• TABLE OF CONTENTS
HIDE
 Copyright
 Front Cover
 Table of Contents
 List of Tables
 Introduction
 The allocation model
 Marginal cost and net marginal...
 Optimum market allocation...
 Summary and conclusions
 Appendix tables
 Acknowledgement
 Literature cited






Group Title: Bulletin - University of Florida. Agricultural Experiment Station - no. 736
Title: Market allocation of Florida orange production for maximum net returns
CITATION PAGE IMAGE ZOOMABLE PAGE TEXT
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00027534/00001
 Material Information
Title: Market allocation of Florida orange production for maximum net returns
Series Title: Bulletin University of Florida. Agricultural Experiment Station
Physical Description: 35 p. : ; 23 cm.
Language: English
Creator: Weisenborn, David Ervin, 1940-
Polopolus, Leo
McPherson, W. W ( Woodrow Wilson )
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1970
 Subjects
Subject: Orange industry -- Florida   ( lcsh )
Oranges -- Marketing   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Bibliography: p. 35.
Statement of Responsibility: David E. Weisenborn, Leo Polopolus, W.W. McPherson.
General Note: Cover title.
General Note: "In cooperation with the Florida Department of Citrus"--T.p.
Funding: Bulletin (University of Florida. Agricultural Experiment Station) ;
 Record Information
Bibliographic ID: UF00027534
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 000929595
oclc - 18405843
notis - AEP0386

Table of Contents
    Copyright
        Copyright
    Front Cover
        Page 1
    Table of Contents
        Page 2
    List of Tables
        Page 3
        Page 4
    Introduction
        Page 5
        Purpose of method
            Page 5
        List of symbols
            Page 6
    The allocation model
        Page 7
    Marginal cost and net marginal revenue functions
        Page 8
        Empirical estimates of marginal cost
            Page 8
            Model equations for total cost
                Page 9
            Data for cost analysis
                Page 9
            Results of cost analysis
                Page 10
        Net marginal revenue functions
            Page 11
    Optimum market allocation results
        Page 11
        Actual market allocations
            Page 12
        Optimum constrained allocation
            Page 12
            Average seasonal quantity
                Page 12
                Page 13
            Above average crop sizes
                Page 14
            Primary and secondary market allocation
                Page 15
        Optimum unconstrained allocation
            Page 16
        Fresh and processed market allocation
            Page 16
            Page 17
    Summary and conclusions
        Page 18
        FOB versus on-tree optimum allocations
            Page 19
        Required adjustments to achieve optimal allocations
            Page 19
            Page 20
        Loses may be necessary in certain product markets in order to maximize overall industry net revenue
            Page 21
        Supply abandonment
            Page 22
        General conclusion and limitations
            Page 23
    Appendix tables
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Acknowledgement
        Page 33
        Page 34
    Literature cited
        Page 35
Full Text





HISTORIC NOTE


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida




Bulletin 736 March 1970


/

Market Allocation of Florida Orange


Production


for Maximum


Net Returns


David E. Weisenborn
Leo Polopolus
W. W. McPherson






HUME LIBRARY

JAN 12 1971

I.F.A.S. Univ. of Florida


Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
J. W. Sites, Dean for Research
University of Florida, Gainesville
in cooperation with the
Florida Department of Citrus












CONTENTS


Page
LIST OF TABLES ...............-........ ....... ----- 3
INTRODUCTION ...........-- .................-. 5
Purpose and Method .............. ............. ...------ -.. 5
List of Symbols --............ .............. 6
THE ALLOCATION MODEL .................................. 7
MARGINAL COST AND NET MARGINAL
REVENUE FUNCTIONS ........................ ....... 8
Empirical Estimates of Marginal Cost ....................-.-- .--.--. 8
Model Equations for Total Cost ............-.....:.---- ----- 9
Data for Cost Analysis ..................... .... ..-. .-- -.. 9
Results of Cost Analysis ----.........~.............-- 10
Net Marginal Revenue Functions -............................ 11
OPTIMUM MARKET ALLOCATION RESULTS .............---------- 11
Actual Market Allocations ----....................-- ---- 12
Optimum Constrained Allocation ...-........ -------.......... 12
Average Seasonal Quantity ................--.......... -..- 12
Above Average Crop Sizes ......-.......--.--.--------- 14
Primary and Secondary Market Allocation ..............------- -- 15
Optimum Unconstrained Allocation ..............---------- 16
Fresh and Processed Market Allocation ............ --------------. 16
SUMMARY AND CONCLUSIONS ...............~.~.-.....- 18
FOB Versus On-Tree Optimum Allocations ...---........--------------- 19
Required Adjustments To Achieve Optimal Allocations ...........-- 19
Losses May Be Necessary in Certain Product Markets in Order
To Maximize Overall Industry Net Revenue .. ...._--------------- 21
Supply Abandonment ....................... -------.-------- -- 22
General Conclusion and Limitations .......--...... -----. ....- 23
APPENDIX TABLES ..... ... ...... -... .....-------------- ------------------ 24
ACKNOWLEDGMENTS .....................----.----- .......33
LITERATURE CITED ...............-...- .... .-...-- ... -- ---... 35













LIST OF TABLES


Table Page

1 Total and Net Revenue for the Average Season Using Actual
Quantities of Oranges Sold in Each Product Market
Category, FOB Level ..................... .. .................. 13

2 Total Revenue and Maximum Net Revenue for the Average
Season With a Total Quantity Constraint of 73.22 Million
Boxes of Oranges ..... ......... .......... ..- 13

3 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 150 Million Boxes of Oranges for the Average
Season ...... ...... ..- -- --.- .. 14

4 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 200 Million Boxes of Oranges for the Average
Season ..... ......... ... .... ........ .. .------. 14

5 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 100 Million Boxes of Oranges with Allocation
of 80% to the Primary Market and 20% to the Secondary
M market ...-. -..... .... .... ... ..... 15

6 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 150 Million Boxes of Oranges With Allocation
of 80% to the Primary Market and 20% to the Secondary
M market ... .......... .. .. .... ......... .... 16

7 Estimated Total Revenue and Maximum Net Revenue for the
Average Season With Quantity and Product Market Allo-
cation of Oranges Unconstrained .............. ..... 17

8 Estimated Total Revenue and Maximum Net Revenue, Uncon-
strained Processed Orange Markets and an Upper Constraint
of 15 million Boxes in the Fresh Foodstore Sector ............ 18

9 Percentage Distribution of Total Orange Quantity Among
Product Markets, Actual, Constrained, and Unconstrained
Allocations ....... ....... ......... 20



APPENDIX TABLES

1 Estimated Total Cost Functions for Selected
Orange Products .. ~. -... .--- -------- ------. 25












LIST OF TABLES (cont.)


Table Page

2 Net Marginal Revenue Functions for Eight Orange Product
Market Categories -- -....................-- 26

3 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 100 Million Boxes of Oranges With Allocation
of 70% to the Primary Market and 30% to the Secondary
M market .. .... ... .. .... .. ..-.- ..- --- 28

4 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 100 Million Boxes of Oranges With Allocation
of 60% to the Primary Market and 40% to the Secondary
M market .......... .....--...... ........... -- -- 29

5 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 150 Million Boxes of Oranges With Allocation
of 70% to the Primary Market and 30% to the Secondary
M market ................... ...........- ...- -. 30

6 Estimated Total Revenue and Maximum Net Revenue Using a
Crop of 150 Million Boxes of Oranges with Allocation
of 60% to the Primary Market and 40% to the Secondary
Market .......... 31








MARKET ALLOCATION OF FLORIDA ORANGE

PRODUCTION FOR MAXIMUM NET RETURNS

David E. Weisenborn, Leo Polopolus and W. W. McPherson'

INTRODUCTION
An important and uncoordinated decision made each year by
the Florida orange industry involves the allocation of a given
supply among alternative product forms and marketing sectors.
Ideally, the industry would prefer to allocate in such a manner
that the net revenue to the industry would be maximized.2 This
requires knowledge of the relevant demand and cost relation-
ships existing for the various product forms in each of the
marketing sectors.
Empirical demand relationships for fresh oranges and pro-
cessed orange products are published in a separate report (12).
Those demand estimates were used in the market allocation
analysis of this report.

