusia 3,412 19 .6

Total 328,173 27,500
SOURCE: Florida Crop and Livestock Reporting Service (5).
aCounties with less than 1000 acres are excluded.






















I


processor-
institutional packer
delay consumption delay behavior delay
decisions retail delay
consumer
behavior
institutional delay ,
prices retail
delay prices
FOB delay
prices




FIGURE 1. Simplified flow diagram of the orange industry.







of 1969 (27). 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, dis-
ease, drought, pest or casualty ." (27, 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 develop-
ment.
The location of the orange producing area is important from the stand-
point of a model which estimates crop size. If the location of the produc-
tion area is rapidly shifting over time, historical data cannot be used as
an estimate of future weather effects on orange production unless adjust-
ments are made. Since the enactment of the Holland Amendment, lo-
cational movement within the producing area seems to be abridged.
Whether or not this is an effect of the amendment is unknown.
A simplified flow diagram of the industry is presented in Figure 1.
Oranges move from the growing activity into the processing-packing sec-
tor where they are converted into processed orange products.3 From
processed inventory, orange products move into wholesale or institu-
tional inventories and eventually consumption. Dotted lines in the dia-
gram represent information flows between various system 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. Informa-
tion passed through the marketing system is the basis for management
decisions.
Several allocation problems must be solved by the market mecha-
nism. The rate at which fruit flows from the growing activity into the
processing sector is controlled by harvesting decisions. This control is
recognized in Figure 1 by hourglass-shaped symbols. The solid lines rep-
resent physical flows. Whole fruit is allocated among alternative prod-
ucts.
The allocation process as visualized in Figure 1 shows the processor-
packer sector as a major decision point. Processor-packers receive in-
formation concerning inventory levels and the rates of flow of various
products from inventory. From past experiences, processors have formu-
lated subjective ideas about the rate of flow of product that will result in
an acceptable level of carryover at the end of the year. That is, past ex-
periences provide an image of a "desired" level of inventory and rate of
product movement. If inventories are larger than desired and the product
is not moving through the market at a sufficient rate to avoid excessive
inventories, processors lower FOB prices. These lower price signals pass

3. Processed products include fresh fruit ready for shipment.







through the marketing system and eventually increase consumption rates.
As consumption rates change, signals are passed back through the sys-
tem in the form of orders. Processors receive information on the adjusted
movement from inventories and evaluate the effects of their pricing poli-
cies. If the effects of the pricing policy are not those desired, a new FOB
price will be forthcoming. An equilibrium price will probably never re-
sult from this process. Consumers react to new prices over a period of
time while decision makers are considering new pricing policies.
The simplified flow diagram in Figure 1 does not reveal the forces
whereby grower profits encourage investments which increase supplies
over a longer time period. The relationship between short-run supply
and price fluctuations and long-run industry investment patterns is more
accurately depicted in the block diagram of Figure 2, which gives a very


FIGURE 2. Block diagram of major components of the Florida orange in-
dustry.








broad overview of the model used in this study. Weather is an exogenous
variable which affects tree numbers and orange supplies. Assuming rela-
tively stable demand relationships for orange products, restricted sup-
plies 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 op-
erating costs received by growers.
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.
Thus, the orange subsector is characterized by forces which lead to pe-
riods of restricted supplies and high prices followed by periods of large
supplies and low prices.
The simulation model developed in this study represents an attempt
to capture the effect of these forces operating in the industry. This mod-
el, like others of complicated systems, should not be viewed as a finished
product but as a step in an ongoing effort to capture the major forces
interacting in a complex real world system within the framework of an
abstract model.



THE MODEL

The simulation model developed in this study was written in DYNA-
MO and was constructed to meet the design and notational requirements
of the DYNAMO II computer compiler.4 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


4. Version four was used in this study. It runs on the IBM S/360 com-
puting system operating under OS or CP/CMS and is distributed by Pugh-
Roberts Associates, Inc., 179 Fifth Street, Cambridge, MA 02141.
5. The time notation used in DYNAMO II is as follows:

+- DT <- DT -
JK KL
interval interval
J K L
In the computational process, DT denotes the period of time between
calculations, K corresponds with the point in time for which calculations are








dynamics group at the Massachusetts Institute of Technology. The in-
dustrial dynamics approach to problem solving is discussed by For-
rester (7).
The model consists of a set of relationships between individual system
components. These relationships together with initial starting values pro-
vided 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 relation-
ships are self-explanatory given the definitions of the variables involved,
others require explanation and justification. The model presented in this
section represents a mathematical formulation of the interrelationships
that underlie the dynamic behavior of the orange industry. It draws
heavily on previous models constructed by Raulerson (25) and Jarmain
(10). No attempt has been made to acknowledge each duplication. Ap-
pendices A and B contain an alphabetic list of variable names and model
equations, respectively. The model is described below in ten sections.
Frequent reference to the variable names, model equations, and flow dia-
gram will facilitate understanding the model. Equation numbers in the
discussion and the corresponding figures refer to the associated equations
in Appendix B.



currently being made, J represents the time for which calculations were pre-
viously 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 for-
ward one step in simulated time and the values associated with time K be-
come associated with time J. In this recursive fashion, the computer moves
through the calculation process and time in the simulation.
The DYNAMO II compiler is designed to handle three principal types of
variables: levels, auxiliaries, and rates. In addition, there are supplementary
equations, constants, and initial values. These six items are referred to by the
symbols L, A, R, S, C, and N, respectively.
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 equa-
tions 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 inter-
val. 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 caculated at time K.
The computational sequence in DYNAMO II is levels, auxiliaries, and
rates. A detailed exposition of DYNAMO II is given by Pugh (24).









TREE NUMBERS SECTION


The major variables determined in this section of the model (Figure
3)6 are as follows:
Productive trees (PT)
Trees becoming productive (TBP)
New trees planted (NTP)
Trees hatracked (THR)
Productive trees lost (PTL)
The number of productive trees was increased by trees becoming pro-
ductive and decreased by productive trees lost (equation 1). During an
initial period after the start of the simulation, the number of trees be-
coming productive was expressed as a fraction of the number of pro-
ductive trees in existence (equations 2 and 2A). This procedure allowed
trees planted but not productive at the start of the simulation to be in-
serted into the system. After the initial period, trees became productive
as a result of increases in the productivity of young trees and the recov-
ery of freeze-damaged (hatracked) trees (equation 2B). The rate at which
young trees became productive depended on the number of new trees
planted and a delay of 13 years in trees becoming fully productive (equa-
tions 3-6).7 The exponential delay used to approximate the yield re-
sponse of newly planted orange trees brought larger proportions of a
newly planted tree into production over simulated time. In Figure 4, 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).
Historically, major investments in new trees have occurred during pe-
riods of high grower profits. As a consequence, one policy which was
tested to control supplies was to restrict new plantings whenever average

6. The following symbols are used in the flow diagrams:
States[ policies

-' -] levels
O- material flows

Sa-- information flows
-- constants
Numbers associated with symbols in the figures and equation numbers in the
text are given in Appendix B. Also, in the figures the reference a b> -- ->
means from section a, equation b, where a and b represent numbers. And,
the reference ---- >a- b means to section a, equation b.
7. See Forrester (7) for detailed explanation of exponential delays.
















\\ I~ r \NEW
N TREES
BECOMING 'I TIG
PRODUCTIVE X TREES RESTRICTION
V 2A BECOMING
PRODUCTIVE -
] -."- -- -\. / i
-- 4
--- ----'---->3-51

ACTIVEE \ RODUCTIV \ NEW '
RETR E TES LOST TREE I
LOST AGING PLANTINGS
19 217

^- S WEEKS PER
I TREE YEAR 10
/ ABANDONMENT I .
S RESTRICTION / YDD 27 \ /1
S FRACTION 7-154
V5CON / Y ADDED
LOST -- -- FRACTION \ 11
NORMALL LOST
22 26 FAT 12
..-- (<4-58 -<7-154 ---<4-63


FIGURE 3. low diagram of section 1 (tree nul bers) of the mo el.









Step input


Empirical estimate


of the model


0 5 10 15 20 25 30 35 geof
Years


FIGURE 4. Comparison of the output from exponential delay and empirical
yield estimates.
SOURCE: Empirical estimates from Cher (2, p. 58).


grower profits were high. Therefore, new tree planting occurred depend-
ing on whether or not a tree planting restriction (the policy tested) was
in effect (equation 7). When this policy was being tested, the restriction
on new tree plantings was effective when average grower profit was
greater than the level set to activate the new tree planting restriction
(equation 8). The rate at which new 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).
Hatracked trees become productive as a delayed response to the num-
ber of trees hatracked (equations 13-17). In order to reflect the rapid
increase in the productivity of hatracked trees, this delay in response was


Tree
productivity
Percent of
mature yield









shorter than the delay which allowed newly planted trees to become pro-
ductive. The number of trees hatracked was expressed as a fraction of
the productive trees in existence (equation 18). The rate at which pro-
ductive 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 were 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).
The value of the "normal" fraction lost variable reflected "normal"
tree losses (equations 23 and 24) or 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 re-
moved from production whenever grower profit was less than the level
specified. The rate at which trees were removed from production was
positively related to crop size (equations 26 and 27).


WEATHER EFFECTS SECTION
Major variables in this section (Figure 5) are:
Fraction of productive trees lost as a result of freeze damage
(FTLF)
Fraction of productive trees hatracked (FHR)
Fraction of yield lost as a result of freeze damage (FYLF)
Weather influence (WI)
Values which determined weather effects were obtained in one of two
ways depending on whether historical data were needed (for model val-
idation purposes) or whether values were to be generated stochastically.
When historical values were desired, Option I was used; otherwise, val-
ues were generated by Option II.8 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).9


8. 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 op-
tion was constructed. This option maintained "average" weather conditions.
For equations see Appendix C, p. 97.
9. Weather conditions for the first season are reflected in initial values.









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).

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 0.06 (equation 37). The total effect of this distribution was
consistent with the "weather index" estimated by Parvin (19). The weath-
er influence selected was subtracted from one to arrive at an adjusted
weather influence (equation 38). The yield effect was set equal to the ad-
justed weather influence when the value of the weather influence was less
than one; otherwise, it was set equal to zero (equation 39). Good weath-
er 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).

