Title Page
 Table of Contents
 List of Tables
 List of Figures
 Structure of the Florida orange...
 Characteristics of dynamo II
 The model
 Policy analysis
 Summary and conclusions
 Biographical sketch

Group Title: model for evaluating alternative policy decision for the Florida orange subsector of the food industry /
Title: A model for evaluating alternative policy decision for the Florida orange subsector of the food industry /
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00098188/00001
 Material Information
Title: A model for evaluating alternative policy decision for the Florida orange subsector of the food industry /
Physical Description: 166 leaves : ill. ; 28 cm.
Language: English
Creator: Powe, Charles E
Publication Date: 1973
Copyright Date: 1973
Subject: Citrus fruit industry -- Florida   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1973.
Bibliography: Bibliography: leaves 163-165.
Statement of Responsibility: by Charles Everitt Powe.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098188
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000415075
notis - ACG2299
oclc - 79608163


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Table of Contents
    Title Page
        Title Page 1
        Title Page 2
        Page i
    Table of Contents
        Page ii
        Page iii
    List of Tables
        Page iv
        Page v
    List of Figures
        Page vi
        Page vii
        Page viii
        Page ix
        Page x
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Structure of the Florida orange subsector
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Characteristics of dynamo II
        Page 15
        Page 16
        Page 17
        Page 18
    The model
        Page 19
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    Policy analysis
        Page 84
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    Summary and conclusions
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    Biographical sketch
        Page 166
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Full Text








The author would like to express his deepest gratitude for the

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

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

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

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

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

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

draft of the manuscript and offering many helpful suggestions.

Many others have aided and befriended the author during his graduate

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

served as chairman of the Food and Resource Economics Department during

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

the Economic Research Service and the Florida Agricultural Experiment

Stations for the much appreciated financial assistance which supported

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

Northeast Regional Data Processing Center of the State University System

of Florida.

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

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

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

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

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

of the manuscript.


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

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

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

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


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

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


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


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

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

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

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

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

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

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

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

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


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

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

Appendix C Derivation of Marginal Net Revenue Relationships 142

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

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

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

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

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


Table Page

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

19 Alphanumeric names used to identify simulation runs . 96

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

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

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

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

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


Figure Page

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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



Charles Everitt Powe

December, 1973

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

A third generation quantitative economic model of the Florida

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

subsector performance of alternative inventory, pricing, advertising

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

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

written in the DYNAMO simulation language.

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

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

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

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

used to measure the correspondence between simulated and empirical data.

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

cated that predictions were better than those that would have been

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

predicted values at time t.

After the model had been accepted as an adequate representation of

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

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


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

by replicating each simulation with five randomly selected weather

patterns. Simulations were started with initial values corresponding

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

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

viewpoints of three major groups of subsector participants: orange

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

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

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

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

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

storage costs provided the information used in policy evaluation.

Policies that reduced long-run supplies of orange products caused

substantially higher grower profits, lower storage costs and higher

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

for other subsector participants. Small gains from policies that failed

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

pletely offset by increased storage costs associated with them.

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

tive advertising proposal, which increased average advertising expendi-

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

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

whether or not one method of collecting and expending advertising funds

was superior to the other.

The characteristic which dominated policy analysis was the presence

of conflicts of interests among subsector participants. In almost every

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


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

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

tribution among subsector participants. With periodic updating, the

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

policy questions develop in the Florida orange subsector.



The Florida orange subsector1 has been characterized by large

variation in orange production and crop value. Production during the

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

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

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

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

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

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

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

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

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

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

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

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

supplies do not readily respond to low prices.

The Problem

Participants within the orange subsector have been concerned with

the large variations in orange prices and supplies. Individual producers

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

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

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

thetic orange beverages and induce the establishment of new orange groves

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

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

run interests of all subsector participants. Supply stabilization would

allow processors to eliminate excess processing capacity and reduce

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

Little is known about the effects of alternative industry policies

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

dynamic and interdependent economic mechanisms operating within the

Florida orange subsector may dampen or amplify the effectiveness of a

policy more than static partial analysis and intuitive judgment would

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

tiveness of policy decisions within the dynamic environment of an

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


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

multiproduct, multimarket model of the orange subsector and to test

policies designed to improve the performance of the orange subsector.

More specific objectives were to:

1. Identify the system structure underlying the orange

subsector's dynamic behavior.

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

orange subsector.

3. Delineate and/or develop measures of performance which

reflect the interest of all participants in the subsector.

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

to improve the performance of the orange subsector. These

policies include:

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

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

tising budget.

c. alternative pricing strategies.

d. alternative supply control policies, including:

(1) elimination of fully productive trees if

grower profits fall below specified levels.

(2) curtailment of new tree plantings when grower

profits are above specified levels.

Previous Work

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

developed a first generation industrial dynamics model of the Florida

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

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

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

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

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

trol policies in stabilizing and raising grower profits. Emphasis was

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

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

Raulerson used average grower profits as a basis for evaluating the

performance of the frozen concentrated orange juice subsector. These

studies provided a basis for the current study.

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

information and it is helpful when this information is summarized in

relatively efficient forms. Information for this model was available

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

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

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

have fostered the entry and proliferation of synthetic and partially

natural citrus flavored drinks.

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

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

orange juice products, orange drinks and synthetic orange flavored

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

strong substitutes. Chilled and canned single strength orange juice

appeared to be weak substitutes. No significant substitution relation-

ship was found between frozen concentrate and canned single strength

orange juice.

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

series data and least squares regression procedures to estimate price-

quantity relationships for major Florida orange products at the FOB level

of the marketing system. These estimates provided the information necessary

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

optimally allocate oranges among product markets for various size crops.

Results based upon the estimated relationships indicated that a 128

million box orange crop maximized industry net revenue at the processor


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

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

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

products in West Europe was elastic and showed development potential.

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

estimate the response of consumer sales with respect to changes in

generic advertising expenditures. These estimates were used in conjunc-

tion with a quadratic programming model to measure possible gains from

allocating advertising funds more efficiently. Information from this

study provided a basis for specifying the influence of advertising on

product demand.