Purpose and Method
The overall purpose of this research is to provide an alloca-
tion scheme for any given supply of Florida oranges that maxi-
mizes the net revenue to the industry at the FOB level of the
processor, packer, or port of export. Any further reference to
FOB in this report refers to these points in the marketing
channels. The allocation process is defined to include selected
alternative forms of the final product (i.e., fresh oranges, frozen
concentrated orange juice, chilled orange juice, and canned single
strength orange juice), and the three alternative market sectors
(i.e., foodstore, institutional, and export).3 The four product
forms chosen for analysis account for approximately 90% ,of
the utilization of an annual crop.

1Formerly Graduate Research Assistant, Agricultural Economist and
Professor, and Graduate Research Professor, respectively, Department of
Agricultural Economics, University of Florida.
'The only available information that bears any close resemblance to this
problem is published by Florida Citrus Mutual and referred to as the "best
economic utilization for Florida oranges" (4). Numbers in parentheses
refer to Literature Cited.
'Technically, abandonment is another alternative sector, although non-
market in character. The role of abandonment in the optimal allocation
analysis is dealt with in a later section of this bulletin.








MARKET ALLOCATION OF FLORIDA ORANGE

PRODUCTION FOR MAXIMUM NET RETURNS

David E. Weisenborn, Leo Polopolus and W. W. McPherson'

INTRODUCTION
An important and uncoordinated decision made each year by
the Florida orange industry involves the allocation of a given
supply among alternative product forms and marketing sectors.
Ideally, the industry would prefer to allocate in such a manner
that the net revenue to the industry would be maximized.2 This
requires knowledge of the relevant demand and cost relation-
ships existing for the various product forms in each of the
marketing sectors.
Empirical demand relationships for fresh oranges and pro-
cessed orange products are published in a separate report (12).
Those demand estimates were used in the market allocation
analysis of this report.

Purpose and Method
The overall purpose of this research is to provide an alloca-
tion scheme for any given supply of Florida oranges that maxi-
mizes the net revenue to the industry at the FOB level of the
processor, packer, or port of export. Any further reference to
FOB in this report refers to these points in the marketing
channels. The allocation process is defined to include selected
alternative forms of the final product (i.e., fresh oranges, frozen
concentrated orange juice, chilled orange juice, and canned single
strength orange juice), and the three alternative market sectors
(i.e., foodstore, institutional, and export).3 The four product
forms chosen for analysis account for approximately 90% ,of
the utilization of an annual crop.

1Formerly Graduate Research Assistant, Agricultural Economist and
Professor, and Graduate Research Professor, respectively, Department of
Agricultural Economics, University of Florida.
'The only available information that bears any close resemblance to this
problem is published by Florida Citrus Mutual and referred to as the "best
economic utilization for Florida oranges" (4). Numbers in parentheses
refer to Literature Cited.
'Technically, abandonment is another alternative sector, although non-
market in character. The role of abandonment in the optimal allocation
analysis is dealt with in a later section of this bulletin.








The methodological framework for solving optimal alloca-
tion problems for agricultural industries was reported in 1964
(10). No publication was found of previous attempts to apply
the available methodology to an allocation of a given supply over
both alternative product forms and marketing sectors. The prob-
lem has been previously defined to maximize returns among
either various products or sectors. The only previous empirical
attempt of a limited allocation problem for the Florida citrus
industry was reported in 1967 by Minden (6). The major ob-
jective of Minden's allocation study was to demonstrate the use
of quadratic programming in solving problems in which an
optimal allocation of different product uses is required. Retail
demand estimates were determined for eight citrus product
forms. On the basis of these estimates, Minden programmed
the allocation of the 1964-65 crop to these eight product forms
in order to obtain an estimate of maximum total revenue.
Neither the institutional and export markets nor the estimation
of cost functions for net revenue maximization was considered
in that study.

List of Symbols
The symbols defined as follows are used in this report:
C FCOJ = deflated annual total cost of frozen concentrated
orange juice in millions of dollars.
C cssoJ = deflated annual total cost of canned single
strength orange juice in millions of dollars.
C coJ = deflated annual total cost of chilled orange
juice in millions of dollars.
C FPO = deflated annual total cost of fresh Florida
oranges in millions of dollars.
Q FCOJ = annual quantity packed of frozen concentrated
orange juice in millions of gallons.
Q cssoJ = annual quantity packed of canned single
strength orange juice in millions of gallons.
Q coJ = annual quantity packed of chilled orange
juice in millions of gallons.
Q FFO = annual quantity packed of fresh Florida oranges
in millions of boxes.
Q FCOJ-F = per capital monthly quantity of frozen concentrated
orange juice sold in gallons, foodstore sector.
Q COJ-F = per capital monthly quantity of chilled orange
juice sold in gallons, foodstore sector.
Q CSSOJ-r = per capital monthly quantity of canned single
strength orange juice sold in cases of 24/2
equivalents, foodstore sector.








Q FFO-F = per capital monthly quantity of fresh Florida
oranges sold in boxes, foodstore sector.
Q FCoJ-I = per capital monthly quantity of frozen concentrated
orange juice sold at the institutional level in gallons.
Q coJ-I = per capital monthly quantity of chilled orange
juice sold at the institutional level in gallons.
Q FCOJ-E = per capital monthly quantity of frozen concentrated
orange juice sold for export in gallons.
Q CSSOJ-E = per capital monthly quantity of canned single
strength orange juice sold for export in gallons.
X = LaGrangean multiplier.


THE ALLOCATION MODEL

Optimum allocation of a given season's production to various
product categories and/or market sectors is based upon the
theory of price discrimination. Basically, the problem is to
determine the maximum net revenue for the Florida orange
industry by equating the marginal revenue and marginal cost
functions on an industry basis. The marginal revenue equations
are derived from the demand equations for each product form
and market sector, while the marginal cost functions are devel-
oped from total cost functions.
Linear total cost functions were derived. These estimates
resulted in constant marginal costs per unit, which then were
deducted from the estimated marginal revenue functions to yield
marginal net revenue functions. Maximum net revenue was then
derived by an allocation which equated the marginal net revenue
functions among product forms and markets.
Quadratic programming and the calculus with LaGrangean
multipliers were the techniques considered for solving the price
discrimination problem posed above. The calculus method was
chosen because of its relative simplicity, programming ease, and
direct translation from economic theory.
Eight product form-market sector empirical demand equa-
tions for Florida oranges and orange products were developed
(12). Thus eight different markets were considered in the
allocation problem. Given these demand or average revenue
functions, marginal revenue functions were derived. Marginal
net revenue functions for each of the eight markets were then
derived by subtracting marginal cost from marginal revenue.
The optimum allocation was obtained by equating these mar-
ginal net revenue functions subject to the total available supply








of Florida oranges acting as a constraint.4 The optimum total
quantity can be determined by not fixing the total supply and
permitting the equalization of the marginal net revenues at the
zero level. In any case, the solution spells out the optimum
quantities, including zero quantities, to be allocated to each
product market. The sum of individual quantities allocated to
the alternative product markets in the constrained maximization
must equal the total supply of oranges available.


MARGINAL COST AND NET MARGINAL REVENUE FUNCTIONS
Each marginal revenue function was derived by taking first
derivative of the appropriate total revenue function. The total
revenue functions for the various product markets were, in
turn, developed from the average revenue equations.


Empirical Estimates of Marginal Cost
Perfectly elastic or constant marginal cost functions were
developed for four product forms fresh oranges, frozen con-
centrated orange juice, chilled orange juice, and canned single
strength orange juice. Since the allocation problem is posed with
reference to the FOB level, the cost estimation work relates
basically to the fresh fruit packing and/or processing activities
and does not include the distribution and retailing activities of
the various market sectors.
On the basis of previous empirical cost function analysis
and the available results from industry data, the authors believe
that a case for a constant marginal cost can be upheld. Constant
marginal cost implies that as output expands or contracts,
variable costs per unit of output remain unchanged. Johnston
reports that the constant marginal cost concept has been verified
in a large number of empirical studies (5).
One possible indicator of a constant marginal cost for Florida
orange products is the nature of the processing operations.
Firms are faced with a seasonal production pattern which does
not allow a full year of operation. However, in seasons of large
supply it is possible for them to extend the beginning and ending
periods of plant operation to reduce the need for overtime pay-

'This crudely states the necessary conditions for optimization. The
sufficient conditions require that the Hessian matrix be negative definite.
Waugh argues that usually in applications involving linear demand equa-
tions, the -.:.luri..n provides a true maximum (10).








of Florida oranges acting as a constraint.4 The optimum total
quantity can be determined by not fixing the total supply and
permitting the equalization of the marginal net revenues at the
zero level. In any case, the solution spells out the optimum
quantities, including zero quantities, to be allocated to each
product market. The sum of individual quantities allocated to
the alternative product markets in the constrained maximization
must equal the total supply of oranges available.