CROP SIZE SECTION
Major variables in this section (Figure 6) are:
Crop size (CS)
Crop remaining (CR)
Fruit used to date (FUTD)
New crop added (NCA)
Yield per tree (BPT)
Crop lost as a result of freeze damage (CLF)
Crop size was equal to the quantity of fruit remaining plus the quan-
tity of fruit used to date (equation 45). The quantity of fruit remaining
at time K was equal to the quantity remaining at time I 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).10
A new crop was added at the beginning of each new crop season
(equation 50). The size of the new crop depended on the number of pro-
ductive trees, yield per tree, and a stochastic weather influence on yield
(equation 51). Yield per tree was considered a function of (lagged) aver-

10. This was accomplished through a fruit discarded pulse which occurred
once every year (equation 49). The pulse that cleared the level equation was
a function of the quantity of fruit used (equation 48).






i-18 < 1-20 <-, /,> 3-56
1-20 <- --3-57
/ /
FRACTION
FRACTION HATRACKED ACTION
3-55 <-------- TREES LOST 29 YIELD LOST
RESULT OF AS RESULT
FREEZE N FREEZE



/OPTION I // / OPTION II/
S\ 3-51

I R ACTION RACTI N WEATHER
SXFTLFT 32 FRACTION YIELD LOST TRES LST YIE LO INFLUENCE
SHATRACKED RESULT OF RESULT O RESULT OF ON YIELD
X 33 FREEZE FREEZE FREEZE 40
FRACTION 4 I / N
TREES LOST / \ k /T
RESULT OF XFHRT 34 XFYL 36 XFTLFT 42 X |I 4-60
F REEZE ---- x \ X
31 FRACTION ADJUSTED I>5-77
TIME TIME HATRACKED / WEATHER
.TIM E INFLUENCE
/ I I 43 38 WEATHER
WEATHER ADJUSTED INFLUENCE
5-77 -- INFLUENCE WEATHER XFHRT 44 WEATHER
36A -- INFLUENCE INFLUENCE
ON YIELD
38A
3-51<--____ --- 36B NORMRN (1,.06)
I----- lN i

FIGURE 5. Fl w diagram of se tion 2 (weat er e ect of the model.





5-70> 1-12-36 >---



S -- -FRUIT


CROP 2
CROP LOSS DIFRU ED
ASSOCIATED 48 ( D
\ WITH TREE 48
YIELD KILLS
LOSSOP LOS 55
2-30>- 57 ASSOCIATED 4-63
SL WITH END FRUIT
HATRACKING SAGE FLOW


2>-- ---------- --------- -_
FI2-29 -G w d m of sn 3 (p s) o t


FIGURE 6. Flow diagram of section 3 (crop size) of the model.







age grower profit and reflected the improved cultural practices provided
by growers in response to higher prices (equations 52 and 53).
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).




1-22 <--
SON-TREE PT 62
PRICE ----
PER BOX 7< 7-189A
GROWER 61 -
PROFIT


CPB 59


TAEP 64
, _'7-


3-52




1-11<-/

1-23 <"


FIGURE 7. Flow diagram of section 4 (grower profit) of the model.







GROWER PROFIT SECTION


Major variables in the section (Figure 7) are:
Grower profit (GP)
Grower cost (GC)
On-tree price (OTP)
Average grower profit (AGP)
Grower profit per box was the difference in on-tree price per box and
grower cost (equation 58). Grower cost was initially set at $0.85 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).

PROCESSOR DISAPPEARANCE SECTION
Major variables in this section (Figure 8) are:
Weeks of crop remaining (WCR)
Average weekly fruit usage (AFU)
Fruit used in the th product (FU(I)) I = 1,...,7
Processor disappearance in the Ith product (PD(I))
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 product1l de-
pended on the disappearance of product I and a conversion factor (equa-

11. The following numerical code was used to identify the Ith product.
In future references, an I enclosed within parentheses as part of a variable
designation refers to the Ith product (I = 1,...,7) unless otherwise indicated.


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)






3-46 >
\


3-46 <-N 3-47 <

\\ /


4-65


7-189A


2-36A >-,

2-37 >

7-175H<- .

7-153 <-'


-> 6-100
/


// 8-225

/ /
PROCESSOR /
yDISAPPEAR-
ANCE
91-97



TIME AVERAGING
S FRUIT USAGE 69
/PROCESSOR -- -


FIGURE 8. Flow diagram of section 5 (processor disappearance) of the model.


,~ 8-218








tions 70-76). The constant portion of the conversion factor was based
on yield figures for the 1969-70 and 1970-71 seasons (Table 2). The
conversion factor remained at the constant level until the weather influ-
ence was generated. When weather Option II was operative, yield was
subjected to a short-run stochastic influence (equations 77-90). Proces-
sor disappearance was a function of retail and institutional demand and
processor availability (equations 91-97). Processor availability was re-
lated to the number of weeks of crop remaining (equations 98 and 99).

TABLE 2. Conversion factors for major orange products.
Conversion factors
(Gallons single strength
Product equivalent per 90 pound box)
Frozen concentrated orange juice (retail) 4.90
Chilled orange juice (retail) 5.29
Canned single strength orange juice (retail) 5.20
Fresh oranges (retail) 5.29
Frozen concentrated orange juice (institutional) 4.90
Chilled orange juice (institutional) 5.29
Canned single strength orange juice (institutional) 5.20

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


ADVERTISING SECTION

Major variables in this section (Figure 9) are:

Advertising tax revenue (ATR)
Advertising tax (AT)
Advertising tax revenue accumulated (ATRA)
Advertising tax spending (ATS)
Average advertising (AA)
Advertising influence on demand (AI(I))

Advertising revenue was equal to fruit usage times the advertising tax
less administrative and other nonadvertising costs (equation 100). Ad-
ministrative and other nonadvertising costs were assumed to be a con-
stant $26,306 per week (equation 101). The advertising tax rate was
based on actual values for the 1962-63 through 1970-71 seasons (Table
3). After the 1970-71 season, the tax was assumed constant at 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 col-
lected minus revenue spent during the JK interval (equation 104). The
weekly advertising expenditure was the product of revenue available for







5-70 (
(








ALTERNATIVE
ADVERTISING
POLICY
APPENDIX D





TIME AVERAGING FOR \
ADVERTISING 109


FIGURE 9. Flow diagram of section 6 (advertising) of the model.


\ ADMINISTRATIVE
\ COST 101
\ ^~^ ~


/-<7-156


FRACTION
SPENT
PER WEEK
106

I

\ FSPWT 107
"---,


7-175A <-


10-276 <-,








TABLE 3. Advertising tax rates for Florida oranges by type of use, 1962-70.

Advertising tax rate

Season 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 the Economic Research Department, Florida De-
partment of Citrus.

advertising and the fraction spent each week (equation 105). The frac-
tion spent each week reflected the seasonal expenditure pattern pre-
sented in Figure 10 and was a function of the number of weeks remain-
ing in the season (equations 106 and 107). Trademark advertising was
not considered in this study.


Weighting
factor
160 -1


.02439
02033a .02033
02033


Sept. 10


Dec. 10


Mar. 10 June 10 Months


FIGURE 10. Seasonal pattern of generic advertising and promotional ex-
penditures for Florida oranges.
SOURCE: Interview with personnel in the Economic Research Department, Florida
Department of Citrus.
aFraction of tax revenue spent per week.


I .00813 t







Consumers were assumed to respond gradually to advertising expendi-
tures in the model. The magnitude of their response at a given time was
a function of the average advertising expenditure for the preceding two
years (equations 108-117). The magnitude of the response acted as a
demand shifter-increasing demand as average advertising expenditures
increased.
Since little data were available, advertising responses for institutional
products were based on the assumption that customer oriented institu-
tional purchasers such as restaurants and drugstore fountains were af-
fected by advertising programs in the same manner as retail consumers.
Noncustomer oriented institutions such as hospitals and military estab-
lishments were assumed to be unaffected by advertising programs (equa-
tions 118-123).12


FOB PRICE SECTION

Major variables in this section (Figure 11) are:
Marginal net revenue (MNR(I))
Suggested processor disappearance (PDS)
Desired disappearance (DD)
Processor disappearance relative to desired (PDRD)
Adjusted average marginal net revenue (XAMNR)
FOB price (FOB(I))
Quantity suggested after price adjustment (AQS)
Smoothed weighted average FOB price (SFOB)

The FOB price of orange products was the mechanism through which
allocation was accomplished. Allocation occurred in a recursive fashion.
A time lag existed during which the model waited for consumers to re-
spond 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 sea-
son, 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 occur, the model increased
prices. Price adjustments designed to alter fruit usage were accompanied
by adjustments in the relative price of orange products. The model ad-
justed relative price whenever the marginal net revenue from the sale of


12. For the data on which these relationships were based, see Appendix F.








one product was different from another. For example, when the mar-
ginal 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.13
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 I (equations 124-
130). Marginal net revenues were weighted by the quantity of each prod-
uct 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 in-
fluences on demand provided estimates of the monthly per capital quanti-
ty 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 4, 5, and 6 show the demand functions, mean values of variables,
and data periods, respectively, for the demand relationships.
In order to maximize profits, economic theory indicates that a product
should be allocated among markets so as to equate the marginal net rev-
enue 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 con-
dition was met. Perhaps this should be illustrated by an example. As-
sume that the FOB prices (P,, P2, and P,) of products 1, 2, and 3 yield
the marginal net revenues (MNR,, MNR2, and MNR,) shown in Figure
12. 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 rela-
tive to product 1 while that of product 3 should be increased. A simple
average of the three marginal net revenues yields a value equal to
AMNR.14 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 re-
duced 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-


13. Net marginal revenue functions were derived from cost and revenue
relationships. See Appendix D.
14. The weighted average actually used in the model reduces the magni-
tudes of the fluctuations in aggregate fruit usage that resulted from relative
price adjustments.






































FIGURE 11. Flow diagram of section 7 (FOB price) of the model.








TABLE 4. Relationships between quantity of orange products demanded by
retail and institutional consumers and FOB prices.

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

QRFCoJ .145935 -.106017 -.009218
QRcoJ .035136 -.047900 -.000294
Q'cssOJ .023731 -.027704 .000131
QRFo .126176 -.117840 c
Q'ICOJ .052886 -.055452 c
Q'coj .078273 -.058530 c
Q'cssoJ .173864 -.185287 c

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
(11, p. 20). Demand relationships for institutional products were obtained from
(35, 36). All relationships have been adjusted.
aSuperscripts represent retail (R) or institutional (I) markets. Subscripts indicate
product type, i.e., frozen concentrated orange juice (FCOJ), chilled orange juice
(COJ), canned single strength orange juice (CSSOJ), and fresh oranges (FO).
( 0 Sept.-Mar.
bSeasonal shifter = I Apr.-Aug.
cNot included in regression model.


TABLE 5. Mean values associated with estimated demand relationships.

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

FCOJR .5242 14.43 cents/6 ounce .0867
COJR .5532 30.74 cents/quart .0085
CSSOJR .5547 32.31 cents/46 ounce .0084
FOR .7618 10.40 cents/pound .0364
FCOJI .7492 $8.99/dozen 32 ounce .0113
COJI 1.0600 $3.18/dozen 32 ounce .0162
CSSOJI .9043 $3.90/dozen 46 ounce .0062

aThe subscripts refer to the retail (R) or institutional (I) markers. The product
symbols represent frozen concentrated orange juice (FCOJ), chilled orange juice
(COJ), canned single strength orange juice (CSSOJ), and fresh oranges (FO).











dollars/ dollars/ dollars/
gallon gallon gallon


P P1
F p2 \
product 31 product 2 product 3

MNR D



SII \ I\\
IN 1_______________ ^R 3 I



\WR MI gR pNR3
S\ 1 1 3
Gallons U Q2 Q 2 0 Q Q3
gallons
product 1 product 2 product 3


FIGURE 12. Relative price adjustment for three product cases.a
aThe diagram simplifies the price adjustment technique by assuming zero cost and ignoring the effect of advertising.








