Title Page
 List of Tables
 List of Figures
 Processing cooperatives and arrangements...
 A conceptual framework for cooperative...
 Empirical procedures: An application...
 Empirical results and discussi...
 Biographical sketch

Group Title: impact of alternative marketing arrangements on the performance of processing cooperatives /
Title: The Impact of alternative marketing arrangements on the performance of processing cooperatives /
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00097421/00001
 Material Information
Title: The Impact of alternative marketing arrangements on the performance of processing cooperatives /
Alternate Title: Processing cooperatives
Physical Description: ix, 141 leaves : ill. ; 28 cm.
Language: English
Creator: Lopez, Rigoberto A ( Rigoberto Adolfo ), 1957-
Publication Date: 1983
Copyright Date: 1983
Subject: Agriculture, Cooperative -- Florida   ( lcsh )
Sugarcane -- Processing -- Florida   ( lcsh )
Cooperative marketing of farm produce   ( 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, 1983.
Bibliography: Bibliography: leaves 137-140.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Rigoberto Adolfo Lopez.
 Record Information
Bibliographic ID: UF00097421
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 - 000381744
oclc - 10331667
notis - ACC2275


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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Processing cooperatives and arrangements structures
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
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        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
    A conceptual framework for cooperative behavior and performance
        Page 30
        Page 31
        Page 32
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        Page 55
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    Empirical procedures: An application to sugarcane processing cooperatives
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
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    Empirical results and discussion
        Page 84
        Page 85
        Page 86
        Page 87
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        Page 134
        Page 135
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        Page 137
        Page 138
        Page 139
        Page 140
    Biographical sketch
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
Full Text







To my parents


It has been a very rewarding learning experience indeed to work

with Dr. Thomas H. Spreen, chairman of my dissertation committee. Dr.

Spreen skillfully provided insights that proved worthwhile to explore.

I also appreciate the fact that he read and re-read the copious drafts

of this manuscript more frequently than those of Alfred Marshall.

I would also like to thank Dr. Jose Alvarez, Dr. Thom Hodgson, Dr.

John VanSickle and Dr. Ronald Ward, members of my dissertation commit-

tee, who provided fruitful input from their expertise areas. My appre-

ciation is also extended to Dr. Max Langham with whom I learned "beyond

the classroom gate." Jim Pheasant deserves thanks for his contribution

in developing the computer program used in this study.

Financially speaking, I am grateful to the Food and Resource

Economics Department of the University of Florida for allowing my sur-

vival through the graduate school years.

Emotionally speaking, I am indebted to the friends I made in

Gainesville, the best in my life, who shared it all and who were my

support mechanism when discouragement was setting in. Many thanks go to

my family who has always endowed me with unconditional love. Finally,

let me recognize that there are many unmentioned heroes of this endeavor

whom I wish to thank, but I have to stop writing somewhere.



ACKNOWLEDGEMENTS ................................................... iii

LIST OF TABLES ...................................................... vi

LIST OF FIGURES .................................................... vii

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


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

The Problem ............................ ............... 3
Behavioral Nature of the Problem ..................... 5
Objectives ........................................... 7
Scope ................................................. 8
Organization of the Study ............................ 9


The Cooperative Association .......................... 11
Processing Cooperatives .............................. 14
Cooperative Theory Development ....................... 17
Cooperative Arrangements ............................. 22
Payment Arrangements .............................. 23
Financial Arrangements ............................ 25
Processing Arrangements ........................... 26
Control and Cooperative Objective .................... 26

AND PERFORMANCE........................................... 30

A Mathematical Model of Processing Cooperatives ...... 31
Cooperative Behavior and Optimal Volume .............. 32
Myopic and Coordinated Behavior ................... 32
Rationale for Myopia .............................. 38
Cooperative Surplus and Price Sensitivity ......... 39
Arrangements to Ensure Coordinated Behavior ....... 40
Benefits from Coordination ........................ 42
Underutilized Cooperative Plant ................... 42
Payment for Quality .................................. 45
Fully Accurate Pricing ............................ 47
Pooling ........................................... 48
Equilibria Location ............................... 50