MARGINAL COST AND NET MARGINAL REVENUE FUNCTIONS
Each marginal revenue function was derived by taking first
derivative of the appropriate total revenue function. The total
revenue functions for the various product markets were, in
turn, developed from the average revenue equations.


Empirical Estimates of Marginal Cost
Perfectly elastic or constant marginal cost functions were
developed for four product forms fresh oranges, frozen con-
centrated orange juice, chilled orange juice, and canned single
strength orange juice. Since the allocation problem is posed with
reference to the FOB level, the cost estimation work relates
basically to the fresh fruit packing and/or processing activities
and does not include the distribution and retailing activities of
the various market sectors.
On the basis of previous empirical cost function analysis
and the available results from industry data, the authors believe
that a case for a constant marginal cost can be upheld. Constant
marginal cost implies that as output expands or contracts,
variable costs per unit of output remain unchanged. Johnston
reports that the constant marginal cost concept has been verified
in a large number of empirical studies (5).
One possible indicator of a constant marginal cost for Florida
orange products is the nature of the processing operations.
Firms are faced with a seasonal production pattern which does
not allow a full year of operation. However, in seasons of large
supply it is possible for them to extend the beginning and ending
periods of plant operation to reduce the need for overtime pay-

'This crudely states the necessary conditions for optimization. The
sufficient conditions require that the Hessian matrix be negative definite.
Waugh argues that usually in applications involving linear demand equa-
tions, the -.:.luri..n provides a true maximum (10).








ments to labor and the possibility that prices of other factors
would be increased. This situation is even more pronounced
when a short supply exists. The firms can still produce at a
fairly constant rate and shut down earlier than would normally
be the case. Such flexibility allows a fairly stable processing
situation and appears to indicate the possibility of constant
marginal costs.

Model Equations for Total Cost
Total cost equations for the four major orange products
were estimated in linear form which results in constant marginal
cost. A least squares regression model, linear in natural num-
bers, was used to estimate the coefficients. The conceptual forms
of the equations for frozen concentrated orange juice, chilled
orange juice, canned single strength orange juice, and fresh
oranges are shown as follows:
a. Frozen concentrated orange juice
[1] C FCOJ = f[Q FCOJ]
b. Chilled orange juice
[2] C coJ = f[Q coJ]
c. Canned single strength orange juice
[3] C cssoJ = f[Q cssoJ]
d. Fresh Florida oranges
[4] C FFO = f[Q FFO]
where C is total cost and Q is total quantity.
As the four equations above indicate, only two variables were
used in the cost analysis for each product form. Total cost, the
dependent variable in each equation, was calculated by multi-
plying the delivered-in price per box of fruit by the total boxes
utilized plus the unit cost of processing or packing times the
total pack.5

Data for Cost Analysis
Basic data on packing (7) and processing (9) costs were
obtained from the reports of Spurlock. Since no delivered-in
price is reported for fresh oranges, the cost of picking and
hauling was included with the cost of packing and selling (8).

"This procedure applies for the three processed products only. For fresh
oranges the "on-tree" price replaces the delivered-in price. This is offset
by including picking and hauling costs in the packing costs.








ments to labor and the possibility that prices of other factors
would be increased. This situation is even more pronounced
when a short supply exists. The firms can still produce at a
fairly constant rate and shut down earlier than would normally
be the case. Such flexibility allows a fairly stable processing
situation and appears to indicate the possibility of constant
marginal costs.

Model Equations for Total Cost
Total cost equations for the four major orange products
were estimated in linear form which results in constant marginal
cost. A least squares regression model, linear in natural num-
bers, was used to estimate the coefficients. The conceptual forms
of the equations for frozen concentrated orange juice, chilled
orange juice, canned single strength orange juice, and fresh
oranges are shown as follows:
a. Frozen concentrated orange juice
[1] C FCOJ = f[Q FCOJ]
b. Chilled orange juice
[2] C coJ = f[Q coJ]
c. Canned single strength orange juice
[3] C cssoJ = f[Q cssoJ]
d. Fresh Florida oranges
[4] C FFO = f[Q FFO]
where C is total cost and Q is total quantity.
As the four equations above indicate, only two variables were
used in the cost analysis for each product form. Total cost, the
dependent variable in each equation, was calculated by multi-
plying the delivered-in price per box of fruit by the total boxes
utilized plus the unit cost of processing or packing times the
total pack.5

Data for Cost Analysis
Basic data on packing (7) and processing (9) costs were
obtained from the reports of Spurlock. Since no delivered-in
price is reported for fresh oranges, the cost of picking and
hauling was included with the cost of packing and selling (8).

"This procedure applies for the three processed products only. For fresh
oranges the "on-tree" price replaces the delivered-in price. This is offset
by including picking and hauling costs in the packing costs.







Total costs include interest payments on borrowed funds but do
not include a return on investment.
The total number of boxes of oranges used in each of the
four product forms is reported on a regular basis by Florida
Citrus Mutual (3). The total pack and "on-tree" prices for
fresh oranges are also reported by Florida Citrus Mutual (3).
The total pack and delivered-in prices for frozen concentrated,
chilled, and canned single strength orange juice are reported by
Florida Canners Association (2).
While the price variables were deflated simply by dividing
by the general wholesale price index, deflating the processing
and packing cost variables required a more elaborate method.
Packing and processing costs were subdivided into several com-
ponents, such as materials, labor, operating, and administrative
and selling costs. The deflation procedure involved four indices
wholesale price index of intermediate materials, production
payroll index, wholesale price index of operating agricultural
machinery, and the wholesale price index of food and beverage
manufactures (11).

Results of Cost Analysis
Constant marginal cost estimates were obtained by taking
the first derivative of each total cost function with respect to
output. The marginal cost estimates for packing or processing
Florida orange products were as follows: $0.9702 per gallon for
frozen orange concentrate, $0.1770 per gallon for canned single
strength orange juice, $0.3749 per gallon for chilled orange
juice, and $1.0108 per box for fresh Florida oranges. The low
level of precision of these estimates, however, leaves room for
substantial error as indicated by the low coefficients of determi-
nation (R2) and the large standard errors of the regression
coefficients for all products except chilled orange juice (Appen-
dix Table 1).
The cost estimates are ordered with respect to product form
in the manner expected. Fresh oranges had the highest mar-
ginal cost followed closely by frozen concentrated orange juice.
This result was expected because of the very high labor require-
ments for fresh oranges, and, in the case of frozen concentrate,
the additional boxes of fruit used to manufacture a given quan-
tity as compared with single strength juice. Chilled juice had
the next highest marginal cost and canned single strength had
the lowest. This relationship was also expected, since canned
single strength juice utilizes the lowest quality fruit.








Net Marginal Revenue Functions

Originally 13 product-market categories were considered:
fresh oranges, frozen concentrate, chilled juice, and canned
single strength juice in the foodstore sector; each of these four
products in the institutional sector; and each of these four
products plus hot pack concentrate in the export sector. Demand
estimates were not made for fresh oranges in the institutional
and export markets because suitable data were not available.
Results of the demand estimates for canned single strength juice
in the institutional market and for hot pack in the export mar-
ket were not acceptable. In the export market chilled juice and
canned single strength juice were combined into one equation."
Thus only eight functions were estimated, but these represented
the major products in each marketing sector.7 Marginal net
revenue functions were developed for the four major foodstore
sector products. Functions for frozen orange concentrate and
chilled orange juice were estimated for the institutional sector,
while the export sector provided one equation for frozen orange
concentrate and one for canned single strength orange juice
combined with chilled juice.
The empirical coefficients for these marginal net revenue
equations are presented in Appendix Table 2. These eight func-
tions were used to optimally allocate given quantities of oranges
among alternative product forms and markets in a manner that
maximizes total net revenue.

OPTIMUM MARKET ALLOCATION RESULTS

The allocative procedure was carried out by solving the
system of net marginal revenue functions for the quantity vari-
ables.8 If the allocation is performed with no overall quantity
constraint, the net marginal revenue functions are equated at

'Chilled orange juice and canned single strength orange juice were
treated as one product category in the export sector, since these products
were not distinguished by the United States Bureau of the 'Census.
7The four excluded product market categories were canned single
strength orange juice and fresh oranges in the institutional sector and hot
pack concentrated orange juice and fresh oranges in the export sector.
These four product markets accounted for an average of about 5 million
boxes of oranges consumed per year for the 1961-1967 period.
'An abortive attempt was made to optimally allocate a given supply of
oranges using net marginal revenue equations that included competitive
and complementary products. The attempt was unsuccessful because the
sufficient conditions for maximization were not met, even though the neces-
sary conditions were satisfied (11).