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

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

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

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

analysis indicated that consumer demand functions for these products

differ by region. Regional price elasticity estimates for canned orange

juice compared closely with Weisenborn's national estimates. Estimates

were lower for chilled orange juice and higher for frozen concentrate

than those reported by Weisenborn.

Parvin [16] used yield estimates and standard regression techniques

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

duction for eighteen Florida counties. These estimates provided a basis

for the construction of a weather index for total Florida orange




An understanding of the essential relationships which give rise to

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

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

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

tative economic model.

General Description

The Florida orange subsector is composed of five major groups of

participants: producers, processors and packers, wholesalers, retailers

and consumers. Producers are those individuals and business organiza-

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

oranges. Processors and packers are involved with the conversion of

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

fruit in fresh form. Wholesalers and retailers provide marketing services

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

and processing area into consumer markets. Consumers are those primarily

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

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

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

and institutional.

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

Institutional purchasers are nontax-supported institutions such as

restaurants and drugstore fountains and tax-supported institutions such

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

purchasers are those who buy orange products through retail grocery



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

variety, age distribution and physical environment of bearing orange

trees plus the cultural and weather conditions that exist prior to

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

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

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

factor most feared by Florida orange producers.

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

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

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

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

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

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

More extensive damage requires that the tree be replaced.

Florida orange production is geographically distributed over the

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

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

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

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

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

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

enactment of the Holland Amendment which was incorporated into The Tax

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

all citrus grove development costs and exempts from capitalization

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

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

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

it provides an incentive for citrus producers to concentrate on the

improvement and maintenance of established groves rather than on new

grove development.

The location of the orange producing area is important from the

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

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

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

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

locational movement within the producing area seems to be abridged.

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

Dynamics of the Florida Orange Subsector

A simplified flow diagram of the subsector is presented in

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

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

or institutional inventories and eventually consumption. Dotted lines

in the diagram represent information flows between various system

Processed products include fresh fruit ready for shipment.

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

groves by Florida

Acreage Nonbearing as
County Bearing Nonbearing percentage of bearing

(acres) (percent)



Indian River

Palm Beach

St. Lucie















Total 328,173 27,500

Source: [5].
Counties with

less than one thousand acres are excluded.


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

Associated with information flows are various delay factors. These

delays represent the time lags required for information to move through

the system. Information passed through the marketing system is the

basis for management decisions.

Several allocation problems must be solved by the market mechanism.

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

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

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

Whole fruit must also be allocated among alternative product forms,

markets and consumers.

Given a competitive market system, economic theory indicates that

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

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

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

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

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

system will allocate products among competing customers according to

their ability and willingness to pay. Since information must be

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

The demand for orange products is derived from the utility function

of the individual consumer and product allocation is accomplished through

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

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

sion point. Processor-packers receive information concerning inventory

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

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

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

through the marketing system and eventually affect consumption rates.

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

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

movement from inventories and evaluate the effects of their pricing

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

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

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

period of time and while decision makers are considering new pricing

policies, consumers are still reacting to previous prices.

The relationship between short-run supply and price fluctuations

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

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

affects tree numbers and orange supplies. Assuming relatively stable

demand relationships for orange products, restricted supplies following

freeze damage reduce product inventories and increase the FOB prices of

orange products. Historical data indicate a strong inverse relationship

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

by growers (Figure 3).

During freezes the orange crops of some producers may be severely

damaged while other producers with relatively undamaged crops benefit

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

orange production profitable, tend to reinvest in new orange groves

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

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

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

Crop size
(million boxes)

140 -

120 -

100 -

80 -

60 -

40 -

20 -


Per box returns
- 2.80








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

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

Per box returns









(million trees)

63-64 64-65 65-66 Crop season

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

costs received by growers for
Florida nurseries, 1961-62

61-62 62-63



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

is a set of computer instructions used to translate mathematical models

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

dynamics group at the Massachusetts Institute of Technology.2

Special Features

DYNAMO II has several special features that facilitate model con-

struction. These features include the following:

1. The compiler will reorder equations within a variable type

whenever necessary in order to perform computations.

Reordering will continue until all calculations have been

made or until the compiler has identified equations that

depend on other equations which in turn depend upon the

equation defined, in which case the system is simultaneous

and DYNAMO II prints an error statement identifying the

equations involved.

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

2. System macros in DYNAMO II includes clipping and limiting

functions, exponential delays, maximum, minimum, random

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

and trigonometric.

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

The output routine includes various scaling alternatives and

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

putted chronologically with respect to simulated time and can

be requested for each calculation interval or some multiple

of it.

Time Notation

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


JK- --KL-
interval interval Time

Figure 5. Time notation for DYNAMO II.

In the computational process, DT denotes the period of time

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

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

calculations were previously made and L denotes the next calculation

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

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

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

For definitions see Pugh [20].

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

this recursive fashion, the computer moves through the calculation

process and time in the simulation.

Type of Variables and Computational Sequence

The DYNAMO II compiler is designed to handle three principal types

of variables: levels, auxiliaries and rates.

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

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

defined by equations of the form:

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

the JK interval.

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

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

sometimes by rates from the preceding time interval.

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

and from auxiliaries previously calculated at time K.

The computational sequence in DYNAMO II is levels, auxiliaries and

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

will be available for calculations, equations must be consistent with

the organizational system presented in Table 2. A detailed exposition

of DYNAMO II is given by Pugh [20].

Table 2. Organizational structure for DYNAMO II equations.

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

L Level K J J JK none none

A Auxiliary K K K JK none none

R Rate KL K K JK none none

S Supplementary K K K JK K none none

C Constant none *

N Initial Value none none none

Source: [20, p. 24].

Not permitted.



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

relationships between individual system components. These relationships

together with initial starting values provided the information necessary

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

expended in the specification and estimation of model equations and to

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

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

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

tion and justification. The model presented in this chapter represents

a mathematical formulation of the interrelationships that underlie the

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

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

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

variable names.