TABLE 6. Base data periods associated with estimated demand relationships.
Market

Product Retail Institutional
Frozen concentrated January, 1968- December, 1963-
orange juice April, 1971 November, 1966
Chilled orange juice January, 1968- December, 1963-
April, 1971 November, 1966
Canned single strength January, 1968- December, 1963-
orange juice April, 1971 November, 1966
Fresh oranges August, 1962- (not applicable)
July, 1963


pare processor disappearance suggested with processor disappearance
desired.15
Desired disappearance was a function of crop remaining, the number
of weeks left in the marketing season, and the end-of-season carryover
(equation 154). The carryover was set equal to an eight week supply,
except when an increased carryover was operative, in which case the de-
sired carryover 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).
Processor disappearance relative to desired was the variable that de-
termined whether an adjustment in product flow was desired (equation
159). However, the model allowed specification of a minimum time pe-
riod during which price adjustments could not occur.16 When adjust-


15. Bharat Jhunjhunwala has pointed out that an alternative approach
would be to solve the constrained maximization problem and to use the re-
sulting relationships as the basis for selecting the new prices. This method
would allow the selection of prices that equate marginal net revenues while
conforming to a quantity constraint. If the constraining quantity was equal
to desired disappearance, the movement suggested by the new prices would
deplete available orange supplies (less carryovers). This method was not used
since it was believed that the iterative technique provided a closer approxi-
mation of real world behavior and was computationally less demanding than
a solution to the constrained maximization problem. The constrained max-
imization problem becomes computationally complex if the B matrix defined
in Appendix D is nondiagonal.
16. When the value of processor disappearance relative to desired 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







ments were allowed, average marginal net revenue was adjusted upward
or downward and prices increased or decreased when processor disap-
pearance suggested was greater or less than the disappearance desired
(equation 166).17 A policy option allowed the specification of a limit
below which average marginal net revenue could not be adjusted (equa-
tions 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).

RETAIL AND INSTITUTIONAL INVENTORY AND SALES SECTION
Major variables in this section (Figure 13) are:
Sales (S(I))
Influence of product availability on sales (IA(I))
Weeks of inventory available (WIA(I))
Inventory level (I(1))
Order rate (D(I))
Inventory influence (II(I))
Competitive influence (CI)
Sales of orange products were equal to the product consumers de-
manded as long as adequate supplies were available at the consumer
level (equations 190-196). The model's ability to satisfy consumer de-
mand 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 7). 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

(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).
The mechanics of the mechanism was as follows: no adjustment was al-
lowed when R.K was equal to zero. R.K was equal to zero when 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.
17. The rate of adjustment was determined by the Q variable (equations
167 and 168).








<5-91


1 -5-91
ORDER --**
IT RATE (D)
IT \ 225-231
\, -/ \ ..-- 7-159


INFLUENCE COMPETITIVE
232-245 1 COMPETI



\ CIT 247


FIGURE 13. Flow diagram of section 8 (retail and institutional inventory and
sales) of the model.

211-217). Inventories were increased by processor disappearance and
decreased by product sales (equations 218-224).
Retail and institutional order rates depended on the level of average
consumer demand, the inventory level relative to "normal" and a com-
petitive 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).









TABLE 7. "Normal" retail inventories of major orange products.

Product Inventory level (C(I))

(weeks)
Frozen concentrated orange juice,
retail and institutional 1.3
Chilled orange juice,
retail and institutional 1.2
Canned single strength orange juice,
retail and institutional 3.7
Fresh oranges,
retail only .5

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

The competitive influence was expressed as a function of processor
disappearance relative to desired disappearance and reflected the influ-
ence 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.

RETAIL AND INSTITUTIONAL PRICE SECTION
Major variables in this section (Figure 14) are:
FOB price (XFOB(I))
Retail price suggested (RPS(I)) I = 1, 2, 3, 4
Retail price (RP(I)) I = 1, 2, 3, 4
Average retail price (ARP(I)) I = 1, 2, 3, 4
Institutional price (IP(I)) I = 5, 6, 7
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 sev-
eral 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).
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 ac-
counted for the consumption of about 88 million gallons of orange juice
during 1971 (1). Of this, 19 percent was reported to have been pur-
chased by restaurants through retail outlets. The total institutional con-
sumption 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 (34). 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 consum-
er prices for orange products sold through institutional outlets.
The FOB prices of institutional products were converted to units con-
sistent with Weisenborn's equations (equations 269-271). They were
then exponentially smoothed and used as inputs to the demand sector
(equations 272-275).


DEMAND SECTION

Major variables in this section (Figure 15) are:

Per capital quantity demanded (PQD(I)) I = 1, 2, 3, 4
Quantity demanded (QD(I))
U. S. population (POP)
Average quantity demanded (AQD(I))

Relationships used to estimate product consumption are presented in
Table 8 and the mean values for prices and quantities are given in Table
5. Advertising and price information (inputs to the section) 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 capi-
ta quantities and multiplied by projected U. S. population, provided an











.O.B.
10-276 <- INSTITUIONAL PRICE
PRICE 4- -- STANDARD
272-274 UNITS
UNITS
248-2,2 9-271



TIME CORRECTING / RETAIL
INSTITUTIONAL PRICE 275 / PRICE
/ SUGGESTED
.252-255
TIME AVERAGING
RETAIL PRICE 268

AVERAGE ------
RETAIL
PRICE
264-267


10-276 f-4


TIME FOR CORRECTING
RETAIL PRICE 260-264



I
I
I


FIGURE 14. Flow diagram of section 9 (retail and institutional price) of the model.


- -- -- 7-176









estimate of the total weekly consumption of each product (equations
283-290). Population level was determined by an equation dependent on
a growth rate (equations 291-293). Average quantity demanded was an
input to the retail and institutional inventory and sales sector (equations
294-301).
The demand section is the last major section of the model. A detailed
flow diagram of the complete model is given in Figure 16.


TM H
OPULATIO 293A
GROWTH
RATE
293


TIME


S8-190
> 7-146
7-175A


7-124
7-132
7-139
7-169

7-156


FIGURE 15. Flow diagram of section 10 (demand) of the model.








INITIAL CONDITIONS
In order to start the computation process, a requirement of computer
simulation is that initial conditions be specified. The values specified in
Appendix B, page 00, 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 com-
pute 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.


TABLE 8. Retail and institutional demand relationships for Florida orange
products.

Quantity Retail or
(gallons single institutional
strength equivalent Pricing price Seasonal
per capital) Intercept unit coefficient shifterb

QRrcoJ .171943 cents/6 ounce -.005654 -.009218
QRcoJ .067536 cents/quart -.001916 -.000294
QRssoJ .033276 cents/46 ounce -.000771 .000131
QRFo .152239 cents/pound -.011138 c
QIrcoJ .052886 dollar/dozen -.004621 c
32 ounce
Q'cor .078273 dollar/dozen -.019510 c
32 ounce
Q'CssoJ .173864 dollar/dozen -.042965 c
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
(11, p. 20). Demand relationships for institutional products were obtained from
(35, 36). All relationships have been adjusted.
aSuperscripts represent retail (R) or institutional (I) markets. Subscripts indicate
product types, i.e., frozen concentrated orange juice (FCOJ), chilled orange juice
(COJ), canned single strength orange juice (CSSOJ), and fresh oranges (FO).
( 0 Sept.-Mar.
bSeasonal shifter = 1 Apr.-Aug.
cNot included in model.




































--- -- ---- ---

WEATHER
EFFECTS ,- -.--- ----
SECTOR 2 ,-

I I


II N.
S,----- -,-.--x -- --














Db SECTOR 108'
/ OPTION I / "i or' /~n i
-.--- -






~(---- -------,-----^.----L---
Sr













,.. -.. . ... ...


,2q
------ ----- ---- ------4-----



































DEMAND SECTOR 10 \



FIGURE 16. Flow diagram of the DYNAMO model of the Florida orange industry.
{lSnicn %M.-- -
\ ffjib/r ^ fr
,*'T1
'9tr























FIGUE 1. Fow dagrm o th DYNMO ode of he lorda rang inusty.\













9

I Is





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i


l


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\ \... ..L








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CROP SIZE --
SECTOR 3 -3 m i

-- - --
\ 'I L
!.. .. . 1 I. / ^

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/ -*- I-
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75AI ----
7 / \







































--- :-- / ^- -~e
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I I / / -
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I- // / / /
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,- / l /
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,, ,, ..... ____/___.

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l// # i
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/, I
aIi-3b
W ..BPICE,-
'/ SCO 7 "

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--_-,_ -- -, J ... .. ... S


/ \ -i.+,WA Sox -,--- 7'
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S T 4---- -
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M _-o,/ N7lrl\ 7 / .
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.,- -- /-
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,,- _-- I




., --------------- ,)



PROFIT A'ITLO"A
SECTOR 4 D .EEC 8

"- N*/ I












--------------- ---------- -
---- -----------
PROFIT 1 -. I .......























INVENTORY AND SALES SECTOR 8
-- -- --' .- -'-A-

--. __ _/ -^
-- -- --N----- ------/- --

-----4---^---- 'I----












INVENTORY AND SALES SECTOR 8


/









/b'EAAS
~p0O~ W-
'N


PROCESSOR
DISAPPEARANCE
SECTOR 5


/
/
/

/1 AL
, \ U






/-


//


/ /
/D / / e
I
// 'I P7\,4-" W



// 0
/ /V M/ s \\ .
I/ i u
A/0 /,\ Ck%,h ADVERTISINI

i ",\ I SECTOR 6


,,. q'S ',,! iT'A
,' / ( I1



AwwReTPi/N~ y '0
A6VtKTWHQ ----------- \ frMC.
l /O \ I I



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\'.: 7 # I,, ---.{ I u --^












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W 0.4. A4\\ I -I





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"'<--' /*' l j (. -7,.~ ll/ofi ,,I\ \ ,-- ,.. I





1, ', i --1,







. .... .i.
-- ; 4 .......... 1. I ./"
/S3 P----,--V---YV-A


---WWMM
----1Irs j -----------------_--




T mi 7 /?/l. PR B a-b
SadS .J f 7-------


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----- ..R.. ,C'.. INSTITUTIOs
SECT(


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. \ n 4n x .
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VALIDATION

The usefulness of the model depends upon its ability to characterize
the response of the Florida orange industry to changes in economic con-
ditions. If the model is a "good predictor" of response, it should be use-
ful 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 evalu-
ated on the basis of a set of criteria established for this purpose. How-
ever, the choice of criteria is a subjective process. The model can also be
evaluated from the standpoint of the reasonableness of its estimates and
assumptions. The purpose of this section is to provide insight into the
model's ability to predict.
In his book, Computer Simulation Experiments with Models of Eco-
nomic 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 predic-
tions of the behavior of the actual system in future time periods? (18,
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 simulated 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.