Net Marginal Revenue Functions

Originally 13 product-market categories were considered:
fresh oranges, frozen concentrate, chilled juice, and canned
single strength juice in the foodstore sector; each of these four
products in the institutional sector; and each of these four
products plus hot pack concentrate in the export sector. Demand
estimates were not made for fresh oranges in the institutional
and export markets because suitable data were not available.
Results of the demand estimates for canned single strength juice
in the institutional market and for hot pack in the export mar-
ket were not acceptable. In the export market chilled juice and
canned single strength juice were combined into one equation."
Thus only eight functions were estimated, but these represented
the major products in each marketing sector.7 Marginal net
revenue functions were developed for the four major foodstore
sector products. Functions for frozen orange concentrate and
chilled orange juice were estimated for the institutional sector,
while the export sector provided one equation for frozen orange
concentrate and one for canned single strength orange juice
combined with chilled juice.
The empirical coefficients for these marginal net revenue
equations are presented in Appendix Table 2. These eight func-
tions were used to optimally allocate given quantities of oranges
among alternative product forms and markets in a manner that
maximizes total net revenue.

OPTIMUM MARKET ALLOCATION RESULTS

The allocative procedure was carried out by solving the
system of net marginal revenue functions for the quantity vari-
ables.8 If the allocation is performed with no overall quantity
constraint, the net marginal revenue functions are equated at

'Chilled orange juice and canned single strength orange juice were
treated as one product category in the export sector, since these products
were not distinguished by the United States Bureau of the 'Census.
7The four excluded product market categories were canned single
strength orange juice and fresh oranges in the institutional sector and hot
pack concentrated orange juice and fresh oranges in the export sector.
These four product markets accounted for an average of about 5 million
boxes of oranges consumed per year for the 1961-1967 period.
'An abortive attempt was made to optimally allocate a given supply of
oranges using net marginal revenue equations that included competitive
and complementary products. The attempt was unsuccessful because the
sufficient conditions for maximization were not met, even though the neces-
sary conditions were satisfied (11).








zero and the true maximum is obtained. If total quantity is
constrained at some given level, the net marginal revenue func-
tions are still equated, but not necessarily at zero. The resulting
allocation provides'a true maximum total net revenue for the
specified quantity at the FOB level.


Actual Market Allocations

In order to provide a basis for comparing the allocation
results, the actual quantities sold in each product market were
estimated for the average of the period used in the demand
analysis. The actual annual total revenue, total cost, and net
revenue figures were also estimated for each product market at
the FOB level (Table 1). For the eight product markets in the
average season, the net revenue was estimated to be $16.07
million. Chilled orange juice sold in the foodstore sector pro-
vided the greatest source of net revenue for the Florida orange
industry in the average season, even though the gross FOB
revenue from chilled orange juice sales was considerably below
the gross amount received in the foodstore orange concentrate
market.


Optimum Constrained Allocation

Average Seasonal Quantity

When the total quantity of oranges to be allocated is limited
to the average seasonal quantity of 73.2 million boxes and the
allocation is made by means of the equations given in Appendix
Table 2, net industry revenue is approximately $27.5 million at
the FOB processor or packer level (Table 2). This finding
represents an increase of $11.4 million over the net revenue
obtained from a comparable total supply as it was actually
allocated in recent years (Table 1). A supply of 73.2 million
boxes for the eight selected product markets represents a total
Florida supply of 91.5 million boxes for all product forms and
market channels.
With a constraint of 73.2 million boxes, the quantity of
frozen concentrated orange juice allocated to the foodstore
dropped from the actual allocation of 38.5 million boxes to 27.8
million boxes in the optimum solution. Decreases from the actual
allocation occurred also for chilled orange juice in the foodstore
and institutional sectors and canned single strength orange juice








zero and the true maximum is obtained. If total quantity is
constrained at some given level, the net marginal revenue func-
tions are still equated, but not necessarily at zero. The resulting
allocation provides'a true maximum total net revenue for the
specified quantity at the FOB level.


Actual Market Allocations

In order to provide a basis for comparing the allocation
results, the actual quantities sold in each product market were
estimated for the average of the period used in the demand
analysis. The actual annual total revenue, total cost, and net
revenue figures were also estimated for each product market at
the FOB level (Table 1). For the eight product markets in the
average season, the net revenue was estimated to be $16.07
million. Chilled orange juice sold in the foodstore sector pro-
vided the greatest source of net revenue for the Florida orange
industry in the average season, even though the gross FOB
revenue from chilled orange juice sales was considerably below
the gross amount received in the foodstore orange concentrate
market.


Optimum Constrained Allocation

Average Seasonal Quantity

When the total quantity of oranges to be allocated is limited
to the average seasonal quantity of 73.2 million boxes and the
allocation is made by means of the equations given in Appendix
Table 2, net industry revenue is approximately $27.5 million at
the FOB processor or packer level (Table 2). This finding
represents an increase of $11.4 million over the net revenue
obtained from a comparable total supply as it was actually
allocated in recent years (Table 1). A supply of 73.2 million
boxes for the eight selected product markets represents a total
Florida supply of 91.5 million boxes for all product forms and
market channels.
With a constraint of 73.2 million boxes, the quantity of
frozen concentrated orange juice allocated to the foodstore
dropped from the actual allocation of 38.5 million boxes to 27.8
million boxes in the optimum solution. Decreases from the actual
allocation occurred also for chilled orange juice in the foodstore
and institutional sectors and canned single strength orange juice








zero and the true maximum is obtained. If total quantity is
constrained at some given level, the net marginal revenue func-
tions are still equated, but not necessarily at zero. The resulting
allocation provides'a true maximum total net revenue for the
specified quantity at the FOB level.


Actual Market Allocations

In order to provide a basis for comparing the allocation
results, the actual quantities sold in each product market were
estimated for the average of the period used in the demand
analysis. The actual annual total revenue, total cost, and net
revenue figures were also estimated for each product market at
the FOB level (Table 1). For the eight product markets in the
average season, the net revenue was estimated to be $16.07
million. Chilled orange juice sold in the foodstore sector pro-
vided the greatest source of net revenue for the Florida orange
industry in the average season, even though the gross FOB
revenue from chilled orange juice sales was considerably below
the gross amount received in the foodstore orange concentrate
market.


Optimum Constrained Allocation

Average Seasonal Quantity

When the total quantity of oranges to be allocated is limited
to the average seasonal quantity of 73.2 million boxes and the
allocation is made by means of the equations given in Appendix
Table 2, net industry revenue is approximately $27.5 million at
the FOB processor or packer level (Table 2). This finding
represents an increase of $11.4 million over the net revenue
obtained from a comparable total supply as it was actually
allocated in recent years (Table 1). A supply of 73.2 million
boxes for the eight selected product markets represents a total
Florida supply of 91.5 million boxes for all product forms and
market channels.
With a constraint of 73.2 million boxes, the quantity of
frozen concentrated orange juice allocated to the foodstore
dropped from the actual allocation of 38.5 million boxes to 27.8
million boxes in the optimum solution. Decreases from the actual
allocation occurred also for chilled orange juice in the foodstore
and institutional sectors and canned single strength orange juice









Table 1. Total and Net Revenue for the Average Season Using Actual Quan-
tities of Oranges Sold in Each Product Market Category.'
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 54.36 gal. 38.49 167.69 153.22 14.47
COJ F 35.85 gal. 6.47 56.79 25.71 31.08
CSSOJ F 6.59 cases 4.07 18.51 27.59 9.08
FFO F 8.89 boxes 8.89 44.32 62.06 -17.74
FCOJ I 6.61 gal. 4.68 19.78 18.62 1.16
COJ I 38.04 gal. 6.87 40.28 27.29 12.99
FCOJ E 3.53 gal. 2.50 11.76 9.95 1.81
CSSOJ E 6.75 gal. 1.23 6.22 24.84 -18.62
Total 73.20 365.35 349.28 16.07
IThe average season quantity means are based on data from October 1961 to October
1967 for the foodstore and export product forms and December 1963 to December 1966 for
institutional product forms.