The following symbols were used in the flow diagram:

S rates 0 policies

Levels -- material flows

O auxiliaries ---> information flows
- constants



~I, ry

k,- F.7

ri -


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

'" w,.l iar 1~
rr*i~uwrr rr~ur
r.,.,. Lz,
"' "' i
----- ------~i- -



r c I PI S


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

.,,Q. KQ.
A?? >


---- i - -

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

- - - - - - -


La?: i

~Cr~ ~,





Tree Numbers Sector

The number of productive trees was increased by trees becoming

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

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

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

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

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

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

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

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

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

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

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

tial delay approximated the yield response of newly planted orange trees

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

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

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

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


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

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


2See Forrester for detailed explanation of exponential delays

(percent of
mature yield)

Step input

80 r exponential
yield estimate
of the model

empirical estimate

0 5 10 15 20 25 30 35 Age of

Figure 7. Comparison of
yield estimates.

output from exponential delay and empirical

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



N XDG = DG/2 5

C DG = 676 weeks 6

PT productive trees (trees)

TBP trees becoming productive (trees/week)

PTL productive trees lost (trees/week)

YTBP young trees becoming productive (trees/week)

HIBP hatracked trees becoming productive (trees/week)

NTBP initial trees becoming productive (trees/week)

NTP new trees planted (trees/week)

DG delay in growing (weeks)

XTBP internal transfer variables (trees/week)3

XDG internal transfer variable (weeks)

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

TIME simulated time (weeks)

WPY weeks per year (weeks)

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

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

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

planting was in effect (equation 7).

The restriction on new tree plantings was effective when average

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

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

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

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

tree plantings would have occurred without considering the restriction

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

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

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

Figure 8 presents the basis for the assumption concerning this

dependency. Supporting data are presented in Table 3.

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

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


C WPY = 52 10

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

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

XNTP the rate at which new tree plantings would have occurred

without the planting restriction (trees/week)

NTPR the value above which the planting restriction

became effective (dollars/box)

FA fraction of new trees added

Hatracked trees becoming productive were expressed as a ninth order

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

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

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

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

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

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



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

0 .50 1.00 1.50 2.00 2.50 3.00

Returns above
operating costs

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

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



a) W
0 I

'4-1 CW


0 m



1) 0


0 4JH
> 4

u a)
0 o

m >
a4 0 a




'0 4J

C 1





3 0.

41 0


4J i4 >

0 -H

e 0

0. 4

0 0


C 0
o i


a C
0 4-
.0 04


0 0

)a N

4 )
0 U)0

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

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

M m LIn N N -4 VI C 1 0

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

-lr- NiNNMlN l

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

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

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


e ed
4 (0
,-4 Ca




N '0

-H *r4


44 C


0) 4




a) C

0 44




0. 0

ai) a





0 4


Cd 0



newly planted trees became productive. This difference reflected the

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

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

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

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

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

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

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

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




N XDP = DP/3 16

C DP = 208 weeks 17

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


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


THR number of trees hatracked (trees/week)

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

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

factors or tree abandonment (trees/week)

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

FTLF fraction of productive trees lost as a result of freeze


FHR fraction of productive trees hatracked

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

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

of tree abandonment

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

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

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

that simulated a consciously applied policy of tree abandonment on the

part of orange producers. The tree abandonment restriction could be

made inoperative by setting its value at a sufficiently low level

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

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

at which trees were removed from production was positively related to

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

A FL.K= or 22

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

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

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

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

C YDD = 2.012E6 27

XFL "normal" fraction of trees lost

YFL fraction of trees lost when tree abandonment restriction

was operative

GP grower profit (dollars/box)

TAR tree abandonment restriction (dollars/box)

DD disappearance desired (boxes/week)

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

Weather Effects Sector

Values which determined weather effects were obtained in one of two

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

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

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

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

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

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

season (equations 28 30).8

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

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

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

Option I

Option I allowed predetermined values which reflected historical

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

expressed as table functions dependent on simulated time (equations

31 36).

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

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

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

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

C XFTLFT* = See Table 4. 32

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

C XFHRT* = See Table 4. 34

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

C XFYLFT* = See Table 4. 36

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

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

Option II

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

population that was normally distributed with mean one and standard

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

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

weather influence selected was subtracted from one to arrive at an

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

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

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

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

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

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

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

A XAWI.K = 1 WI.K 38

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

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

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

hatrack loss factors, 1962-63

Lossa (proportion)
eason Tree Hatrack Yield Total

1962-63 .226 .080 .066 .372

1963-64 .185 0 .051 .236

1964-65 0 0 .246 .246

1965-66 0 0 .155 .155

1966-67 0 0 -.189 -.189

1967-68 0 0 .176 .176

1968-69 0 0 -.029 -.029

1969-70 0 0 -.057 -.057

1970-71 0 0 -.058 -.058

1971-72 0 0 .012 .012

1972-73 0 0 0 0

aNegative fractions indicate
increase crop size above expected.

that the effect of the factor was to

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

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

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

C XFTLFT* = 0/.15 42

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

C XFHRT* = 0/.35 44

WI weather influence

AWI adjusted weather influence

WIY weather influence on yield

Crop Size Sector

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

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

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

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

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

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

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

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

used (equation 49).

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

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

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


CS crop size (boxes)

CR crop remaining (boxes)

FUTD fruit used to date (boxes)

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

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

FD fruit discarded (boxes/week)

FDP fruit discarded pulse (boxes)

N number of orange products considered in the model

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

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

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

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

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

improved cultural practices provided by growersin response to higher

prices (equations 52 and 53).

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

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

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

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

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.


Error Note

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

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

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

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

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

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

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

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

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

The major effects of the error are the following.

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

ing seasons of unfavorable (favorable) weather.

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

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

the stochastic effect was small.

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

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

on the level of grower profits.


The problem may be corrected by changing equation 60 to


and adding the following equations:

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


N LWI=1 4 60B


A comparison of results from uncorrected and corrected versions of

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

96) considered in the study.

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

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

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

a Large values preferred.

Small values preferred.

cU uncorrected; C corrected.