LONG-RUN STABILITY
The model was initialized 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 sup-
pressed and weather effects were set equal to constants that reflected av-
erage weather conditions. With 1961-62 initial conditions, there was
reason to expect the model to start from a disequilibrium position. How-
ever, a run period of 100 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.
In Figure 17, variables are 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



















A







T productive trees

P U.S. population

R average marginal net revenue
(dollar/gallon single strength)

F average fruit usage
(boxes/week)

A average FOB price
(dollars/gallon single strength)


FIGURE 17. Simulated time path of selected variables.
aScale numbers on the vertical axis are in the same order as the variables listed. Scales with an M are in millions.


90.M
600.M
.2
9.M
.7


Scalesa
T
P
R
F
A


60.M
400.M
.0
6.M
.5


30.M
200.M
-.2
3.M
.3









number increased at a rapid but decreasing rate for approximately 16
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 sustained 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
figure was immediately adjusted downward by the model seemed consis-
tent with the behavior that would have been expected from the orange
industry, if rather than having experienced the 1962-63 freeze, "nor-
mal" 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 $.09 to $1.99 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 con-
sidering that the model, operating with "normal" weather conditions gen-
erated larger supplies than those actually experienced by the industry.
Other variables in Figure 17 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 plant-
ings relative to average grower profits. As specified in the model (equa-
tions 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 simu-
lation, which used a response function that allowed new tree plantings to
fall to zero, reached a stable position after approximately the same num-
ber of years with an average marginal net revenue of $-.03 per box.
Differences between the two runs indicate behavior of the model is sensi-
tive 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 dur-
ing the 1961-62 through 1971-72 period. Results were compared with
empirical data reflecting the behavior of the Florida orange industry
during the same period.
Figure 18 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 initial-
ized at 18.7 million and had increased to 22 million trees by the end of
the 1961-62 crop season.'8 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. Carryover effects of the
freeze also caused a reduction in productive trees during 1963-64. Dur-
ing this period, an almost identical pattern of change was reflected in the
observed data; however, levels of observed tree numbers were approx-
imately ten percent lower than those generated by the model. Following
the 1963-64 season, the combined effect of new trees becoming produc-
tive and damaged trees recovering 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 ob-
served than simulated in 1964-65. Further comparison of the time paths
revealed high correspondence between observed and simulated tree num-
bers 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 points.
Of six observed versus simulated changes in tree numbers, the model
overestimated realized changes four times, underestimated change once,
and predicted change perfectly one time.
A quantitative measure of the correspondence between observed and
simulated values was provided by Theil's inequality coefficient (28, p.
28). Of the several versions of the coefficient, the one used in this study
was defined as follows:

U F (at Pt)2 1/2
S(at ati)2.


18. Initialization of tree numbers at 18.7 million probably overstated the
number of trees in existence at the beginning of the 1961-62 season. Re-
flection indicated that this figure was more nearly associated with the end
than with the beginning of the season.








Mature productive orange trees
(millions)


61-62 63- 64 65-66 67-68 69-70 71-72
Season
FIGURE 18. Simulated and actual numbers of mature productive orange trees,
1961-62 through 1971-72 seasons.
SOURCE: Table 3 and simulated.


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 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 pt = at-1. For the tree numbers data, the coefficient was
equal to 0.5513, 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-1.
Figure 19 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 model overestimated the
magnitude of five changes and underestimated four and had one turning
point error. Theil's coefficient, equal to 0.98, indicated that predictions
were slightly better than those that would have been realized with the no-
change model.








Crop size (millions of boxes)


200


Simulated ,





150 Actual















50 t

1961-62 1963-64 1965-66 1967-68 1969-70 1971-72
Season
/ -
/
/
/
/
150 /\\ / Actual

















1961-62 1963-64 1965-66 1967-68 1969-70 1971-72
Season

FIGURE 19. Simulated and actual crop size, 1961-71.
SOURCE: Florida Citrus Mutual (3, 1971-72 season) and simulated.



A comparison of observed and simulated on-tree prices of Florida
oranges is presented in Figure 20. Again, the general behavior of the
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 model underestimated
the magnitude of four changes, overestimated three, and made two turn-
ing point errors-one between the 1963-64 and 1964-65 seasons and
another between 1969-70 and 1970-71. The Theil coefficient equaled
0.67.
As mentioned in the section describing the model, in order to maxi-
mize net returns, processors as a group should attempt to allocate oranges
so as to equate marginal net revenues among product markets. Table 9
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








On-tree price
(dollars/box)

3.50


3.00


2.50
/ \
I I


2.00 /


1.50 \/
Ssinulated




.50

1961-62 1963-64 1965-66 1967-68 1969-70 1971-72
Season

FIGURE 20. Simulated and actual on-tree price, 1961-62 through 1970-71
seasons.
SOURCE: Florida Citrus Mutual (3, 1968-69 season, p. 95, and 1971-72 season,
p. 104).



during the validation period.19 As can be seen from the data, the propor-
tion 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. This result,
although somewhat different from the observed, followed directly from
the derived marginal net revenue equations (equations 129-135).20 See
Appendix D.



19. Simulated figures corresponded to the end of each season; however,
there was little variation within seasons.

20. The demand equations used in the derivations were obtained from
several sources and most included variables exogenous to the simulator. To
adopt them to the recursive model, the coefficients of these exogenous vari-
ables were removed from the equations by incorporating them into the inter-
cepts. The resulting equations, along with cost and margin information, were
used to derive marginal net revenue equations for each product market. An








TABLE 9. Observed and simulated fruit usage, by product-market.

Product-Marketa
Season 1 2 3 4 5 6 7


(percent)


41.6 7.3
44.7 7.0
41.9 8.0


33.5b
27.8b
26.2b


42.8 7.5 4.0 28.7b


Observed
1963-64
1964-65
1965-66
Average
1963-66


Simulatede
1961-62
1962-63
1963-64
1964-65
1965-66
1966-67
1967-68
1968-69
1969-70
1970-71
1971-72
1972-73
Average
1961-73


4.4 3.5
7.5 3.1
11.5 2.9


5.7 8.2 3.1

17e


31.0
29.8
28.6
26.8
27.3
18.4
27.0
24.3
24.7
22.7
22.9
22.5


18.7
16.0
15.9
15.8
18.3
24.3
19.5
22.2
22.4
23.1
22.6
23.0


24.1 5.3 2.7 24.9 8.6 13.7 20.9

57d 43e


SOURCE: Weisenborn (34, Appendix C) and simulated.
aRows may not add to 100 due to rounding.
bAssumes 12,000 fresh oranges equals 396.75 gallons single strength equivalent.
cSimulated figures were at the end of each season; however, within season varia-
tion was minor.
dTotal for four retail product markets.
eTotal for three institutional product markets.


examination of these relationships revealed that several cross-product coeffi-
cients had signs different from those expected and in some cases the cross-
price effect outweighed the own-price effect. Further examination indicated
that these coefficients could lead to results inconsistent with economic theory,
e.g., when all prices increased, total quantity demanded increased. In order
to prevent this problem, cross-product coefficients were also incorporated into
intercept terms. The loss of these coefficients resulted in relatively naive de-
mand equations. A different set of equations might have led to results more
consistent with the observed data.


22.6
25.7
26.5
27.7
25.1
24.8
24.2
23.3
22.8
23.3
23.5
23.5








The obvious implication of the preceding comparisons is that there
exists room for improvement in the predictive accuracy of the DYNA-
MO model. However, a definite similarity existed between real world and
model behavior, especially with regard to turning points, which indicates
the model does capture some of the dynamic behavior of the orange in-
dustry.




POLICY ANALYSIS

The term "policy" as used in this section refers to changes in either
the model's operating rules or structure. Most policies were implemented
by parameter changes in functions listed in Appendix B. These changes
altered the operating rules of the model and affected performance by
reducing orange supplies, by increasing desired carryovers, or by modi-
fying pricing and advertising schemes.

POLICIES
The policies examined in this study were as follows.
1. Restricted tree planting. A restriction was placed on new tree plant-
ing whenever average grower profits rose above specified levels. Three
levels of this policy were considered in the study, $1.25, $1.50, and
$1.75 per box. When the policy was operative, tree planting was per-
mitted 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 industry, grow-
ers have tended to react to high profits as if a permanent shift in mar-
keting 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 industry to be characterized by produc-
tion and price cycles, and it was believed that a restriction on tree plant-
ings during periods of high grower profits might exert a stabilizing in-
fluence.
2. Tree abandonment. The tree abandonment policy, when operative,
removed fully productive trees from the system whenever grower 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 re-







during tree numbers, was similar to the sale of grove acreage for non-
agricultural purposes.
3. Increased carryover. A policy which increased the end-of-season
carryover of orange supplies from 8 to 16 weeks of average consumer
demand was implemented. The purpose of this policy was to determine
if increased carryovers would improve system performance by providing
buffer inventories. Carryovers were specified as a constant multiple of
the quantity given by average consumer demand. Thus, when large sup-
plies remained at the end of the season, price would be low, the quantity
demanded (level of average consumer demand) would be 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 carryover could contribute to even lower prices.
An increase in carryover from 8 to 16 weeks provided an opportunity to
evaluate the model's reaction to changes in carryover while other com-
ponents 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, pric-
ing was continuous and price adjustments could be made as often as
twice each week. Price adjustments do not occur this frequently in the
orange industry. When the price adjustment restriction was in effect,
price could'be altered only twice each month. In reality, the citrus indus-
try 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 pe-
riod when conditions indicated that a price change was necessary. The
system could become more or less stable as this response function is
changed.
5. 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 quanti-
ties 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.
6. Alternative advertising.21 An alternative method of determining ad-
vertising revenues and expenditures was adapted from a proposal by
Myers (15).22 In his report, 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 produc-
tion level. This procedure was designed to change the incidence of the
tax by causing a larger per box tax to be collected during periods of
small crops which are generally associated with high per box prices. Rev-
enue collection based upon the procedure was expected to be more
stable than if it was collected by the method currently used in the indus-
try. Advertising expenditures, on the other hand, were larger when there
was a large crop to be sold.
7. Restricted tree planting and price floor. The final policy consisted
of a combination of restrictions that limited increases in productive ca-
pacity 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 $-.20 per box on average marginal net revenue.