III (Continued)

Heterogeneous Membership ............................. 53
The Coordinated Case .............................. 54
Payment Based on Raw Product ...................... 56

PROCESSING COOPERATIVES .................................. 57

Florida Sugarcane Cooperatives ....................... 58
Production Environment and Value Added ............... 60
A Mathematical Programming Model ..................... 61
Payment Based on Raw Product .. ................... 66
Payment Based on Finished Product ................. 68
The Coordinated Cooperative .. .................... 69
Processing Arrangements ........................... 69
Estimation of Parameters and Data Management ......... 70
Estimation of Yields .............................. 70
Processing and Cooperative Structures ............. 76
Estimation of Costs ............................... 78
Summary of Estimations ............................ 81
Implementation of the Model .......................... 81

V EMPIRICAL RESULTS AND DISCUSSION ......................... 84

The Performance Measures ............................. 84
Baseline Results and Discussion ...................... 87
Sensitivity Analysis ................................. 91
Membership Homogeneity ............................ 92
Alternative Quality Choice Spectra ................ 94
Summary of Results .................................... 99

VI CONCLUSION ............................................... 101

Summary .............................................. 101
Conclusions .......................................... 103
Limitations and Suggestions for Further Research ..... 105



B VARIABLES IN THE YIELD MODELS ............................ 115

FLOW PROBLEM ............................................. 119

D THE COMPUTER PROGRAM ..................................... 127

REFERENCES .......................................................... 137

BIOGRAPHICAL SKETCH ............................................... 141


Table Page

2.1 Differences Between Cooperative Associations and
Noncooperative Corporations .................................. 14

2.2 Differences Between Pure Marketing and Processing
Cooperatives ................................................ 15

4.1 Notation Used in the Mathematical Programming Model
for Sugarcane Processing Cooperatives ....................... 64

4.2 Notation Used in the Specification of Yield Models .......... 72

4.3 Notation Used in the Regressions for Predicting Percent of
Recoverable Sugar and Net Tons of Sugarcane ................. 74

4.4 Estimated Coefficients and Selected Statistics for Predicting
Percent of Recoverable Sugar ................................ 75

4.5 Estimated Coefficients and Selected Statistics for
Predicting Net Tons Per Acre ................................ 77

4.6 Comparison of Varieties of Cane in the Mathematical
Programming Model ........................................... 80

4.7 Parameter Estimates for the Mathematical Programming
Model for Sugarcane Processing Cooperatives ................. 82

5.1 Results of Performance Measures of Alternative Marketing
Arrangements for Sugarcane Processing Cooperatives .......... 88

5.2 Results of Performance Measures of Alternative Marketing
Arrangements for Sugarcane Processing Cooperatives with
Identical Members ........................................... 93

5.3 Results of Performance Measures of Alternative Marketing
Arrangements for Sugarcane Processing Cooperatives with
Alternative Specification of Raw Product Quality ............ 96

5.4 Results of Performance Measures of Alternative Marketing
Arrangements for Sugarcane Processing Cooperatives with
Alternative Processing Cost Indices ......................... 98

B.1 List of Factors that Affect Sugarcane Growth and
Sucrose Accumulation in Florida ............................. 116

C.1 Payoffs and Bounds for the Hypothetical Network
Flow Example .................................... ............ 124



2.1 Inter-Flows of Inputs and Outputs in a Generalized
Hypothetical Cooperative Association Environment ............ 12

3.1 Myopic and Coordinated Cooperative Equilibria ............... 37

3.2 Alternative Membership and Open Market Purchase Policies
for an Underutilized Cooperative Plant ...................... 43

3.3 Equilibria Locations for Two Quality Levels ................. 52

A.1 Myopic and Coordinated Equilibria in the Long Run ........... 110

A.2 Variable Cooperative Plant Size in the Long Run ............. 113

B.1 A Two-Stage Assignment of Varieties ......................... 121

B.2 Network of the Example Problem .............................. 125

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



Rigoberto Adolfo Lopez

August 1983

Chairman: Thomas H. Spreen
Major Department: Food and Resource Economics

The thrust of this study concerned a theoretical and empirical

assessment of the impact of alternative marketing arrangements on the

performance of processing cooperatives. The main distinction made

between a pure marketing cooperative and a processing cooperative was

the existence of a fixed cooperative plant.