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

CSP crop size pulse (boxes)

BPT yield per tree (boxes/tree)

AGP average grower profit (dollars/box)

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

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

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

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





TLOSS crop loss associated with tree kills (boxes)

HLOSS crop loss associated with hatracking (boxes)

YLOSS yield loss (boxes)

Grower Profit Sector

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

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

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

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

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

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

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

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

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

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

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

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

C CPB = .85 dollars per box 59

A GC.K = CPB/WI.K 60

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

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

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

C TAGP = 104 weeks 64



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


OTP on-tree price (dollars/box)

GC grower cost (dollars/box)

CPB cost per box (dollars/box)

AFOB weighted average FOB price of orange products

(dollars/gallon single strength equivalent)

TAGP time for averaging grower profits (weeks)

PROFT profit (dollars/week)

TFU total fruit usage per week (boxes)

CP cumulative profit per year (dollars)

CPD cumulative profits discarded (dollars)

CPDP cumulative profit discard pulse (dollars)

Processor Disappearance Sector

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

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

to fruit usage exponentially smoothed with a four week averaging period

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

depended on the disappearance of product I and a conversion factor

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

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

The conversion factor remained at the constant level until the weather

influence was generated. When the weather influence was available,

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

cessor disappearance was a function of retail and institutional demand

and processor availability (equations 91 97). Processor availability

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



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

C TAFU = 4 weeks 69

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


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

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

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

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

WCR weeks of crop remaining (weeks)

AFU average weekly fruit usage (boxes)

TAFU time for averaging fruit usage (weeks)

PD(I) processor disappearance product I (gallons

single strength equivalent/week)

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

single strength equivalent)

GPB(I) conversion factor for product I (gallon

single strength equivalent/box)

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

single strength equivalent/week)

PA processor availability

Table 5. Conversion factors for major orange products.

Conversion factors
Product Gallons single strength
equivalent per 90 pound box

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

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

Advertising Sector

Advertising revenue was equal to fruit usage times the advertising

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

Administrative and other nonadvertising costs were assumed to be a

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

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

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

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

Season Advertising tax rate
Fresh Processed


1962-63 9 9

1963-64 9 9

1964-65 10 8

1965-66 10 8

1966-67 10 8

1967-68 10 8

1968-69 10 8

1969-70 10 8

1970-71 10 10

Source: Personal interview with
Florida Department of Citrus.

the Economic Research Department,

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

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

revenue collected minus revenue spent during the JK interval (equation

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

available for advertising and the fraction spent each week (equation

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

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

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

was not considered in this study.

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

C AC = 26,306 101

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

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



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

C FSPWT* = See Figure 9. 107

ATR advertising tax revenue (dollars/week)

AC administrative cost (dollars/week)

AT advertising tax (dollars/box)

ATRA advertising tax revenue accumulated (dollars)

ATS advertising tax spending (dollars/week)

FSPW fraction spent per week

WP weeks passed (weeks)

Consumers were assumed to respond gradually to advertising expendi-

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




120 I I
.02033a | .02033


40 I .00813

40 .------------------------- ---

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

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

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

determined on the basis of the average advertising expenditure for the

preceding two years (equations 108 117).

Since little data were available, advertising responses for insti-

tutional products were based on the assumption that customer oriented

institutional purchasers such as restaurants and drugstore fountains

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

sumers. Noncustomer oriented institutions such as hospital and military

establishments were assumed to be unaffected by advertising programs

(equations 118 123).11

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

C TAA = 104 weeks 109

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

AA average advertising (dollars/week)

TAA time for averaging advertising (weeks)

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

FOB Price Sector

The FOB price of orange products was the mechanism through which

allocation was accomplished. Allocation occurred in a resursive fashion.

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

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

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

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

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

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

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

attempted to increase consumption and order rates by reducing prices.

When it appeared that shortages would occursthe model increased prices.

Price adjustments designed to alter fruit usage were accompanied by

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

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

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

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

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

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

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

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

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

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

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

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

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

Suggested FOB prices along with demand equations and advertising influ-

ences on demand provided estimates of the monthly per capital quantity

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

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

these estimates suggested processor disappearance (equations 146 153).

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

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

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

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

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

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

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

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

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

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

gallon single strength equivalent)

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

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

QC .145935 -.106017 -.009218

QR .035136 -.047900 -.000294

QR .023731 -.027704 .000131

O .126176 -.117840 c

1 .052886 -.055452 c

Q .078273 -.058530 c

QCSSOJ .173864 -.185287

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

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

Table 8. Mean values associated with estimated demand relationships.

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

FCOJR .5242 .0867

COJR .5532 .0085

CSSOJR .5547 .0084

FOR .7618 .0364

FCOJI .7492 .0113

COJI 1.0600 .0162

CSSOJI .9043 .0062

The subscript refers to the retail or institutional market.


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

Product Market
Retail Institutional

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

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

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

Fresh oranges August, 1962 a
July, 1963

aNot applicable.

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

strength equivalent)

AMNR weighted average marginal net revenue (dollars/

gallon single strength equivalent)

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

(gallons single strength equivalent/week)

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

gallon single strength equivalent)

XPQS(I) monthly per capital consumption of product I

suggested (gallons single strength equivalent

per capita/month)

POP U.S. population

XQS(I) suggested consumption of Ith product (gallons

single strength equivalent/week)

PDS suggested processor disappearance (boxes/week)

In order to maximize profits, economic theory indicates that a

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

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

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

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

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

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

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

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

Since prices and marginal net revenues are positively related, profit

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

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




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

Prices suggested by this average value will be associated with equal

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

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

and increased, respectively. This technique adjusts relative prices;

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

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

pare processor disappearance suggested with processor disappearance


Desired disappearance was a function of crop remaining, the number

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

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

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

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

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

the beginning of each season (equations 156 158).