ANALYSIS

In theory, for a given set of alternatives, it is possible for groups of
industry participants to bargain with each other until they arrive at a
preferred position. In practice, and particularly in the short run, it is
difficult to arrive at such a position, since participants must be able to
determine the relevant factors on which to base their decisions and ob-


21. 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 equation 59, 60, and 62), and administrative and other costs
were allowed to increase over time (a change in equation 100). A new base
was then generated in order to be comparable with the advertising policy.
Specific changes in the model are presented in Appendix C. For explanation,
see footnote 26.
22. There are differences between the procedure presented here and the
one proposed by Myers. The most important difference is that Myers' pro-
posal 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.







tain the information necessary to evaluate the effect of the dynamics of
the system.23 This analysis examined two factors believed to be of major
importance for each major interest group participating in the orange in-
dustry. No attempt was made to define the trade-offs between partici-
pants.
Policies were examined from the viewpoints of three major groups of
participants: orange growers, orange handlers, and consumers. The as-
sumption was made that the interests of participants within each of these
groups were homogeneous enough to be represented by a variable se-
lected from the mathematical model. This is, of course, an oversimplifi-
cation 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.24 Present
values were used in the analysis, since it was believed that participants
within the orange industry 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 10 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 dol-
lars. Assuming that no time preference exists and that both streams will
occur with a probability of one, they would be equally preferred. How-
ever, 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 vari-
ance compared to other policies. It was believed that participants in the
orange industry 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
evaluating policies for each group.
Grower profit was selected as the variable which best represented the
interests of growers. The premise underlying this assumption was that
the utility of growers was directly related to the present value of profits
and inversely related to the variance of profits.


23. For a theoretical discussion see Langham (12).
24. 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 E.







TABLE 10. Discounted valuesa of two hypothetical streams of income re-
ceived over a five-year period.
Value discounted
Income stream to time t
Year A B A 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

aDiscounted to time t at the rate of seven percent per year.


Handlers were assumed to be interested in the return on their invest-
ments; however, this return was believed to be related to the volume of
oranges moving through the marketing system. Handlers tend to formu-
late 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
was calculated.
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 handlers. 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 pro-
vided a less complex and computationally more efficient basis for evalu-
ating 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, ex-
cept 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 the variance of the present value of average FOB
price.
A set of five runs, each covering a 25-year period, was made to pro-
vide a base with which to compare policy results. This base was an at-
tempt to characterize the orange industry with its existing structure. Ten
policies (including three levels for Policy 1 and two levels for Policy 2)







were then examined. Each run was started with a set of initial conditions
based on the 1961-62 crop season. Weather effects for seasons after
1961-62 were computed by the stochastic procedure. These weather ef-
fects were used for both the base and policy simulations to provide com-
parable results for a variety of weather conditions.25 Policy simulations
were replicated five times--once with each of the weather sets presented
in Table 11. Weather effects greater than, equal to, or less than one de-
noted better than average, average, or poorer than average weather con-
ditions, respectively.
The alphanumeric names used to identify the simulation runs are pre-
sented in Table 12. Fifty of the runs were for the ten policies described
in this chapter and the other ten for the two versions of the base model.26
Tables 13, 14, and 15 present the simulated output of the three evalu-
ation variables (grower profits, crop size, and FOB price) for each policy,
averaged over the five sets of weather conditions. The tree planting re-
striction policies exerted the most impact on industry performance and
are graphed in Figures 21, 22, and 23. These policies reduced crop size
and increased FOB price and grower profits. The planting restriction,
price floor combination (PR2 + F) had almost the same effect as the
planting restrictions alone. The tree abandonment policies also reduced
crop size, increased FOB price and grower profits, but had minor effect


25. DYNAMO contains a function which generates "pseudo-random num-
bers" 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 nor-
mal 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. See Pugh (24).
26. 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, ad-
ministrative costs were compounded at the rate of 5 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 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 with-
out the benefits, and the policy which accumulated the largest unspent reve-
nue would have been unfairly penalized in the comparison. A change in the
model which made grower profits net of advertising expenditures rather than
net of advertising receipts partially corrected the problem in that accumu-
lated advertising funds were no longer deducted from grower profits; how-
ever, some discrepancy remained because the potential gain from the use
of these funds was ignored.








TABLE 11. Weather conditions used in simulation runs.

Weather setsa

Season 1 2 3 4 5


1.14
1.01
1.11
.95
1.08
1.00
.98
.94
1.11
1.00
.93
1.00
.97
1.06
1.05
1.07
1.05
1.00
.99
1.00
1.04
.92
1.03
.97


1.10
.92
.95
.95
1.11
1.06
1.00
.98
1.08
.97
.91
.88
.98
1.06
.96
1.07
.97
.99
.98
1.00
1.00
.95
1.03
.97


1.07
.89
1.01
.99
.99
1.00
1.05
.95
1.03
.98
1.05
1.07
.97
.96
.94
.94
1.06
1.06
1.01
1.04
.92
1.08
1.08
1.00


1.07
.99
.92
.98
.96
1.08
1.02
1.01
1.03
.98
1.01
.96
1.03
1.04
.95
.96
1.01
1.04
1.04
.90
.92
1.01
1.03
1.02


1.10
1.03
1.06
.97
.89
1.08
.87
1.02
.99
1.01
1.04
.98
1.02
1.01
.99
.97
1.06
1.03
.96
.96
.97
1.01
.98
1.04


aWeather 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 func-
tion.
bInitial values were used for the first season.

on industry performance (Figures 24, 25, and 26). The other five policies
had very minor impacts, as is reflected in the tabular data.
The results of policy analysis emphasized that trade-offs exist among
industry participants. Discounted values of the averages of the variables
over the five weather replications are presented in Table 16. In the base
(B), the discounted values of grower profits, average FOB price apd crop
size were $1,007.48 million, $7.15, and 1,747.96 million boxes, respec-
tively. 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 nonad-
vertising policies in Table 17.











TABLE 12. Alphanumeric names used to identify simulation runs.a

Weather replications

Policy 1 2 3 4 5


Base (except for advertising)
Restricted tree planting:
$1.25
$1.50
$1.75
Tree abandonment:
a $.15
$.25
Increased carryover
Price adjustment restriction
Price floor
Restricted tree planting and
price floor
Base (for advertising)
Alternative advertising


Bl B2 B3 B4 B5


PR11
PR21
PR31

TA11
TA21
CO1
PA1
F1

PR2 + F1
B21
ADVI


PR12
PR22
PR32

TA12
TA22
C02
PA2
F2

PR2 + F2
B22
ADV2


PR13
PR23
PR33

TA13
TA23
C03
PA3
F3

PR2 + F3
B23
ADV3


PR14
PR24
PR34

TA14
TA24
C04
PA4
F4

PR2 + F4
B24
ADV4


PR15
PR25
PR35

TA15
TA25
C05
PA5
F5

PR2 + F5
B25
ADV5


aThe last number in each name identifies the weather replication and was dropped when referring to the average for the five replications.





TABLE 13. Average simulated grower profits for the five sets of weather conditions, by year and policy.
Policy
Year B PR1 PR2 PR3 TA1 TA2 CO PA F PR2+F B2 ADV


1
2
3
4
5
6
7
8
9
10
S;11
12
13
14
15
16
17
18
19
20
21
22
23
24
25


117.0 117.0 117.0 117.0
109.6 109.6 109.6 109.6
103.4 103.4 103.4 103.4
84.4 84.4 84.4 84.4
89.0 105.6 105.6 105.6
89.0 120.8 120.8 120.8
70.8 125.8 125.8 125.6
73.2 131.2 130.8 130.6
80.0 137.4 137.0 136.8
58.6 143.8 143.0 142.0
62.8 143.8 143.4 142.4
67.8 146.0 145.4 144.6
74.6 146.4 146.0 145.4
74.4 149.8 149.8 148.8
62.6 153.0 152.6 151.2
78.6 152.0 152.4 151.2
82.2 155.6 155.8 154.4
70.4 158.8 157.2 154.4
69.6 162.0 158.8 155.0
80.0 162.0 158.8 155.0
92.8 163.6 159.8 156.2
106.0 161.8 160.0 156.4
117.2 167.8 165.6 161.4
113.8 173.2 167.6 160.8
116.8 174.0 167.4 158.8


117.0
109.6
103.4
84.4
91.4
93.4
75.2
76.2
84.0
65.0
74.0
79.2
83.0
82.6
75.8
95.2
97.4
92.2
94.2
100.6
107.2
116.4
125.6
121.6
124.0


Million dollars per year
117.0 124.2 120.2
109.6 114.4 102.8
103.4 102.6 77.0
84.4 86.8 94.2
95.4 87.0 81.2
97.4 89.8 89.6
79.6 73.6 75.2
78.6 73.0 55.0
89.6 79.0 76.2
74.4 63.2 83.4
88.8 61.2 44.0
91.8 67.0 60.0
93.4 73.0 76.0
92.0 73.8 77.8
87.2 63.4 65.6
108.2 74.6 52.4
110.6 80.8 88.6
98.6 70.4 83.6
97.8 68.2 64.0
103.2 76.0 64.0
109.2 89.8 96.8
117.4 102.8 104.2
127.6 115.8 116.4
124.0 114.2 115.8
125.6 115.4 97.6


117.0 117.0
109.6 109.6
103.4 103.4
92.6 92.6
84.0 100.2
91.6 120.2
75.6 125.8
77.8 130.8
73.4 137.0
78.6 143.0
66.6 143.4
70.6 145.4
81.0 146.0
82.6 149.8
77.0 152.6
77.0 152.4
83.6 155.8
85.0 157.2
82.6 158.8
78.8 158.8
73.0 159.8
81.6 160.0
91.0 165.6
98.6 167.6
100.0 167.4


119.2
112.6
107.2
88.0
92.2
92.2
74.4
75.0
80.4
59.2
63.6
68.8
75.4
75.4
63.0
79.2
83.0
70.6
69.8
80.4
93.8
107.0
118.6
115.0
117.8


116.4
113:6
106.0
86.8
89.8
90.0
71.8
72.8
78.6
57.2
59.8
65.0
68.4
71.0
59.0
74.2
78.8
67.6
66.0
76.6
88.6
100.8
111.4
110.4
113.4








TABLE 14. Average simulated crop size for the five sets of weather conditions, by year and policy.
Policy
Year B PR1 PR2 PR3 TAl TA2 CO PA F PR2+F B2 ADV


1 121.3
2 116.3
3 134.0
4 130.0
5 136.4
6 150.8
7 145.4
8 146.5
9 166.5
10 160.5
11 160.1
12 157.3
13 163.5
14 173.1
15 163.5
16 168.3
17 177.5
18 181.6
19 176.8
20 170.9
21 163.2
22 164.6
23 174.8
24 172.3
25 169.9