Table 2. Total Revenue and Maximum Net Revenue for the Average Season
With a Total Quantity Constraint of 73.22 Million Boxes of Oranges.
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 39.21 gal. 27.76 150.76 126.44 24.32
COJ F 27.02 gal. 4.88 46.79 32.30 14.49
CSSOJ F 15.91 cases 9.82 37.05 33.16 3.89
FFO F 20.12 boxes 20.12 84.79 73.41 11.38
FCOJ I 7.83 gal. 5.55 22.28 25.26 2.98
COJ I 3.82 gal. 0.69 5.01 4.57 0.44
FCOJ E 5.84 gal. 4.14 17.02 18.82 1.80
CSSOJ E 1.44 gal. 0.26 1.64 23.90 -22.26
Total 73.22 365.34 337.86 27.48


to export markets. Increases occurred for canned single strength
orange juice and fresh oranges in the foodstore sector and
frozen concentrated orange juice for institutional and export
markets. The most notable increase was in fresh oranges for
the foodstore market which increased from 8.9 to 20.1 million
boxes. Although negative total net revenues occurred in three
product markets, the marginal net revenues in these markets
were positive. The negative figures occurred because total rev-
enue after variable costs were deducted failed to cover fixed
cost. The quantity at which marginal net revenue becomes
negative in each product market is given later in the uncon-
strained quantity allocation in Table 7.









Above Average Crop Sizes

In order to determine optimum allocations under the assump-
tion of relatively large crop sizes, as expected in the future, two
additional constrained allocations were made. Quantity con-
straints of 150 million and 200 million boxes were used in this
analysis for the eight product markets. The 150 and 200 million
box quantities are equivalent to 187.5 and 250 million boxes,
respectively, of overall Florida orange supply for all uses, in-
cluding home use. The 150 million box constraint resulted in
a net revenue of $26.2 million. However, with a constraint of
200 million boxes, net revenue was a negative $373.3 million
(Tables 3 and 4). When these quantities were forced into the


Table 3. Estimated Total Revenue and Maximum Net Revenue Using a Crop
of 150 Million Boxes of Oranges for the Average Season.
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 57.39 gal. 40.63 168.31 137.57 30.74
COJ F 81.71 gal. 14.75 67.01 40.48 26.53
CSSOJ F 33.49 cases 20.66 47.44 43.66 3.78
FFO F 28.07 boxes 28.07 92.80 81.45 11.35
FCOJ I 15.20 gal. 10.76 29.38 36.44 7.06
COJ I 128.21 gal. 23.15 51.00 63.52 -12.52
FCOJ E 10.95 gal. 7.77 21.96 26.24 4.28
CSSOJ E 23.32 gal. 4.20 5.41 27.78 -22.37
Total 149.99 483.31 457.14 26.17


Table 4. Estimated Total Revenue and Maximum Net Revenue Using a Crop
of 200 Million Boxes of Oranges for the Average Season.
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 73.85 gal. 52.29 155.61 150.76 4.85
COJ F 131.27 gal. 23.70 0.76 58.13 58.89
CSSOJ F 49.40 cases 30.47 29.21 53.17 23.96
FFO F 15.73 boxes 15.73 74.19 68.98 5.21
FCOJ I 21.87 gal. 15.48 24.23 44.63 20.40
COJ I 240.90 gal. 43.50 -103.14 106.69 -209.83
FCOJ E 15.58 gal. 11.06 18.38 31.80 13.42
CSSOJ E 43.14 gal. 7.77 25.63 31.29 56.92
Total 200.00 172.09 545.45 -373.36









allocation model, marginal net revenue became negative in the
markets. This result indicates that abandonment of part of the
crop would have produced a higher net revenue.

Primary and Secondary Market Allocation

The primary market was defined as the sum of the four
foodstore product markets, while the secondary market included
the institutional and export product markets. On the basis of
the actual quantities marketed in the average season in the
eight product markets, the primary market accounted for ap-
proximately 80% of the total. The allocation procedure was
applied on an 80% primary-20% secondary market basis for
constrained total quantities of 100 and 150 million boxes. The
100 million box allocation yielded an optimized net revenue of
$77.1 million, compared to only $14.8 million for the 150 million
box quantity (Tables 5 and 6).
Attempts to improve the net return by varying the relative
percentage allocated to the secondary market met with mixed
success. For a 100 million box constraint, increasing the sec-
ondary market share from 20% to 30% led to a reduction of
only $1 million in net revenue. However, a 100 million box
constraint that allocated 40% of the total to the secondary mar-
ket yielded $41.1 million, or $36 million less than the 80-20
splits. (Compare Table 5 with Appendix Tables 3 and 4.)

Table 5. Estimated Total Revenue and Maximum Net Revenue Using a Crop
of 100 Million Boxes of Oranges With Allocation of 80% to the
Primary Market and 20% to the Secondary Market.
Product and Quantity Total Total Net
Market Sector Revenue Cost Revenue
(Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 46.86 gal. 33.18 162.18 132.96 29.22
COJ F 49.95 gal. 9.02 67.41 33.28 34.13
CSSOJ F 23.28 cases 14.36 45.30 37.56 7.74
FFO F 23.46 boxes 23.46 89.92 76.79 13.13
Primary Total 80.02 364.81 280.59 84.22
FCOJ I 9.79 gal. 6.93 25.48 27.78 2.30
COJ I 36.88 gal. 6.66 39.36 24.57 14.79
FCOJ E 7.19 gal. 5.11 19.25 20.41 1.16
CSSOJ E 7.25 gal. 1.31 6.53 24.93 -18.40
Secondary
Total 20.01 90.62 97.69 7.07
OVERALL
TOTAL 100.03 455.43 378.28 77.15









Table 6. Estimated Total Revenue and Maximum Net Revenue Using a Crop
of 150 Million Boxes of Oranges With Allocation of 80% to the
Primary Market and 20% to the Secondary Market.
Product and Quantity Total Total Net
Market Sector Revenue Cost Revenue
(Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 64.34 gal. 45.55 166.27 152.82 13.45
COJ F 102.61 gal. 18.52 48.42 53.32 4.90
CSSOJ F 40.18 cases 24.79 42.97 47.66 4.69
FFO F 31.14 boxes 31.14 92.02 84.55 7.47
Primary Total 120.00 349.68 338.35 11.33
FCOJ I 11.87 gal. 8.40 27.83 28.18 0.35
COJ I 72.17 gal. 13.03 58.35 37.50 20.85
FCOJ E 8.64 gal. 6.14 20.89 20.53 0.36
CSSOJ E 13.46 gal. 2.42 8.65 26.03 -17.38
Secondary
Total 29.99 115.72 112.24 3.48
OVERALL
TOTAL 149.99 465.40 450.59 14.81


For the extremely large quantity constraint of 150 million
boxes, industry net revenue is increased by enlarging the rela-
tive share of the secondary market from 80-20 to 70% primary
and 30% secondary market. The 70-30 scheme provides a net
revenue of $27.7 million for a 150 million box constraint, com-
pared with $14.8 million for an 80-20 ratio. However, increasing
the secondary market's share to 40% of the total of a 150
million box quantity leads to a low net revenue of a negative
$5.1 million. (Compare Table 6 with Appendix Tables 5 and 6.)

Optimum Unconstrained Allocation
It was found that when the supply of oranges was left
unconstrained, net FOB revenue was maximized at 111.4 million
boxes for the eight product markets or about 139 million boxes
of total Florida orange supply. More importantly, the net
revenue for the unconstrained solution was $85.4 million or
$69.3 million above the actual net revenue estimated for an
average season (Tables 1 and 7).

Fresh and Processed Market Allocation

While the unconstrained allocation in Table 7 provides the
largest overall net revenue among the various allocations at-
tempted, the allocation of 24 million boxes of fresh oranges to









Table 6. Estimated Total Revenue and Maximum Net Revenue Using a Crop
of 150 Million Boxes of Oranges With Allocation of 80% to the
Primary Market and 20% to the Secondary Market.
Product and Quantity Total Total Net
Market Sector Revenue Cost Revenue
(Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 64.34 gal. 45.55 166.27 152.82 13.45
COJ F 102.61 gal. 18.52 48.42 53.32 4.90
CSSOJ F 40.18 cases 24.79 42.97 47.66 4.69
FFO F 31.14 boxes 31.14 92.02 84.55 7.47
Primary Total 120.00 349.68 338.35 11.33
FCOJ I 11.87 gal. 8.40 27.83 28.18 0.35
COJ I 72.17 gal. 13.03 58.35 37.50 20.85
FCOJ E 8.64 gal. 6.14 20.89 20.53 0.36
CSSOJ E 13.46 gal. 2.42 8.65 26.03 -17.38
Secondary
Total 29.99 115.72 112.24 3.48
OVERALL
TOTAL 149.99 465.40 450.59 14.81


For the extremely large quantity constraint of 150 million
boxes, industry net revenue is increased by enlarging the rela-
tive share of the secondary market from 80-20 to 70% primary
and 30% secondary market. The 70-30 scheme provides a net
revenue of $27.7 million for a 150 million box constraint, com-
pared with $14.8 million for an 80-20 ratio. However, increasing
the secondary market's share to 40% of the total of a 150
million box quantity leads to a low net revenue of a negative
$5.1 million. (Compare Table 6 with Appendix Tables 5 and 6.)