The theoretical framework involved modeling of two types of

members' behavior: (1) individualistic or "myopic" behavior where

members strive to maximize only their own net returns and (2) coordi-

nated behavior that leads to a Pareto optimal solution where total and

individual profits are maximized. The model was extended to allow for

variable raw product characteristics and heterogeneous members. It was

concluded that a preferred coordinated solution can be attained by

inducing compliance through quotas and individualized penalties and

rewards that can be embodied in payment policies.


The empirical procedures involved a mathematical programming model

applied to sugarcane processing cooperatives in Florida. This model was

conceptualized as having two strata of decision making: (1) the level

at which policies are set and (2) that at which a member maximizes own

net returns taking policies set at level I and other members' actions as

given. Although the resulting problem was large and data intensive, it

was manageable. To operationalize the model, the parameters were esti-

mated by statistical models and the resulting problem was solved as a

network flow.

The empirical results reinforced the internal validity of the

theoretical model. For instance, a coordinated sugarcane cooperative

made net returns that were twice as large as those attained by a cooper-

ative where members' raw product was pooled and the members behaved

individualistically. The use of processing quotas tended to equalize

members' net returns and in some cases increased coordination. Overall,

it was concluded that if members behave individualistically and not in

the collective interest, the achievement of preferred performance out-

comes must be devised through policies at the individual level--the

particular level of their response.



A cooperative association is a coalition of firms that pursues

economic activities for the benefit of its members. Farmer cooperatives

are usually classified, depending on the vertical position of such

activities, into marketing cooperatives and (input) supply cooperatives.

The agricultural economics literature has not distinguished between

processing cooperatives and pure marketing cooperatives. In addition to

buy-sell and first-handler operations, processing cooperatives internal-

ize the processing of the raw product supplied by the patrons by alter-

ing its form. This encompasses a greater dominion of a value-added

system than pure marketing cooperatives. Since integration is costly

and capital intensive, by extending downstream boundaries these coopera-

tives involve higher capital investment. This increases the likelihood

of limited processing plant capacity and of inflexibility in membership,

financial, marketing and organizational policies.

Processing cooperatives in the U.S. are important in agricultural

activities such as sugarcane, citrus, fruits and vegetables, dairy and

poultry. For instance, processing cooperatives in California handle 85

percent of Freestone peaches, 60 percent of spinach, 60 percent of

apricots and 25 percent of tomato volumes (Garoyan, 1979). In the U.S.

dairy sector in 1973, cooperatives processed 28 percent of the milk

volume (O'Day, 1978).

Two factors are likely to enhance the future importance of proces-

sing cooperatives. One is the continuation of the past growth trend in

agricultural cooperatives which has been one of the most rapid struc-

tural development in the U.S. farming sector in recent decades.1 Second

is the increase of forward integration from producers-first handler

activities which is essential for the future survival of marketing

cooperatives (Kraenzle et al., 1979).2 However, as farmer cooperatives

attempt to forward integrate into the processing segments of the U.S.

food industries, they will undoubtedly face entry barriers in which

financial and operational sophistication is needed.

The impressive growth of the agricultural cooperatives has expanded

the set of questions among policy makers and agricultural economists

about the impact of agricultural cooperatives on members' income, output

level, consumer prices and overall performance (e.g., Lang et al., 1982,

and Vitaliano and Condon, 1982).3 At the same time, the growth in

cooperative theory and studies has less than matched the growth of

cooperatives and the increasing concern about them. Vitaliano and

Condon (1982) identified three important questions relating to further

iThe importance of these organizations in the metamorphosis of the
U.S. agricultural industry is reflected by the fact that in the 25 year
period from 1950 to 1975, agricultural cooperatives increased their
share of cash receipts of products marketed at the first-handler level
from 20 percent to nearly 30 percent (USDA, 1977).