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

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

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

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

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

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

N WDP = (WPY/DT) 158

WCO weeks of carry-over (weeks)

WD weeks discarded (weeks)

WDP weeks discarded pulse (weeks)

Processor disappearance relative to desired was the variable that

determined whether an adjustment in product flow was necessary (equation

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

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

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

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

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

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


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

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

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

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

A Z.K = R.K/DT 163

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

N E = 165

PDRD processor disappearance relative to desired

When adjustments were allowed, average marginal net revenue was

adjusted and prices increased or decreased according to processor dis-

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

disappearance was greater than desired, average marginal net revenue was

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

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

adjustment was increased by the Q variable as the disappearance ratio

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

policy option allowed the specification of a limit below which average

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

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

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

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

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

smoothed (equations 189B and 189C).

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

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

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


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

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

(DS.K) 169-175

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

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

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

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

C TCFP(I) = 4 weeks 183-189

E (FU(I).JK)(FOB(I).K)
A AFOB.K = I = 1 189A
C TSFOB = 12 weeks 189C

ZAMNR average marginal net revenue before considering

the policy limit

FLOOR lower limit on XAMNR

XAMNR average marginal net revenue after the overall adjust-

ment (dollars/gallon single strength equivalent)

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

adjustment (dollars/gallon single strength equivalent)

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

adjustment (gallon single strength equivalent/week)

AQS total quantity suggested after the price adjustment


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

I product (weeks)

SFOB smoothed weighted average FOB price (dollars/box)

TSFOB time for smoothing weighted average FOB price (weeks)

Retail and Institutional
Inventory and Sales Sector

Sales of orange products were equal to the product consumers

demanded as long as adequate supplies were available at the consumer

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

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

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

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

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

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

197 210).

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

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

217). Inventories were increased by processor disappearance and

decreased by product sales (equations 218 224).

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

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

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

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

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

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

C IA3T* = 0/.85/1.0 202

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

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

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


Inventory level (C(I))


FCOJR and 1.3
R and I

COJ 1.2
R and I

R and I

FOR .5

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

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

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

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

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

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

C IA7T* = 0/.85/1.0 210

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

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

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


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

Ith product

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

strength equivalent/week)

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

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

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

single strength equivalent/week)

Retail and institutional order rates depended on the level of

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

competitive influence which was associated with future price expecta-

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

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

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

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

processor disappearance relative to desired and reflected the influence

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

When the ratio of suggested and desired processor disappearance

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

and retail and institutional purchasers increased their orders in an

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

when processor disappearance relative to desired was less than unity,

order rates were reduced in anticipation of lower FOB prices.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

II(I) inventory influence associated with Ith product

CI competitive influence

Retail and Institutional Price Sector

Retail prices of orange products normally adjust to levels suggested

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

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

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

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

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

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

product sales, and the level of inventories probably influence the

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

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

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

exponentially smoothed over an adjustment period determined the retail

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

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

264 268).

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

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

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

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

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

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

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

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

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

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

C TCRP1 = 2 weeks 260

C TCRP2 = 2 weeks 261

C TCRP3 = 4 weeks 262

C TCRP4 = .5 weeks 263

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

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

C TARP = 2 weeks 268

XFOB1 FOB price of frozen concentrated orange juice

(dollars/dozen 6 ounce cans)

XFOB2 FOB price of chilled orange juice

(dollars/dozen quarts)

XFOB3 FOB price of canned single strength orange juice

(dollars/dozen 46 ounce cans)

XFOB4 FOB price of fresh oranges

(dollars/45 pound carton)

RPSI retail price suggested for frozen concentrated

orange juice (cents/6 ounce can)

RPS2 retail price suggested for chilled orange juice


RPS3 retail price suggested for canned single strength

orange juice (cents/46 ounce can)

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

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

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

product (weeks)

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

as retail price suggested)

TARP time for averaging retail price (weeks)

The heterogeneity of the institutional market makes data collection

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

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

chase orange products through retail stores. For example, restaurant

sales accounted for the consumption of about 88 million gallons of

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

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

tutional consumption of orange products during 1971 was estimated to be

196 million single strength gallons. This represented about 28 percent

of total 1971 orange juice consumption.

Demand estimates for institutional products at the FOB level were

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

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

should be noted that the model estimates neither wholesale nor consumer

prices for orange products sold through institutional outlets.

The FOB prices of institutional products were converted to units

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

were then exponentially smoothed and used as inputs to the demand

sector (equations 272 275).

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

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

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

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

C TCIP = 2 weeks 275

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

XFOB6 FOB price of COJ (dollars/dozen quarts)

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

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

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

TCIP time for correcting institutional price (weeks)

Demand Sector

Relationships used to estimate product consumption are presented

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

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

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

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

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

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

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

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

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

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

institutional inventory and sales sector (equations 294 301).

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

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

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

(I = 5, 6, 7)


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

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

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

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

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

QFO .152239 cents/pound -.011138 c

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

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

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

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

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

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

cNot included in model.

Table 12. Mean values associated with estimated demand relationships.

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

FCOJR 14.43 cents/6 ounce .0867

COJR 30.74 cents/quart .0085

CSSOJR 32.31 cents/46 ounce .0084

FOR 10.40 cents/pound .0364

FCOJI $8.99/dozen 32 ounce .0113

COJI $3.18/dozen 32 ounce .0162

CSSOJ $3.90/dozen 46 ounce .0062

The subscript refers to the retail or institutional market.

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

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

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

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

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

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

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

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

C TAQD = 2 weeks 301

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

(gallons single strength equivalent/month)

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

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

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

TM TIME proxy (TM -4)

TAQD time for averaging quantity demanded (weeks)

Initial Conditions

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

puter simulation is that initial conditions be specified. The values

specified in this section roughly approximate subsector conditions at

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

specified, the DYNAMO compiler had the information required to compute

initial values for level equations. These values were then available

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

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

solution order of equations when necessary.

PT = 18.7E6

WI = 1

CR = 108.8E6

FUTD = 0


CP = 0

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

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

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


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

N WP = 0

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


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

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

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

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

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

Initialization for
Sector Equation(s)

1 1

2 37

3 46

3 47

4 63

4 66

) 5



7) 7


7) 7


XQD(I) = QD(I)

POP = 184.8E6

AQD(I) = QD(I)















(I = 1, . 7)


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

0 1

*i 4 0 Co ) 0 r.