Optimum Unconstrained Allocation
It was found that when the supply of oranges was left
unconstrained, net FOB revenue was maximized at 111.4 million
boxes for the eight product markets or about 139 million boxes
of total Florida orange supply. More importantly, the net
revenue for the unconstrained solution was $85.4 million or
$69.3 million above the actual net revenue estimated for an
average season (Tables 1 and 7).

Fresh and Processed Market Allocation

While the unconstrained allocation in Table 7 provides the
largest overall net revenue among the various allocations at-
tempted, the allocation of 24 million boxes of fresh oranges to








Table 7. Estimated Total Revenue and Maximum Net Revenue for the Average
Season With Quantity And Product Market Allocation of Oranges
Unconstrained.
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
FCOJ F 48.27 gal. 34.17 163.75 131.27 32.38
COJ F 54.22 gal. 9.79 69.31 31.77 37.54
CSSOJ F 24.64 cases 15.20 46.21 38.37 7.84
FFO F 24.08 boxes 24.08 90.59 77.42 13.17
FCOJ I 11.49 gal. 8.14 27.49 31.26 3.77
COJ I 65.67 gal. 11.86 56.22 38.48 17.74
FCOJ E 8.38 gal. 5.95 20.64 22.78 2.14
CSSOJ E 12.32 gal. 2.22 8.50 25.83 -17.33
Total 111.41 482.71 397.18 85.43


the foodstore sector seems unattainable from a practical stand-
point. On the basis of historical experience for the period
1959-60 through 1966-67, the largest quantity of fresh Florida
oranges marketed in all three sectors foodstore, institutional,
and export was 16.6 million boxes in the 1959-60 season.
Florida's fresh fruit market is not only affected by the quantities
of oranges marketed from California and Arizona, but also by
the generally declining per capital consumption of fresh oranges
over time. Because of these factors and the difficulties involved
in estimating cross-price elasticities,9 Florida's orange market
in the foodstore sector was arbitrarily fixed at an upper limit of
15 million boxes. This fresh fruit constraint appears realistic
in terms of Florida's historical volume of fresh fruit shipments
and Florida's potential market in light of increased plantings
in California, Arizona, and Texas.
Given a Florida fresh fruit constraint of 15 million boxes,
the allocation problem reduces to a solution of the seven remain-
ing product markets in an unconstrained fashion. The net
revenue from the sale of 15 million boxes of fresh oranges can
be simply added to the net revenue obtained from the optimum
allocation among the seven product markets (Table 8). In doing
so, net industry revenue is $77.89 million for the eight product

'Weisenborn (11) included California fresh orange sales as a substitute
variable in the demand equation for fresh Florida oranges.. The coefficient
for this variable was nonsignificant and the sign illogical. C(':liinmarii (1)
was able, however, to define logical and competitive relationships between
Florida and California Valencia oranges sold in foodstores by utilizing
an experimental pricing approach.








Table 8. Estimated Total Revenue and Maximum Net Revenue, Unconstrained
Processed Orange Markets and an Upper Constraint of 15 Million
Boxes in the Fresh Foodstore Sector.
Quantity Total Total Net
Product and Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions
Processed
FCOJ F 48.27 gal. 34.17 163.75 131.27 32.48
COJ F 54.22 gal. 9.79 69.31 31.77 37.54
CSSOJ F 24.64 cases 15.20 46.21 38.37 7.84
FCOJ I 11.49 gal. 8.14 27.49 31.26 3.77
COJ I 65.67 gal. 11.86 56.22 38.48 17.74
FCOJ E 8.38 gal. 5.95 20.64 22.78 2.14
CSSOJ E 12.32 gal. 2.22 8.50 25.83 -17.33
Subtotal 87.33 392.12 319.76 72.36
Fresh
FFO F 15.00 boxes 15.00 73.77 68.24 5.53
OVERALL
TOTAL 102.33 465.89 388.00 77.89


markets, and the optimum supply to be allocated is reduced to
approximately 102 million boxes, as opposed to 111 million
boxes when all eight product markets were unconstrained. A
supply of 102 million boxes in the eight product markets is
equivalent to an overall industry supply of 128 million boxes.


SUMMARY AND CONCLUSIONS

Of the various allocations performed, the unconstrained
allocation of the seven processed product markets, plus the
addition of a fixed quantity of fresh orange sales, gives a useful
result with considerable implications for industry policy. This
allocation required an orange supply of 102 million boxes for
the eight product markets. A quantity of 102 million boxes is
equivalent to an aggregate industry supply of 128 million boxes
for all uses. Maximum net industry revenue was estimated to
be approximately $78 million, or slightly less than the $85
million obtained when both the fresh and processed product
markets were left unconstrained.10 Either of these net revenue
results is substantially above the $16.1 million actually realized
in the average season.

"It is believed that the allocation involving eight unconstrained product
markets overstates the potential net revenue from the fresh orange food-
store section and, thus, overstates overall industry net revenue.








FOB Versus On-Tree Optimum Allocation


The results of this report relate to the maximization of net
industry revenue at the FOB processor or packer level. If how-
ever, the problem had been solved for maximization of net
revenue at the on-tree or grower level, the optimum quantity
of industry supply would be somewhat less than the amount
obtained for the FOB level. This is because the price elasticities
of demand at the on-tree level are believed to be relatively lower
than those obtained at the FOB level.
The differences in price elasticities of demand between on-
tree and FOB levels also draw attention to the possible conflict
of economic interest between the growers and the handlers
and/or processors. What is often overlooked, however, is the
fact that growers and handler/processors have vertically inte-
grated in recent years by either forming cooperatives or by
jointly engaging in various types of participation plans. Parti-
cipation plans are simply legal contracts that provide a market
outlet for the growers' fruit and a reasonable expectation of
raw material for a handler/processor. Vertical integration
through grower cooperatives and extensive use of participation
plans tend to offset the economic conflict of interest between
growers and handler/processors.


Required Adjustments To Achieve Optimal Allocations

To obtain some indication of future industry adjustments
necessary to maximize net revenue, the actual historical alloca-
tion was compared with various constrained and unconstrained
allocations (Table 9). The findings suggest that the industry's
net revenue can be increased by decreasing the relative share
of frozen orange concentrate in the foodstore sector. Except for
the case of allocating a 200 million box crop among eight product
markets, the optimal solutions also indicated that fresh Florida
oranges and canned single strength orange juice in the food-
store sector should receive relatively larger shares of the total
supply.
A crop size of 100 million boxes generates a net FOB revenue
of about $77 million if 80% of the total supply is allocated to
processed product markets. In this case, approximately one-
third of the total orange supply should be allocated to frozen
concentrated orange juice in the foodstore sector (Table 9).
When total quantity to be allocated among the eight product








FOB Versus On-Tree Optimum Allocation


The results of this report relate to the maximization of net
industry revenue at the FOB processor or packer level. If how-
ever, the problem had been solved for maximization of net
revenue at the on-tree or grower level, the optimum quantity
of industry supply would be somewhat less than the amount
obtained for the FOB level. This is because the price elasticities
of demand at the on-tree level are believed to be relatively lower
than those obtained at the FOB level.
The differences in price elasticities of demand between on-
tree and FOB levels also draw attention to the possible conflict
of economic interest between the growers and the handlers
and/or processors. What is often overlooked, however, is the
fact that growers and handler/processors have vertically inte-
grated in recent years by either forming cooperatives or by
jointly engaging in various types of participation plans. Parti-
cipation plans are simply legal contracts that provide a market
outlet for the growers' fruit and a reasonable expectation of
raw material for a handler/processor. Vertical integration
through grower cooperatives and extensive use of participation
plans tend to offset the economic conflict of interest between
growers and handler/processors.