Million boxes per year
121.3 121.3 121.3 121.3 121.3 122.8 123.0 121.3 121.3 121.4 121.2
116.3 116.3 116.3 116.3 116.3 117.3 116.8 116.3 116.3 116.4 116.4
134.0 134.0 134.0 134.0 134.0 135.0 133.1 134.0 134.0 134.4 134.3
117.7 117.7 117.7 128.4 125.8 130.7 130.1 130.1 117.8 130.3 130.1
112.7 112.7 112.8 134.3 131.8 137.0 136.3 136.4 112.7 136.7 136.6
114.7 114.8 115.0 149.0 146.6 151.4 150.8 150.9 114.8 151.2 151.0
103.0 103.3 103.8 143.9 142.2 146.0 145.6 145.6 103.3 145.8 145.6
97.6 98.2 99.1 144.2 140.2 147.2 146.3 146.8 98.2 147.0 146.7
105.1 106.5 108.0 163.8 159.0 167.2 166.1 166.6 106.5 167.0 166.7
97.0 99.0 101.0 155.2 147.5 161.4 160.9 161.1 99.0 161.0 160.6
93.6 96.4 99.0 154.6 148.1 161.0 160.1 160.9 96.4 160.6 160.1
89.9 93.4 96.6 152.8 147.2 158.3 157.0 158.2 93.5 157.9 157.2
92.1 96.7 100.6 159.2 154.3 164.5 163.4 164.6 96.8 164.1 163.3
97.1 103.0 107.6 166.9 161.3 174.3 173.2 174.6 103.0 173.9 172.8
92.1 98.5 103.4 154.8 147.9 164.7 163.8 165.3 98.6 164.3 163.2
95.4 103.3 108.7 160.2 153.8 169.5 167.8 170.2 103.4 169.1 167.8
101.9 111.6 117.7 167.4 164.4 178.8 177.1 179.7 111.6 178.5 177.0
105.4 117.0 123.8 170.6 168.9 183.0 181.7 184.4 117.1 182.7 181.0
103.8 117.0 124.1 167.1 165.5 178.2 176.7 179.9 117.1 177.9 176.1
100.9 116.0 123.7 163.3 162.1 172.2 170.5 174.0 116.0 172.1 170.3
97.2 113.6 121.9 156.9 156.1 164.3 162.9 165.9 113.6 164.3 162.4
97.9 117.5 127.0 159.2 158.0 165.6 164.4 166.4 117.6 165.8 163.7
104.0 128.1 139.3 170.1 168.8 175.9 174.8 176.1 128.1 176.2 173.7
101.7 128.8 141.3 168.3 167.5 173.4 172.5 173.3 128.8 173.7 171.1
99.6 130.0 143.2 166.8 166.4 170.9 169.6 170.6 130.0 171.3 168.7






TABLE 15. Average simulated FOB price for the five sets of weather conditions, by year and policy.
Policy

Year B PR1 PR2 PR3 TA1 TA2 CO PA F PR2+F B2 ADV
Cents per gallon single strength
1 72 72 72 72 72 72 77 75 72 72 72 72
2 65 65 65 65 65 65 66 62 65 65 65 66
3 67 67 67 67 67 67 67 64 67 67 67 68
4 61 61 61 61 61 61 62 65 63 63 61 62
5 63 67 67 67 63 64 63 63 62 66 63 64
6 62 70 69 69 62 63 62 63 62 69 61 62
7 57 69 69 69 58 59 58 58 58 69 57 58
8 60 73 73 73 61 61 60 58 61 73 60 60
9 60 76 76 75 61 62 60 62 59 76 60 60
10 55 75 74 74 56 58 56 58 58 74 55 55
u 11 57 77 76 76 59 61 57 55 58 76 57 57
12 58 78 77 77 60 62 58 59 58 77 58 58
13 60 80 79 78 61 63 59 61 61 79 59 60
14 58 80 78 77 59 61 58 60 59 78 58 58
15 56 78 77 75 57 59 56 56 58 76 55 56
16 59 80 78 77 62 64 59 58 59 78 59 59
17 59 80 78 76 62 63 59 61 59 78 59 59
18 57 78 76 74 59 60 57 58 58 76 56 57
19 56 78 74 73 59 60 56 56 58 74 56 56
20 58 78 75 73 61 61 58 58 58 75 58 58
21 60 80 75 73 62 63 60 63 57 75 60 60
22 63 81 76 74 65 65 62 64 59 76 62 63
23 63 81 75 73 64 65 63 65 59 75 63 63
24 61 80 73 70 62 63 61 62 59 73 60 61
25 63 81 74 70 63 64 62 61 60 74 62 63










Grower Profits
(million
dollars / year)
180





160

PLANTING
RESTRICTION 1


140



J


PLANTING
RESTRICTION 2


RESTRICTION 3


120 +


100 4-


80 +


60







0


- Year
25


FIGURE 21. Average simulated grower profits for the five sets of weather
conditions for planting restriction policies 1, 2, 3, and base, by
year.










Crop Size
(million
boxes / year)
200





180- BASE





160


PLANTING
RESTRICTION 3

140 '
i



120 \ \ .
PLANTING
/ RESTRICTION 2



100\ /



PLANTING
RESTRICTION 1
80





T| -| Year
0 5 10 15 20 25


FIGURE 22. Average simulated crop size for the five sets of weather condi-
tions for planting restriction policies 1, 2, 3, and base, by year.







FOB price
(cents / gallon
single strength)
90 T


PLANTING


80 +


70 +


60 j-


50 +


I I I


FIGURE 23. Average simulated FOB price for the five sets of weather condi-
tions for planting restriction policies 1, 2, 3, and base, by year.

RESTRICTED TREE PLANTING
Each of the tree planting restrictions considered in the study increased
the present value of grower profits by at least 50 percent, indicating that
growers would benefit from the policy. Each of the restrictions also re-
duced crop size by 23.7 or more percent and caused an increase in the
prices paid by consumers by 16 percent or more. The variance of grow-
er profits decreased but remained essentially unchanged or increased for
the other variables.
Estimates of the cost of storing the end-of-season carryovers asso-
ciated with the policies are presented in Table 18. For the planting re-
strictions (PR1, PR2, and PR3), reductions in storage costs ranged from
$9 to $11 million. These cost changes were directly associated with the
reduced crop size and inversely related to the changes in grower profits.
The increase in grower profits ranged from $504 to $524 million (Table
16).


,- -
PLANTING
RESTRICTION 2


r








Grower profits
(million
dollars / year)
140 T


TREE
ABANDONMENT 2


120 +


TREE
ABANDONMENT 1


100 +


80 4


60 +


Year


FIGURE 24. Average simulated grower profits for the five sets of weather
conditions for tree abandonment policies 1, 2, and base, by year.



TREE ABANDONMENT
Tree abandonment policies (TA1 and TA2), while not as successful at
increasing grower profits as the planting restrictions, were the most suc-
cessful 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.


INCREASING CARRYOVER

The present value of grower profits increased by $7.6 million as a
result of increasing carryovers (CO) to a level equal to 16 weeks of aver-
age product demanded. 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 growers, the policy seemed desirable;









Crop size
(million
boxes / year)

200 -r


180 +


BASE


160 +


140


120 -


TREE
ABANDONMENT 2


TREE
ABANDONMENT 1


I I I I


Year


FIGURE 25. Average simulated crop size, for the five sets of weather condi-
tions for tree abandonment policies 1, 2, and base, by year.



however, assuming "normal" returns, the additional storage costs of
$38.5 million more than offset the benefits of the policy from the view-
point of processors.

PRICE ADJUSTMENT RESTRICTION

The price adjustment restriction (PA), partially implemented to test
the sensitivity of the model to changes in the adjustment mechanism, re-
duced grower profits and caused an increase in average FOB price rela-
tive to the base run. Taking the more rigid pricing as the norm, the










FOB price
(cents / gallon
single strength)


70 +


TREE
ABANDONMENT


TREE
ABANDONMENT 2


60 +


BASE


50 +


Year


5 10 15 20
5 10 15 20 21


FIGURE 26. Average simulated FOB price for the five sets of weather condi-
tions for tree abandonment policies 1, 2, and base, by year.


simulation indicated that growers and consumers would benefit from in-
creased price responsiveness and that processors would benefit from re-
duced 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.

PRICE FLOOR
Advantages of the price floor (F) were offset by an increase in storage
costs to $66.24 million from the base of $40.91 million. This cost in-
crease, even after deducting the $16.4 million increase in grower profits,
would have required a return above variable costs (excluding storage)
of $1.02 per box on the increased volume handled in order to break
even. And, if processors had been required to bear the total cost in-
crease, the break-even return would have been $2.88 per box on the in-
creased volume handled. The cost and return estimates presented in
Table 19 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.








TABLE 16. The level and standard deviation of the present value of grower profits, average FOB price, and crop size for 12 sets
of base and policy simulations.a

Grower profits Average FOB price Crop size

Present Standard Present Standard Present Standard
Policy value deviatione values deviation value deviations

(million dollars) (dollars) (million boxes)
B 1007.48 100.02 7.15 .20 1747.96 64.33
PR1 1531.66 47.22 8.51 .23 1248.33 76.80
PR2 1523.94 51.54 8.39 .21 1301.26 70.07
PR3 1511.90 54.34 8.31 .20 1333.23 64.08
TA1 1083.34 71.00 7.27 .17 1706.73 52.47
TA2 1139.58 63.11 7.36 .17 1673.84 52.07
CO 1015.24 101.45 7.21 .20 1759.51 64.96
PA 967.19 99.38 7.21 .20 1748.69 64.00
F 1023.84 87.45 7.17 .19 1756.76 69.08
PR2 + F 1525.95 48.44 8.39 .21 1301.49 70.30
B2d 1029.77 100.75 7.13 .20 1754.63 64.55
ADVd 996.67 101.06 7.20 .21 1746.72 63.84

aPresent values were based on the average of the variable for the five weather replications.
bLarge values preferred.
cSmall values preferred.
dGrower profits were net of advertising tax spending rather than tax receipts for these two runs.






TABLE 17. Relative valuea of the level and standard deviation of the present value of grower profits, average FOB price, and
crop size for policies comparable with the base (B) run.

Grower profits Average FOB price Crop size

Present Standard Present Standard Present Standard
Policy value deviation values deviatione value deviationc

Percent of base
B 100.0 100.0 100.0 100.0 100.0 100.0
PR1 152.0 47.2 119.0 115.0 71.4 119.4
PR2 151.3 51.5 117.3 105.0 74.4 108.9
PR3 150.1 54.3 116.2 100.0 76.3 99.6
TA1 107.5 71.0 101.7 85.0 97.6 81.6
TA2 113.1 63.1 102.9 85.0 95.8 80.9
CO 100.8 101.4 100.8 100.0 100.7 101.0
PA 96.0 99.4 100.8 100.0 100.0 99.5
F 101.6 87.4 100.3 95.0 100.5 107.4
PR2 + F 151.5 48.4 117.3 105.0 74.5 109.3

aPercent of the base (B) value.
bLarge values preferred.
cSmall values preferred.








TABLE 18. Size and discounted costs of the carryovers associated with alter-
native policies.

Policy Average carryover Cost of storage Relative cost

Million gallons Million dollars B = 100
concentrate
B 25.08 40.91 100.0
PR1 16.76 29.93 73.2
PR2 17.88 31.00 75.8
PR3 18.52 31.66 77.4
TA1 24.35 40.00 97.8
TA2 23.88 39.27 96.0
CO 48.98 79.43 194.2
PA 27.76 47.34 115.7
F 47.05 66.24 161.9
PR2 + F 18.04 31.45 76.9
B2 25.20 41.06 100.4
ADV 25.04 40.87 99.9

aAveraged across weather replications.
bDiscounted to the present at seven percent per year. Storage costs were based on
the rate of $148,983 per year for one million gallons of concentrate.