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


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

*> a3 'i- r r^

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


p1 4J rQ rQ '--

0 144

.0 CA -4 C! O

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

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

a) -4 a) a)

4.3 a) -4
4J a) a)

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

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


Table 14. Net marginal revenues used to initialize model.

Product Market
Retail Institutional

(dollars/gallon single
strength equivalent)

FCOJ .105654 .516743

COJ .410560 1.043205

CSSOJ .145009 .523586

FO .560814 a

Source: Calculated.

aNot applicable.

Table 15. FOB prices used to initialize model.

Product Market
Product Retail Institutional

(dollars/gallon single
strength equivalent)

FCOJ .862362 .856507

COJ .660564 1.278780

CSSOJ .688240 .918408

FO .911312 a

Source: Calculated.

aNot applicable.



The usefulness of the model presented in the preceding chapter

depends upon its ability to characterize the response of the Florida

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

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

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

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

basis of a set of criteria established for this purpose. However, the

choice of criteria is a subjective process. The model can also be

evaluated from the standpoint of the reasonableness of the estimates

and assumptions presented in Chapter IV. The purpose of this chapter

is to provide insight into the model's ability to predict.

In his book, Computer Simulation Experiments with Models of

Economic Systems, Naylor makes the following statement:

In general, two tests seem appropriate for validating
simulation models. First, how well do the simulated values
of the endogenous or output variables compare with known
historical data, if historical data are available? Second,
how accurate are the simulation model's predictions of the
behavior of the actual system in future time periods? [15, p. 21]

In this study, a simulation was made to determine whether or

not the model would converge when run for a long period of time with

weather conditions held constant. The model was then evaluated on the

basis of its ability, when given empirical weather data, to reproduce

the behavior of the orange subsector during the 1961-71 period.


Long-run Stability

The model was intitialized to reflect, as nearly as possible,

conditions that existed in the orange subsector at the beginning of the

1961-62 crop season. During the run stochastic weather generation was

suppressed and weather effects were set equal to constants that reflected

average weather conditions. With 1961-62 initial conditions, there was

reason to expect the model to start from a disequilibrium position.

However, a run period of one hundred years was believed long enough to

allow the model to overcome initial disequilibrium and to provide an

opportunity for observing whether the model, if left undisturbed, would

come to a stable position. Partial results of this run are presented

in Figure 11.

In Figure 11 variables were plotted against time and the appropriate

vertical scale. The vertical scales are identified by groups of numbers.

Each number is associated with a respective variable identified by

letter. The number of mature productive orange tree equivalents,

represented by T, was initialized at 18.7 million. After the start of

the simulation this figure increased at a rapid but decreasing rate for

approximately sixteen years. After this period, tree numbers remained

relatively stable within the 40-41 million range for about six years,

before taking a slight dip and beginning a substained increase that

lasted the remainder of the run. At the end of the simulation the

number of mature productive orange trees stood at 94.7 million and had

been increasing by 1.2 million trees per year. This behavior may be

compared to the behavior of average grower profit during the same period.

At the beginning of the run, prices were initialized at levels which

yielded an average grower profit of $1.99 per box. The fact that this

m a
) 0I
4J 4J


U 441

o cl


S 4

4d b 444

44 044 0 0
*-4 l-4 60 4J .Q -
'o rlM M -

o W 040 4 01

t4 bH- I' 4 0 (b P

Id P 4
> 1 4 il 4

0~N0 '440~ C'N~0
'44 -.1 c-i'
10 oom



dG d

F) X
4 4J
440 44





O 4



a )
4 4

o 4




0 441 441

4 4J

z4 4
M 0r
44 U t
'44 44-
44 .44a
44 4

figure was immediately adjusted downward by the model seemed consistent

with the behavior that would have been expected from the orange sub-

sector, if rather than having experienced the 1962-63 freeze, "normal"

weather conditions had been encountered. The absence of freeze damage

would have resulted in an estimated 42-44 million additional boxes of

fruit during the 1962-63 season and would have prevented the temporary

or permanent loss of approximately 13.5 million trees. In the simula-

tion, average grower profit ranged from $1.99 to $.09 per box. Compared

to a realized range during the 1961-70 period of $2.52 to $.21 per box,

the simulated range seemed reasonable, particularly considering that the

model, operating with "normal" weather conditions generated larger

supplies than those experienced by the orange subsector. Other variables

in Figure 11 follow similar patterns.

Average marginal net revenue stabilized at a negative 16 cents per

box. This behavior seemed inconsistent with the behavior required to

maximize long-run net revenue at the FOB level and reflected a tendency

of the model to overplant trees even under "normal" weather conditions.

This overplanting tendency may represent a hedge against recurring crop

damage. At any rate, it resulted from the specification of new tree

plantings relative to average grower profits. As specified in Chapter

IV (equations 11 and 12), the response table required that new tree

plantings occur at the minimum rate of 2.2 percent of productive orange

trees even when average grower profit was zero or negative. An earlier

simulation, which used a response function that allowed new tree plantings

to fall to zero, reached a stable position after approximately the same

number of years with an average marginal net revenue of $-.03 per box.

Differences between the two runs indicate behavior of the model is

sensitive to changes in this relationship.

The purpose of this run was to determine whether the model would

stay within reasonable ranges and exhibit relatively stable behavior or

whether it would explode if given time to overcome its initial disequi-

librium. Results of the run seemed to affirm reasonable behavior, i.e.,

the model converged.

Retrospective Comparison

A simulation was made with initial values corresponding to

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

weather effects specified to replicate as nearly as possible those that

occurred during the 1961-62 through 1971-72 period. Results were com-

pared with empirical data reflecting the behavior of the Florida orange

subsector during the same period.

Tree Numbers

Figure 12 presents a comparison of simulated and observed numbers

of mature productive orange tree equivalents during the 1961-62 through

1971-72 period. In the simulation, the tree numbers variable was

initialized at 18.7 million and had increased to 22 million trees by the

end of the 1961-62 crop season.I As a result of the freeze which

occurred in the simulation at the beginning of the 1962-63 season, tree

numbers were reduced to 16.9 million by mid-season. Carry-over effects

of the freeze also caused a reduction in productive trees during 1963-64.