Required Adjustments To Achieve Optimal Allocations

To obtain some indication of future industry adjustments
necessary to maximize net revenue, the actual historical alloca-
tion was compared with various constrained and unconstrained
allocations (Table 9). The findings suggest that the industry's
net revenue can be increased by decreasing the relative share
of frozen orange concentrate in the foodstore sector. Except for
the case of allocating a 200 million box crop among eight product
markets, the optimal solutions also indicated that fresh Florida
oranges and canned single strength orange juice in the food-
store sector should receive relatively larger shares of the total
supply.
A crop size of 100 million boxes generates a net FOB revenue
of about $77 million if 80% of the total supply is allocated to
processed product markets. In this case, approximately one-
third of the total orange supply should be allocated to frozen
concentrated orange juice in the foodstore sector (Table 9).
When total quantity to be allocated among the eight product













Table 9. Percentage Distribution of Total Orange Quantity Among Product Markets, Actual, Constrained, and Unconstrained Alloca-
tions.1
Constrained Optimal Allocation Unconstrained
80% 80% All
Product Form Extra Primary- Primary- Eight Processed
and Actual Average Large Large 20% 20% Product Only; Fresh
Market Sector Unit Allocation Season Supply Supply Secondary Secondary Markets Market Fixed
FCOJ F Pet. 52.58 37.92 27.10 26.14 33.16 30.37 30.66 33.40
COJ F Pet. 8.84 6.66 9.83 11.84 9.02 12.35 8.79 9.57
CSSOJ F Pct. 5.56 13.41 13.77 15.24 14.36 16.53 13.64 14.85
FFO F Pet. 12.14 27.48 18.72 7.87 23.45 20.76 21.61 14.66
FCOJ I Pet. 6.39 7.58 7.17 7.74 6.93 5.60 7.31 7.95
COJ I Pet. 9.39 .94 15.43 21.75 6.66 8.69 10.65 11.59
FCOJ E Pct. 3.42 5.65 5.18 5.53 5.11 4.09 5.34 5.81
CSSOJ E Pct. 1.68 .36 2.80 3.89 1.31 1.61 2.00 2.17
TOTAL Pet. 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
TOTAL Mil.
SUPPLY boxes 73.20 73.22 150.00 200.00 100.00 150.00 111.41 102.33
NET
REVENUE Mil. $ 16.1 27.5 26.2 --373.4 77.2 14.8 85.4 77.9
1Based on complete results as given in Tables 1 through 8.








markets exceeded 111.4 million boxes, equivalent to a total
supply of 139 million boxes, the allocation model indicated that
marginal net revenue would reach zero in each product market
and that FOB net revenue would be maximized by abandoning
any excess over this quantity. When fresh oranges in the food-
store sector were fixed at 15 million boxes these total quantities
were reduced to 102.3 and 128 million boxes, respectively.

Losses May Be Necessary in Certain Product
Markets in Order To Maximize Overall
Industry Net Revenue
What is often overlooked is the fact that optimization of
net industry revenue may require that certain product markets
suffer market losses, at least in the short run. For example, the
largest industry revenue, $85 million, was obtained without
quantity constraints upon individual product markets or sectors.
While this was the largest positive net return obtained, total
cost exceeded total industry revenue for FCOJ in the institu-
tional sector, as well as for FCOJ and CSSOJ in the export
sectors (Table 7). Similar results were obtained when fresh
orange sales in the foodstore sector were limited to 15 million
boxes (Table 8). In each of these cases, marginal net revenue
reaches zero before sufficient total revenue is generated to cover
both fixed and variable costs. The economics of price discrimina-
tion, as applied here, attempts to maximize the overall industry
net revenue. In doing so, several institutional and export prod-
uct markets incur losses. But in each of these cases the revenues
exceeded variable costs and thus contribute some payment on
fixed costs. Under these circumstances, industry net revenue
would be reduced if no allocation were made to these markets.
If the results given in Table 7 or Table 8 (unconstrained
product markets; or unconstrained processed product markets
with fresh orange sales limited to 15 million boxes) were some-
how required by industry policy, exporters of processed products
and marketers of FCOJ in the institutional market would seek
subsidies from the positive net revenue product marketers to
cover at least enough of their fixed cost to break even. Thus,
the policy problem becomes one of restricting the industry
supply to approximately 102 million boxes (assuming a limit of
15 million boxes of fresh oranges) for eight product markets,
as well as compensating the losers (exporters and sellers of
FCOJ in the institutional market) from the net gains of the








other product markets. If a subsidy cost is involved, the magni-
tude of the aggregate subsidy will affect the overall net benefit
to the industry.


Supply Abandonment
When referring to the completely unconstrained allocation,
economic abandonment of oranges becomes a logical alternative
if the total crop size exceeds 111.4 million boxes for the eight
product markets or 139 million boxes overall. If one deems the
unconstrained allocation of the seven processed product mar-
kets, plus a 15 million box constraint for fresh oranges, as a
better solution for policy purposes, supply abandonment becomes
a logical alternative when overall orange supply exceeds 127
million boxes. Stated another way, net industry revenue at the
FOB level is maximized when the supply of oranges in excess
of either 139 or 127 million boxes is abandoned in the groves
of Florida.
Such a finding assumes that changes in the demand relation-
ships are unlikely and that a program of market regulation is
feasible and enforceable. Simple upward adjustments in the
supply that maximizes net industry revenues must be made over
time, of course, to reflect population and income changes.
The Florida legislature approved in 1967 the Orange Stabi-
lization Act of Florida which is enabling legislation for a State
Marketing Order for Florida Oranges. With this legislation, a
marketing order could be enacted which would contain some
provisions for implementing abandonment. A Federal Market-
ing Order would also be an alternative. However, a marketing
order is weak in actual control of production. Abandonment
would likely occur after growing costs were incurred. This
would be less economical than a program that would lead to
abandonment before growing costs were incurred or to place a
restraint on new plantings. Thus a more logical alternative would
be the use of quotas to control actual production before growing
costs or at least to control entry and new plantings.
Another possibility, in high volume years, is voluntary inter-
nal supply management by the industry to accomplish abandon-
ment. There are several alternative methods of accomplishing
supply management; but implementation, in general, is more
difficult than the implementation of marketing orders or quota
systems.








General Conclusion and Limitations


This study strongly suggests that the net revenue to the
Florida orange industry can be maximized by a program that
controls the allocation of oranges to individual product forms
and market channels. The eight product markets specifically
considered in the analysis accounted for approximately 80% of
the total utilization.
What must be carefully recognized with this type of economic
analysis, however, are the following limitations:
1. A control structure must be developed to insure proper
product allocations;
2. High profit levels encourage excessive production, which
applies pressure against the control structure;
3. Maximized net revenues may be only a short run phe-
nomena as the control structure develops leaks and loop-
holes;
4. Unless growers, as well as marketing firms, share
equitably in the net revenue benefits, those who feel
disadvantaged may provide the leadership to subvert the
control apparatus;
5. The optimum allocation, given the cost and revenue
relationships derived in this study, requires that certain
product markets sustain net losses from operations.
Unless these groups are provided an opportunity to share
in the extra income in the system through subsidies, they
may withdraw their support of the program;
6. Maximized short-run profits to the Florida orange indus-
try invite additional competition in the long run from
other potential suppliers domestic and foreign, natural
and synthetic;
7. The empirical estimates of marginal revenue and mar-
ginal cost require frequent reappraisal. Reestimation is
deemed particularly necessary as crop size exceeds the
range of observations recorded for the 1961-1967 period
or as noticeable changes in consumers' tastes and prefer-
ences occur.























APPENDIX TABLES














Appendix Table 1. Estimated Total Cost Functions for Selected Orange Products.


Estimated Equation1


Frozen orange concentrate


C FCcO


= 119.21022


Canned single strength orange juice C cssOJ = 23.64957 +



Chilled orange juice C coJ = 25.30252 +



Fresh Florida oranges C FFO = 53.07698 +


IValues in the parentheses, (), are the estimated standard errors of the regression


.97018 Q FcoJ
(.53075)


.17704 Q cssoJ
(.10730)


.37488 Q coj
(.11194)


1.01076 Q FFO
(.52579)

coefficients.