RESTRICTED TREE PLANTING AND PRICE FLOOR
With supplies restricted (PR2 + F), the price floor performed some-
what better. The increase in grower profits exceeded additional storage
costs by $1.56 million. The addition of the price floor to the planting re-
striction (PR2) had little effect on FOB price and crop size, except for
a slight increase in the level and variance of the latter. Administrative
costs of maintaining a price floor would likely outweigh small net gains.


ALTERNATIVE ADVERTISING
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 per-
cent. Given the advertising response functions of the model, the addi-
tional advertising was not profitable, as indicated by the present values
presented in Table 17. With increased advertising and higher taxes, the
present value of grower profits decreased from $1,029.77 to $996.67
million, or by 3.2 percent. Smaller grower profits led to a reduction in
the present value of crop size, which in turn was associated with an in-
crease in FOB prices. Thus, from the standpoint of all three groups of
subsector participants, the policy seemed undesirable. However, these








TABLE 19. Estimated costs and returns to orange processors, 1961-70a.

Total cost FOB Return above total
Season less storage price cost less storage

(dollars/box)
1961-62 2.73 2.36 .37
1962-63 3.57 3.90 .33
1963-64 5.09 4.00 -1.09
1964-65 3.26 2.76 .50
1965-66 2.74 2.76 .02
1966-67 1.97 2.02 .05
1967-68 3.12 2.76 .36
1968-69 2.77 3.03 .26
1969-70 2.49 2.50 .01
1970-71 2.93 2.72 .21

SOURCE: Calculated from data obtained from Florida Citrus Mutual (3) and
Spurlock (26).
NOTE: These data, intended only as a guide, are based upon several simplifying
assumptions such as constant conversion rates and should not be considered a
substitute for the data presented in the sources.
aBased on the cost of processing and price of frozen concentrate.


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 meth-
od 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, Polopolus, and Myers (14) which basically reflected condi-
tions during the 1960-67 period. As the functions were specified, adver-
tising 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 25 years of the simulation and
probably considerably more. The average decrease in grower profits
(without discounting) was $88 million thus, had the expenditure level
been lower, performance would have improved.
Figures 27 and 28 show simulated tax collections, expenditures, and
crop size associated with weather set 1. Tax collections in the base simu-
lation (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 tended to be more stable except when reserves fell below
the $3.8 million minimum and the additional two-cent tax was collected.
The latter method had the most intuitive appeal since it advertised rela-
tively more during seasons of large crops. It would have been interesting









Million dollars


Expenditures (ADV)


Collections (B2)


5 10
5 10


I I I Simulation
15 20 25 period (years)


FIGURE 27. Collections and expenditures of advertising tax revenues for the
alternative advertising policy (ADV) and base (B) runs, weather
set 1.


Million boxes


200



C Crop size


I III I Simulation
0 5 10 15 20 25 period (years)


FIGURE 28. Crop size, weather set 1.


to compare the two procedures with
levels.27


average advertising at the same


27. In order to make such a comparison, a series of simulations with in-
cremental changes in the parameters of the total revenue and expenditure
functions would be needed. Then, the run with an average advertising ex-
penditure 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.


30 1








Perhaps the most consistent characteristic of the results was the pres-
ence of conflicts of interests. As can be seen from the summary presented
in Table 20, none of the nonadvertising policies was clearly preferred
by all three groups of subsector participants. If CO and F are eliminated
on the basis of increased storage costs, TA1 and TA2 are left as the only
policies which might have been preferred by all participants. Whether
either TA1 or TA2 was preferred would depend on how consumers and
handlers view trade-offs between present values and variance in their re-
spective decision variables. The remaining policies were preferred by
some participants, but not by others.
The fact that none of the policies was clearly preferred to the base by
all participants would support the supposition that the base was Pareto
optimal in the sense that no group can be made better off by changing
from the base without making another group worse off. An industry
characterized by perfect competition would be expected to organize itself
in a Pareto optimal fashion; and, in fact, perfect competition in the ab-
sence of external economies and diseconomies is a sufficient condition
for Pareto optimality. However, other forms of market organization can
also lead to positions that are Pareto optimal. Thus, one cannot conclude
from these results that the orange industry is competitive.
In summary, policies that reduced orange supplies led to substantially
higher grower profits, lower storage costs, and higher retail prices. Sup-
ply restrictions also reduced risks for growers, but not necessarily for
other participants. The increased carryover and price floor policies


TABLE 20. Nonadvertising policies classified for major groups of participants
by preference category relative to the base (B)a.

Participant
Policy Producers Consumers Handlers

PR1 X 0 0
PR2 X 0 0
PR3 X 0
TA1 X
TA2 X
COb 0
PA 0 X
Fb X
PR2 F X 0 0

aThe letter X indicates that the policy was clearly preferred to the base. A 0 indi-
cates 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.
bThe increase in storage cost was believed sufficient to rule out the policy.








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 simula-
tion 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 re-
quired to maximize retail sales. Restricting price adjustments to every
two weeks reduced the present value of grower profits by $40 million
and increased FOB prices. Taking the more stable pricing as the norm,
the industry would benefit from increased price responsiveness. How-
ever, these benefits could be easily offset by externalities associated with
frequent price changes.
In addition to economic feasibility, there are other factors that should
be considered in the selection of a policy. In many cases, legal mecha-
nisms 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 require-
ments. Also, popular support is usually necessary in order for a policy
to be effective, and policies that are easily understood and intuitively ap-
pealing often succeed where more complex policies fail. Undoubtedly,
there are additional factors that should be considered in formulating al-
ternative policies. This study provides an example of simulation as an
ex ante method of policy investigation and, for the policies examined in
this section, the results provide some insights into potential costs and
returns and their distribution among industry participants.



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.so-
phisticated in their decision making, they have altered their responsive-
ness to changes in grower profits. Also, real estate values within the or-
ange producing area have increased rapidly. In estimating the response
relationship, the effect of these changes was not completely understood.
Several demand equations had coefficients with signs differing from
theoretical expectations and cross-product terms that outweighed the
own-price effect. 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 mar-
ket 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 consumer response to advertising were also bothersome.
The response relationships developed by McClelland could not be ac-
commodated in the DYNAMO model without making alterations in
structure. Thus, advertising functions were based upon a simplified adap-
tation 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 discon-
tinuity 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 industry.
This characteristic was dampened by averaging and by making operating
rules dependent upon conditions that changed as the end-of-season ap-
proached. However, the model overstated the end-of-season discontinu-
ity.
Finally, answers provided by the model for particular policies need to
be carefully evaluated. Also, questions asked of the model need to be
evaluated. Other approaches may be more suitable for studying a par-
ticular question. Sometimes partial analysis will be more reliable and less
expensive.
System simulation models of the type used in this study provide an ef-
ficient way of looking at the implications of the information which goes
into them. Simulation models require rather than provide structural esti-
mates. In this sense they complement rather than compete with aggregate
econometric models designed for structural estimation. The model devel-
oped in this study provides a demonstration of how a general system
simulation model might be used to explore policy issues in an industry.
At the time it was constructed the model utilized the best information
available regarding structural parameters in the industry. However, dy-
namics within the industry have probably made parts of the model ob-
solete. Because of this the model should be looked upon as being unfin-
ished. It should be continually updated and modified and treated as a
dynamic if it is to be used for on-going policy analysis.



SUMMARY

The Florida orange industry has been characterized by shifts in pro-
duction, and crop value and market participants-particularly growers
and processors-have been interested in evaluating the effects of alterna-
tive policies on industry performance. Computer simulation provides a
method of studying the effectiveness of alternative policies within the







dynamic environment of an abstract model without the risk of experi-
mentation on the actual system. Objectives in the study were (1) to iden-
tify the structure underlying the industry's dynamic behavior, (2) to
construct a quantitative model which captured the essential characteris-
tics of this structure, and (3) to use the model to evaluate the effects on
industry performance of alternative inventory, pricing, advertising, and
supply control policies.
The model was a third generation effort drawing from previous work
by Jarmain (10) and Raulerson (25). It was written in the DYNAMO
simulation language, and was composed of ten interrelated sections: tree
numbers, weather effects, crop size, grower profit, processor disappear-
ance, advertising, FOB price, retail and institutional inventory and sales,
retail and institutional price, and demand.
Validation was on the basis of the model's ability, when given empir-
ical estimates of weather conditions, to reproduce the behavior of the
industry over the 1961-71 period. A quantitative measure of the cor-
respondence between simulated and empirical data was provided by
Theil's inequality coefficient, values of which ranged from 0.55 to 0.98,
indicating that predictions were better than those that would have been
realized with the model pt = at-l, where at and Pt 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.28 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 begin-
ning of the 1961-62 season and covered a 25-year period.
The results were examined from the viewpoints of three major groups
of participants: orange growers, handlers (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.29


28. Two bases were actually used in the study, one for advertising and the
other for nonadvertising policies.
29. The FORTRAN program is available from the authors. See Appendix
E.








The first policy examined placed restrictions 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. These restric-
tions caused the present value of grower profits to increase. They also
reduced crop size and caused an increase in the prices paid by the con-
sumers. 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 handlers or consumers.
Policies that abandoned fully productive orange trees whenever grow-
er 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 also reduced the variance of
FOB price and crop size. Thus, it is possible that these policies could
benefit all three groups of industry participants. Whether this would be
true, however, depends on how handlers and consumers view trade-offs
between the present value and variance of their respective decision vari-
ables.
Three policies were examined which, respectively, increased carry-
overs from 8 to 16 weeks of average consumer demand, restricted price
adjustments to twice each month (rather than twice each week, as pre-
viously assumed) and placed a lower limit on average marginal net reve-
nue which, in effect, placed a floor on prices. Results indicated some
benefits would accrue from more flexible prices; however, these benefits
might be offset by additional costs associated with frequent price changes
which were not evaluated in the study. Gains from the larger carryovers
and the price floor were offset by increased storage costs.
A policy consisting of a combination of restrictions that limited in-
creases in productive capacity whenever grower profits were above
$1.50 per box and also placed a lower limit on average marginal net
revenue was examined. The small gains from this policy, when compared
to the planting restriction alone, probably would not justify the adminis-
trative costs of the price floor.
Finally, a policy which altered the collection and expenditure of ad-
vertising 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 was inversely related to crop size based on the rationale
that a small crop is normally associated with high prices. Also, the pro-
cedure allowed a large proportion of advertising funds to be spent when
there was a large crop to be sold. The policy increased average advertis-
ing from $11.9 million to $19.8 million per season, or by 66 percent.
Given the advertising response functions in the model, this much addi-
tional advertising was unprofitable. Thus, the policy was undesirable
from the viewpoints of all three groups of industry participants. No at-








tempt 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 summary, 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 in-
dustry 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
industry were partially or completely offset by increased storage costs.
The characteristic which dominated policy analysis was the presence of
conflicts of interests among industry participants. In almost every in-
stance, in order for one group to gain, another was placed in a less de-
sirable position. For the policies considered in the study, results provided
insights into costs and returns and their distribution among participants.
The model has potential usefulness in the continuing evaluation of al-
ternative policies, since, as specific proposals develop in the orange in-
dustry, 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
to be studied. 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 in-
crease along with the complexity of policy evaluation.