During this period, an almost identical pattern of change was reflected

Ilnitialization of tree numbers at 18.7 million probably over-
stated the number of trees in existence at the beginning of the 1961-62
season. Reflection indicated that this figure was more nearly associated
with the end than with the beginning of the season.

04J 0 > ) 4 0
Z ) 0 0 4 -4
0 9 0-r- 0 0

0d a- -o I --





13 1



0 co


4 0

0 a


r n

in the observed data; however, levels of observed tree numbers were

approximately ten percent lower than those generated by the model.

Following the 1963-64 season, the combined effect of new trees becoming

productive and damaged tree recovery produced a sharp increase in tree

numbers. This increase was particularly evident in the time path of the

observed variable and may have partially resulted from the reassessment

of freeze damage. At any rate, there were 3.5 million more trees

observed than simulated in 1964-65. Further comparison of the time

paths revealed high correspondence between observed and simulated tree

numbers during the 1966-67 and 1968-69 seasons. However, after the

1968-69 season, simulated tree numbers increased at a rate faster than

the rate based on the observed data point.

A summary of observed versus simulated changes in tree numbers is
presented in Figure 13. In this diagram, completely accurate predic-

tions fall on the line of perfect forecasts. As points move away from

this line, predictive accuracy decreases. The second and fourth quad-

rants of the diagram map turning point errors, i.e., the prediction of

a change in direction when no change occurred or a change in direction

not predicted. For the six points for which comparable tree numbers

data were available, the model overestimated realized changes three

times, underestimated once and predicted one point on the perfect

forecast line.

A quantitative measure of the correspondence between observed and

simulated values was provided by Theil's inequality coefficient [24,

p. 28]. Of the several versions of the coefficient, the one used in

A detailed discussion of the prediction-realization diagram is
given in [24, pp. 19-26].




Figure 13. Prediction-realization
of mature productive orange trees.

I I (hundred
25 50 75 thousands)

diagram for changes in numbers

A = a -aP = -p
t t t-l t t t-l

this study was defined as follows:

E (a Pt)2
S t t 1/2
U= E (at at-1) 2

where at represents the observed or actual value at time t and pt repre-

sents the simulated or predicted value. In the case of perfect fore-

casts, Theil's coefficient takes on the value zero. The value of one

indicates that predictions are no better than those that would have

been made with the model pt = at-,. For the tree numbers data, the

coefficient was equal to .5513 indicating that the root mean square

prediction error was 55 percent of the root mean square error that would

have been realized had predictions been made with the model pt = at-l.

Crop Size

Figure 14 presents a comparison between simulated and observed crop

size data. In general, the path of the simulated variable corresponded

fairly closely with observed behavior; however, noticeable disparities

existed in 1963-64 and after the 1967-68 crop season. After 1967-68,

estimates made by the model overstated crop size and the magnitude of

the overstatement increased each season. The prediction-realization

diagram, Figure 15, indicated that of the nine changes generated, the

model overestimated five and underestimated the remainder. Theil's

coefficient, equal to .98, indicated that predictions were slightly

better than those that would have been realized with the no-change model.

On-Tree Price

A comparison of observed and simulated on-tree prices of Florida

oranges is presented in Figure 16. Again, the general behavior of the

Crop size (millions of boxes)


150- / actual

100- y

\ /
\ /

\ /

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

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

Source: [3, 1971-72 season] and simulated.

o 10

"I I (millions
10 20 30 of boxes)

0 0
4 *

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

At = at-at-

t = t t-1

Source: [3, 1971-72 season] and simulated.

u' o u o

CN C' r-

CN C d

I Vo

0' 01


r--i t

I d




I 0


'o CO



\D l0

, I

C' C
so ,-

O 0

cn W o


1 *4 0 4
0 C-0 O
o 0o.-'.0

simulated variable corresponded with observed data. Restricted supplies

following the 1962 freeze led to increased prices; whereas, the large

crop of 1966-67 caused a sharp price dip. A relatively small crop in

1967-68 was again associated with increased prices. The prediction-

realization diagram, Figure 17, indicated that the model underestimated

the magnitude of four changes, overestimated three and made two turning

point errors--one between the 1963-64 and 1964-65 seasons and another

between 1969-70 and 1970-71. The Theil coefficient equaled .67.

Market Proportions

As mentioned in Chapter IV, in order to maximize net returns,

processors as a group should attempt to allocate oranges so as to equate

marginal net revenues among product markets. Table 16 shows proportioned

allocations of the orange crop as observed during the 1963-64, 1964-65

and 1965-66 seasons and as performed by the model during the validation

period.3 As can be seen from the data, the proportion of the orange

crop allocated into a given product-market varied somewhat from season

to season. This variance, however, was relatively insignificant compared

to differences between simulated and observed allocations. Relative to

observed, the model allocated fewer oranges to each retail product and

more to each institutional product.

The allocation performed by the model, though somewhat different

from the observed, followed directly from the derived marginal net

revenue equations (equations 129 135). The demand equations used in

the derivations were obtained from several sources and most included

variables exogenous to the simulator. Since the model was designed to

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


.0 .50
0 0

per box)

per box)



Figure 17. Prediction-realization diagram for changes in on-tree
At = at-at-1 t = P t-i

Source: [3, 1968-69 season, p. 95, and 1971-72 season, p. 104] and

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

Season Product-Marketa
1 2 3 4 5 6 7


1963-64 41.6 7.3 4.2 33.5b 5.5 4.4 3.5
1964-65 44.7 7.0 3.6 27.8b 6.3 7.5 3.1
1965-66 41.9 8.0 4.2 26.2b 5.3 11.5 2.9