Coefficient of
Determination
R2



.2178



.1849



.8487



.2354


Product









Appendix Table

Product Form
and Market
Sector


2. Net Marginal Revenue Functions for Eight Orange Product Marke
Categories.
Coefficients of Net Marginal Revenue Functions

Q FCOJ-F Q COJ-F Q CSSOJ-F Q FFO-F


FCOJ F -231.71126
COJ F -76.98596
CSSOJ F -239.59314
FFO F -530.4248(
FCOJ I
COJ I
FCOJ E
CSSOJ E
Constraint 136.25483 34.74396 118.72281 193.35485









Appendix Table 2. Extension

Coefficients of Net Marginal Revenue Functions

Q FCOJ-I Q coJ-I Q FCOJ-E Q CSSOJ-E X:= Constant'
-1 = -4.84208
-1 = -1.80728
-1 = -2.55641
-1 = -5.50361
-577.01530 -1 -2.84414
-34.17022 -1 = -0.96260
-.00428 -1 = -2.98796
-.00100 -1 = -1.02630
137.55591 35.07572 .00071 .00018 = 6.09985

'These constants are the original a estimates from the product demand functions
vith a negative sign and the appropriate marginal cost added. The constraint equation
vould ordinarily exhibit coefficients for the Q's (quantity variables) with a positive
ralue of one. However, since the demand functions were estimated using different
[uantity units, it was necessary to adjust the equations in order to obtain results on
in equivalent, i.e., box, unit basis. The reader is referred to Weisenborn (11, p. 150)
'or a detailed explanation of the adjustment procedure.















Appendix Table 3. Estimated Total Revenue and Maximum Net Revenue Using a Crop of 100 Million Boxes of Oranges With Alloca-
tion of 70% to the Primary Market and 30% to the Secondary Market.

Total Total Net
Product and Quantity Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions

FCOJ F 42.47 gal. 30.07 156.34 121.60 34.74
COJ F 36.81 gal. 6.65 57.74 22.35 35.39
SCSSOJ F 19.05 cases 11.75 41.26 35.03 6.23
FFO F 21.53 boxes 21.53 87.27 74.84 12.43
Primary Total 70.00 342.61 253.82 88.79
FCOJ I 11.87 gal. 8.40 27.83 33.97 6.14
COJ I 72.17 gal. 13.03 58.35 43.81 14.54
FCOJ E 8.64 gal. 6.14 20.89 24.75 3.86
CSSOJ E 13.46 gal. 2.42 8.65 26.03 -17.38
Secondary Total 29.99 115.72 128.56 -12.84
OVERALL TOTAL -99.99 458.33 382.38 75.95















Appendix Table 4. Estimated Total Revenue and Maximum Net Revenue Using a Crop of 100 Million Boxes of Oranges With Alloca-
tion of 60% to the Primary Market and 40% to the Secondary Market.
Total Total Net
Product and Quantity Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions

FCOJ F 38.11 gal. 26.98 148.62 110.04 38.58
COJ F 23.65 gal. 4.27 42.28 13.43 28.85
o CSSOJ F 14.83 cases 9.15 35.35 32.51 2.84
FFO F 19.62 boxes 19.62 83.78 72.91 10.87
Primary Total 60.02 310.03 228.89 81.14
FCOJ I 13.96 gal. 9.89 29.13 40.32 -11.19
COJ I 107.46 gal. 19.40 59.09 61.03 1.94
FCOJ E 10.10 gal. 7.17 21.78 29.15 7.37
CSSOJ E 19.67 gal. 3.54 7.55 27.13 -19.58
Secondary Total 40.00 117.55 157.63 -40.08
OVERALL TOTAL 100.02 427.58 386.52 41.06















Appendix Table 5. Estimated Total Revenue and Maximum Net Revenue Using a Crop of 150 Million Boxes of Oranges With Alloca-
tion of 70% to the Primary Market and 30% to the Secondary Market.

Total Total Net
Product and Quantity Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)

in Millions
FCOJ F 57.78 gal. 40.91 168.33 138.44 29.89
COJ F 82.86 gal. 14.96 66.37 41.14 25.23
SCSSOJ F 33.86 cases 20.89 47.31 43.88 3.43
FFO F 28.26 boxes 28.26 92.81 81.64 11.17
Primary Total 105.02 374.82 305.10 69.72
FCOJ I 15.01 gal. 10.62 29.37 35.97 6.60
COJ I 125.11 gal. 22.59 52.61 62.12 9.51
FCOJ E 10.82 gal. 7.68 21.95 25.92 3.97
CSSOJ E 22.77 gal. 4.10 5.80 27.68 -21.88
Secondary Total 44.99 109.73 151.69 -41.96
OVERALL TOTAL 150.01 484.55 456.79 27.76















Appendix Table 6. Estimated Total Revenue and Maximum Net Revenue Using a Crop of 150 Million
tion of 60% to the Primary Market and 40% to the Secondary Market.


Boxes of Oranges With Alloca-


Total Total Net
Product and Quantity Revenue Cost Revenue
Market Sector (Units) (Boxes) (Dollars) (Dollars) (Dollars)
in Millions


FCOJ F
COJ F
CSSOJ F
FFO F
Primary Total
FCOJ I
COJ I
FCOJ E
CSSOJ E
Secondary Total
OVERALL TOTAL


51.22 gal.
63.12 gal.
27.50 cases
25.38 boxes

18.14 gal.
178.05 gal.
13.00 gal.
32.08 gal.


36.27
11.39
16.97
25.38
90.01
12.84
32.15
9.23
5.78
60.00
150.01


166.07
71.32
47.50
91.71
376.60
28.47
5.79
21.32
- 4.28
51.30
427.90


123.84
30.28
40.08
48.73
242.93
43.85
85.43
31.42
29.33
190.03
432.96


42.23
41.04
7.42
42.98
133.67
- 15.38
- 79.64
- 10.10
- 33.61
-138.73
- 5.06





















ACKNOWLEDGMENTS

This publication is based heavily upon David E. Weisenborn's
Ph.D. dissertation, "Market Allocation of Florida Orange Pro-
duction for Maximization of Net Revenue," Department of
Agricultural Economics, University of Florida, 1968. Members
of Dr. Weisenborn's supervisory committee included Dr. R. L.
Lassiter, Dr. Leo Polopolus, Dr. D. L. Brooke, and Dr. F. W.
Williams, with Dr. W. W. McPherson serving as chairman.
The authors are indebted to several firms in the Florida
citrus industry for supplying data and information. The infor-
mation provided by Professor A. H. Spurlock dealing with
packing and processing costs was particularly useful. The sup-
port and assistance of the Florida Department of Citrus is also
gratefully acknowledged.
Our colleagues, C. D. Covey, J. L. Pearson, and F. H. Tyner,
plus four anonymous reviewers of the Florida Agricultural
Experiment Station, made numerous constructive suggestions
toward improving the manuscript.
The computing work was conducted at the University of
Florida Computing Center.









LITERATURE CITED


(1) Chapman, W. F., Jr. Demand and substitution relationships for Flor-
ida and California Valencia oranges produced for fresh market. Ph.D.
dissertation. Univ. of Fla. December 1963.
(2) Florida Canners Association. Statistical summary, 1961-62 through
1966-67 annual summaries. Winter Haven, Florida.
(3) Florida Citrus Mutual. Annual statistical report, 1953-54 through
1966-67 issues. Lakeland, Florida.
(4) ---. Triangle. Vol. 18. February 13, 1969.
(5) Johnston, J. Statistical cost analysis. McGraw-Hill Book Company,
Inc. 1960.
(6) Minden, A. J. Quadratic programming: A tool for estimating optimal
final product combinations. The So. J. of Bus. pp. 1-8. April 1967.
(7) Spurlock, A. H. Costs of packing and selling Florida fresh citrus
fruits. Fla. Agr. Exp. Sta., Agr. Economics Mimeo Report. 1953-54
through 1966-67 annual reports.
(8) Costs of picking and hauling Florida citrus fruits. Fla. Agr.
Exp. Sta., Agr. Economics Mimeo Report. 1953-54 through 1966-67
annual reports.
(9) Costs of processing, warehousing, and selling Florida citrus
products. Fla. Agr. Exp. Sta., Agr. Economics Mimeo Report. 1953-54
through 1966-67 annual reports.
(10) Waugh, F. V. Demand and price analysis. Economic and Statistical
Analysis Division, Economic Research Service, U. S. Dept. of Agri-
culture, Washington, D. C. November 1964.
(11) Weisenborn, D. E. Market allocation of Florida orange production
for maximization of net revenue. Ph.D. dissertation. Univ. of Fla.
1968.
(12) Weisenborn, D. E., W. W. McPherson, and Leo Polopolus. Demand
for Florida orange products in foodstore, institutional, and export
market channels. Fla. Agr. Exp. Sta. in cooperation with the Florida
Department of Citrus, Bull. 737. 1970.




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