APPENDICES










APPENDIX A
ALPHABETIZED LIST OF VARIABLE NAMES


AA average advertising (dollars/week)
AC administrative cost (dollars/week)
AFOB weighted average FOB price of orange
products (dollars/gallon single strength
equivalent)
AFU average weekly fruit usage (boxes)30
AGP average grower profit (dollars/box)
AI(I) advertising influence on demand for the Ith
product
AMNR weighted average marginal net revenue
(dollars/gallon single strength equivalent)
AQD(I) average quantity of Ith product demanded
(gallons single strength equivalent/week)
AQS total quantity suggested after the price
adjustment (boxes/week)
AQS(I) quantity of Ith product suggested after
price adjustment (gallon single strength
equivalent/week)
ARP1 average retail price of frozen concentrated
orange juice (cents/6 ounce can)
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)


Defined by
equation(s)
108
101



189A
68
63

110-123

131

294-300

175H


175A-175G

264

265

266

267
102


30. "Box" when used in a definition refers to a 90-pound field box.







Defined by
equation(s)
ATR advertising tax revenue (dollars/week) 100
ATRA advertising tax revenue accumulated
(dollars) 104
ATS advertising tax spending (dollars/week) 105
AWI adjusted weather influences (AWI 1) 38A
BPG(I) conversion factor for product I (boxes/
gallon single strength equivalent) 77-83
BPT yield per tree (boxes/tree) 52
CI competitive influence (.9 CI 1.1) 246
CLF crop lost as a result of freeze damage
(boxes) 54
CP cumulative profit per year (dollars) 66
CPB cost per box (dollars/box) 59
CPD cumulative profits discarded (dollars) 66A
CPDP cumulative profit discard pulse (dollars) 66B
CR crop remaining (boxes) 46
CS crop size (boxes) 45
CSP crop size pulse (boxes) 51
D(I) order rate for the Ith product (gallons
single strength equivalent/week) 225-231
DD desired disappearance (boxes/week) 154
DG delay in growing (weeks) 6
DP length of delay in recovery of hatracked
trees (weeks) 17

DS demand shifter = 0 Sept.-Mar. 283
1 Apr.-Aug.
FA fraction of new trees added 11
FD fruit discarded (boxes/week) 48
FDP fruit discarded pulse (boxes) 49
FHR fraction of productive trees hatracked 29







Defined by
equation(s)
FL fraction of productive trees lost "normally"
or as result of tree abandonment 22
FLOOR lower limit on XAMNR 168B
FOB(I) FOB price of the Ith product (dollars/gal-
lon single strength equivalent) 176-182
FOB(I)S FOB price of Ith product suggested after
the overall adjustment (dollars/gallon
single strength equivalent) 169-175
FSPW fraction spent per week 106
FTLF fraction of productive trees lost as a result
of freeze damage 28
FU(I) fruit used in Ith product (boxes/weeks) 70-76
FUTD fruit used to date (boxes) 47
FYLF fraction of yield lost as a result of freeze
damage 30
GC grower cost (dollars/box) 60
GP grower profit (dollars/box) 58
GPB(I) conversion factor for Ith product (gallons
single strength equivalent/box) 84-90
HLOSS crop loss associated with hatracking
(boxes) 56
HTBP 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 Ith product 197-210
II(I) inventory influence associated with Ith
product 232-245
IP5 smoothed institutional FOB price of frozen
concentrated orange juice (dollars/dozen
32 ounce cans) 272







Defined by
equation(s)
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 Ith 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 restric-
tion became effective (dollars/box) 8
OTP on-tree price (dollars/box) 61
PA processor availability 98
PD(I) processor disappearance of Ith product
(gallons single strength equivalent/week) 91-97
PDRD processor disappearance relative to desired 159
PDS suggested processor disappearance
(boxes/week) 153
PG U.S. population growth (people/week) 292
PGR weekly U.S. population growth rate
(percent) 293
POP U.S. population 291
PQD(I) per capital quantity of the Ith product de-
manded; I = 1, 2, 3, 4 (gallons single
strength equivalent/month) 276-279
PROFT profit (dollars/week) 65
PT productive trees (trees) 1
PTL productive trees lost (trees/week) 19







Defined by
equation(s)

PTLA productive trees lost as a result of "nor-
mal" aging factors or tree abandonment
(trees/week) 21
PTLF productive trees lost as a result of freeze
damage (trees) 20
QD(I) quantity of the Ith product demanded
(gallons single strength equivalent/week) 284-290
RP1 retail price of frozen concentrated orange
juice (cents/6 ounce can) 256
RP2 retail price of chilled orange juice
(cents/quart) 257
RP3 retail price of canned single strength
orange juice (cents/46 ounce can) 258
RP4 retail price of fresh oranges (cents/pound) 259
RPS(I) retail price suggested for the Ith product
(same units as retail prices above) 252-255
S(I) sales of the Ith product (gallons single
strength equivalent/week) 190-196
SFOB smoothed weighted average FOB price
(dollars/box) 189B
TAA time for averaging advertising (weeks) 109
TAFU time for averaging fruit usage (weeks) 69
TAGP time for averaging grower profits (weeks) 64
TAQD time for averaging quantity demanded
(weeks) 301
TAR tree abandonment restriction (dollars/box) 25
TARP time for averaging retail price (weeks) 268
TBP trees becoming productive (tree/week) 2
TCFP(I) smoothing period for FOB price of Ith
product (weeks) 183-189
TCIP time for correcting institutional prices
(weeks) 275

81








Defined by
equation(s)
TCRP(I) time for correcting the retail price of the Ith
product; I= 1, 2, 3, 4 (weeks) 260-263
TFU total fruit usage (boxes/week) 76A
THR trees hatracked (trees/week) 18
TIME simulated time (weeks)
TLOSS crop loss associated with tree kills (boxes) 55
TM time proxy (TM t 4) 293A
TSFOB time for smoothing weighted average FOB
price (weeks) 189C
WCO weeks of carry-over (weeks) 155
WCR weeks of crop remaining (weeks) 67
WD weeks discarded (weeks) 157
WDP weeks discarded pulse (weeks) 158
WI weeks influence 37
WIA(I) weeks of inventory available (weeks) 211-217
WIY weather influence on yield 40
WP weeks passed (weeks) 156
WPY weeks per year (weeks) 10
XAMNR average marginal net revenue after the
overall adjustment (dollars/gallon single
strength equivalent) 168A
XFB(I)S suggested FOB price for Ith product
(dollars/gallon single strength equivalent) 132-138
XFL "normal" fraction of trees lost 23
XFOB1 FOB price of frozen concentrated orange
juice (dollars/dozen 6 ounce cans) 248
XFOB2 FOB price of chilled orange juice (dol-
lars/dozen quarts) 249
XFOB3 FOB price of canned single strength orange
juice (dollars/dozen 46 ounce cans) 250








Defined by
equation(s)
XFOB4 FOB price of fresh oranges (dollars/45
pound carton) 251
XFOB5 FOB price of frozen concentrated orange
juice (dollars/dozen 32 ounce cans) 269
XFOB6 FOB price of chilled orange juice
(dollars/dozen quarts) 270
XFOB7 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 restric-
tion (trees/week) 9
XPQS(I) per capital monthly consumption of Ith
product suggested (gallons single strength
equivalent/week) 139-145
XQD(I) quantity of the Ith product demanded at
time J (gallons single strength equiva-
lent/week) 290A-290G
XQS(I) suggested consumption of Ith product (gal-
lons single strength equivalent/week) 146-152
YDD disappearance associated with profits of
$1.00 per box (boxes/week) 27
YFL fraction of trees lost when tree abandon-
ment restriction was operative 26
YLOSS yield loss (boxes) 57
YTBP young trees becoming productive
(trees/week) 3
ZAMNR average marginal net revenue before con-
sidering whether or not the policy limit
was effective 166
ZTBP trees becoming productive after initial
period (trees/week) 2B










APPENDIX B
LIST OF MODEL EQUATIONS31


Type32


L PT.K = PT.J + (DT) (TBP.JK PTL.JK)
SZTBP.JK if TIME.K t 156
R TBP.KL = or
NTBP.JK if TIME.K < 156
R NTBP.KL = (.178)(PT.K)/WPY
R ZTBP.KL = YTBP.JK + HTBP.JK
R YTPB.KL = DELAY3(XTBP.JK, XDG)
R XTBP.KL = DELAY3(NTP.JK, XDG)
N XDG = DG/233
C DG = 676 weeks
XNTP.JK if NTPR AGP.K
R NTP.KL = or
0 if NTPR < AGP.K


Number
1

2

2A
2B
3
4
5
6


7


1.25, 1.50 or 1.75 if the policy was operative
C NTPR = or
1,000.0 if the policy was inoperative
R XNTP.KL = (PT.K)(FA.K)/WPY34


C WPY = 52


31. Some equations are not in the format required for DYNAMO II, but
can be easily adapted by referring to the DYNAMO II User's Manual (24).
Alternatively, See Powe (22).
32. Type refers to the type of variable as recognized by DYNAMO II on
the left of equation: L = level, A = auxiliary, R = rate, S = supplemen-
tary, C = constant, and N = initial condition.
33. Internal transfer variables are defined only when their meaning is not
readily apparent.
34. The division of WPY was necessary since XNTP was expressed as
trees per week.








Type Number
A FA.K = TABHL(FAT, AGP.K, 0, 3.00, 150) 11
C FAT*= .022/.054/.086/.118/.150/.182/.214 12
R HTBP.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)]35 20
R PTLA.KL = (PT.K)(FL.K)/WPY 21
SXFL.K if GP.K z 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
.15 or .25 if the tree abandonment policy
was operative
C TAR = or 25
.1,000.00 if the tree abandonment policy
was inoperative

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

C YDD = 2.012E636 27




35. Division by DT is necessary as a result of the multiplication that
occurs in equation 1.
36. A disappearance rate of 2.012 million boxes per week was associated
with grower profits of $1.00 per box when weather and inventories were
normal, the demand shifter was equal to its mean value, advertising influ-
ences were equal to 1, U. S. population was 193.89 million, and the yield of
oranges was 4.9 single strength gallons per box.








Type Number
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 137
A XFTLF.K = TABHL(XFTLFT, TIME.K,
52, 572, 52) 31
C XFTLFT* = See table F-10 32
A XFHR.K = TABHL(XFHRT, TIME.K,
52, 572, 52) 33
C XFHRT* = See table F-10 34
A XFYLF.K = TABHL(XFYLFT, TIME.K,
52, 572, 52) 35
C XFYLFT* = See table F-10 36
A WI.K = SWITCH(l, 1, TIME.K)38 36A
A WIY.K = CLIP(WI.K, 1, WI.K, 1) 36B

Option II
A WI.K = NORMRN(1, .06) 37
A XAWI.K = 1 WI.K 38
A AWI.K = MIN(XAWI.K, 1) 38A
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



37. Only one weather option may be included in the card deck during a
given run.
38. Equations 36A and 36B have only mechanical significance in option I.
They set to constants variables determined stochastically under option II.




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