1963-66 42.8 7.5 4.0 28.7b 5.7 8.2 3.1
1- -- ^ - I -
83 17

1961-62 22.6 4.7 2.3 31.0 7.8 12.9 18.7
1962-63 25.7 3.9 1.7 29.8 7.8 15.1 16.0
1963-64 26.5 3.9 1.7 28.6 7.8 15.6 15.9
1964-65 27.7 3.8 1.6 26.8 8.0 16.4 15.8
1965-66 25.1 4.5 2.2 27.3 8.1 14.5 18.3
1966-67 24.8 6.0 3.2 18.4 9.4 13.9 24.3
1967-68 24.2 4.8 2.4 27.0 8.3 13.8 19.5
1968-69 23.3 5.6 2.9 24.3 8.7 13.1 22.2
1969-70 22.8 5.6 3.0 24.7 8.7 12.8 22.4
1970-71 23.3 5.9 3.1 22.7 9.0 13.0 23.1
1971-72 23.5 5.8 3.0 22.9 8.9 13.2 22.6
1972-73 23.5 5.9 3.0 22.5 9.0 13.1 23.0

1961-73 24.1 5.3 2.7 24.9 8.6 13.7 20.9

57 43

Source: [25, Appendix C] and simulated.

aRows may not add to one hundred due to rounding.

Assumes 12,000 fresh oranges equals 396.75 gallons single strength

CSimulated figures were at the end of each season; however, within
season variation was minor.

operate in a recursive fashion, the coefficients of these variables were

removed from the equation by incorporating them into the intercept. The

resulting equations, along with cost and margin information, were used

to derive marginal net revenue equations for each product-market. An

examination of these relationships revealed that several cross-product

coefficients had signs different from those expected and in some cases

the cross-price effect outweighted the own-price effect. Further examina-

tion indicated that these coefficients could lead to results inconsistent

with economic theory, e.g.,when all prices increase, total quantity

demanded increased. In order to prevent this problem cross-product

coefficients were incorporated into intercept terms. The loss of these

coefficients resulted in relatively naive demand equations. A different

set of equations might have led to results more consistent with the

observed data.


The obvious implication of the preceding comparisons is that there

exists room for improvement in the predictive accuracy of the DYNAMO

model. However, a definite similarity existed between real world and

model behavior especially with regard to turning points and it was

believed that the model captured the dynamics of the orange subsector.



The term "policy" as used in this chapter refers to changes in

either the model's operating rules or its structure. Most policies

were implemented by parameter changes in functions discussed in Chapter

IV. These changes altered the operating rules of the model and affected

performance by reducing orange supplies, increasing desired carry-overs,

and by modifying pricing and advertising schemes.

A set of five runs, each covering a twenty-five year period, was

made to provide a base with which to compare policy results. This base

was an attempt to characterize the orange subsector as it is currently

structured. Ten policies were then examined. Each run started with a

set of initial conditions based on the 1961-62 crop season and was

associated with weather effects computed by the stochastic procedure.

The weather effects used for the base run were also used for each policy

and provided comparable results for a variety of weather conditions.1

Policies were replicated five times--once with each of the weather sets

presented in Table 17. The weather effect for each season was greater

than, equal to, or less than one and denoted better than average,

average or poorer than average weather conditions, respectively.

DYNAMO contains a function which generates "pseudo random numbers"
that satisfy all of the statistical tests for randomness. However, each
number is calculated from the previous one by a fixed procedure. Thus,
a given noise seed always generates the same sequence of numbers. In the
normal distribution mode, the DYNAMO procedure does not perfectly repro-
duce a normal distribution in that no number can diverge from the mean by
more than 2.4 standard deviations. For more information, see Pugh [20].

Table 17. Weather conditions used

in the five simulation runs for each

Season Weather sets
1 2 3 4 5

2b 1.14 1.01 1.07 1.07 1.10
3 1.01 .92 .89 .99 1.03
4 1.11 .95 1.01 .92 1.06
5 .95 .95 .99 .98 .97
6 1.08 1.11 .99 .96 .89
7 1.00 1.06 1.00 1.08 1.08
8 .98 1.00 1.05 1.02 .87
9 .94 .98 .95 1.01 1.02
10 1.11 1.08 1.03 1.03 .99
11 1.00 .97 .98 .98 1.01
12 .93 .91 1.05 1.01 1.04
13 1.00 -88 1.07 .96 .98
14 .97 .98 .97 1.03 1.02
15 1.06 1.06 .96 1.04 1.01
16 1.05 .96 .94 .95 .99
17 1.07 1.07 .94 .96 .97
18 1.05 .97 1.06 1.01 1.06
19 1.00 .99 1.06 1.04 1.03
20 .99 .98 1.01 1.04 .96
21 1.00 1.00 1.04 .90 .96
22 1.04 1.00 .92 .92 .97
23 .92 .95 1.08 1.01 1.01
24 1.03 1.03 1.08 1.03 .98
25 .97 .97 1.00 1.02 1.04

Weather conditions are based on an index (average weather = 100).
The larger (smaller) the index the more favorable (unfavorable) the
weather. The noise seeds used to generate weather sets 2 through 5 were
943805, 7641403, 10861407 and 86451509, respectively. The seed for
weather set 1 was already in the noise function.

Initial values were used for the first season.



The policies examined in this study are briefly described as


1. Restricted tree planting. A restriction was placed on new

tree planting whenever average grower profits rose above

specified levels. Three levels were considered in the study,

$1.25, $1.50 and $1.75 per box. When the policy was opera-

tive, tree planting was permitted or not permitted depending

on whether grower profits were below or above the level

specified. On first glance, this restriction may seem in

conflict with logical decision making since high profits would

be expected to call forth increased supplies. However, in

the orange subsector, growers have tended to react to high

profits as if a permanent shift in marketing structure has

occurred in spite of the fact that high grower profits have

normally been associated with a freeze. Consequently, they

tend to overinvest in new orange groves. It takes several

years for these groves to become fully productive, after which

the additional supplies have precipitated periods of relatively

low returns and low grove investment. These reactions have

caused the subsector to be characterized by production and

price cycles and it was believed that a restriction on tree

plantings during periods of high grower profits might exert a

stabilizing influence on the system.

2. Tree abandonment. The tree abandonment policy, when operative,

removed fully productive trees from the system whenever grower

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