2These authors also indicate other reasons for cooperatives to
forward integrate such as the enhancement of their share of the consumer
dollar, the protection of members' markets, and the enhancement of their
members' bargaining strength.

3These questions were raised and discussed in a 1977 workshop of
the North Central Regional Research Committee 117 under the topic
"Agricultural Cooperatives and the Public Interest."

developments of cooperative theory: (1) internal organization of the

cooperative and the objective of the participants, (2) information,

monitoring and control of cooperatives, and (3) technical and organiza-

tional efficiency of cooperatives.

The Problem

The foregoing suggests the need for research dealing with organiza-

tional and behavioral aspects of cooperatives. Clearly, the set of

arrangements among cooperative members constitutes the core of the

cooperative structure along which resource allocation is guided, there-

fore constituting an important determinant of their performance. Even

though these arrangements replace the mechanism of open market forces

for a raw product, they retain the role as prime coordinator of market-

ing and production among the decision units.

A conflict-free or harmonious cooperative operation is rarely, if

ever, the case. The likelihood of conflict increases as the degree of

downstream integration increases, making conflict issues of foremost

importance to processing cooperatives. The conflicts are settled in

part by contractual arrangements, which are essential instruments of

coordination among the members in order to achieve their objectives. To

the degree that members are interdependent in the operation of the

cooperative plant, arrangements among the members are essential for

workable guidelines of mutual (proportional) share of benefits and


Arrangements among members of a processing cooperative converge to

three areas: (1) payment to each member relative to the actual value or

contribution of the raw product delivered; (2) the share of a fixed

processing capacity of the cooperative plant; (3) financial arrangements

regarding deferred patronage refunds and other financial parameters.

Below concentration is placed on the first two areas.

The role of arrangements for payment is of primary importance in

providing adequate incentive and equity structures among the members.

These arrangements concern the mechanism for computing payments to each

member for their deliveries from the net savings of the cooperative.

All cooperatives are bound morally, but not legally, by the arrangement

that they must redistribute all net savings in "proportion" to the use

of cooperative services (Abrahamsen, 1976). Ideally, each member should

be paid in accordance to the use value of his delivery. The use value

of agricultural commodities varies with quantity, quality, delivery time

and distance from the processing plant.4

In establishing payment arrangements, cooperatives resort to pool-

ing, a process of averaging costs and returns generated by the

members. The degree' of pooling affects the rationalization of raw

product prices perceived by the patrons from the cooperative, since the

individual in isolation does not receive the full benefit or penalty

from his actions. At the farm level, quality of raw product depends

upon numerous factors, including delivery time, variety of the crop,

A raw product may offer a set of quality parameters associated
with the demand of the final commodity (characteristics that affect the
consumer evaluation of the product) and/or quality parameters associated
with the supply of the final commodity (that affect production costs).
Examples of the latter are in citrus where specialty fruit costs 15
percent more to process (Polopolus and Lester, 1969) and high fiber
sugarcane which increases the cost of extraction of raw sugar (Meade and
Chen, 1977).

production practices and weather. A disincentive for better quality

induces a lower general level of quality than when quality is explicitly

compensated. An equity problem arises if raw products are co-mingled

with pooling, despite the fact that individual growers may have deliv-

ered different qualities of raw product.

Cross-externalities among the members regarding the use of the

processing plant result from limited processing capacity, especially

when coupled with production seasonality and perishability of the

product. There are two aspects regarding processing arrangements. One

is the use of individual quotas among the members throughout the proces-

sing season as an instrument of "fairness." The other aspect is the

sovereignty of the members in determining the volume of their delivery

in the spirit of the democratic nature of cooperative institutions.

This sovereignty holds also in determining the quality of the raw

product delivered.

To discern the impact of alternative arrangements (structure) among

cooperative members on the performance of the cooperative, one must

incorporate the individual members and cooperative (group) behavior.

The above situation allows a broader class of group behavior problems,

in particular free riding and the cooperative analogy of the prisoner's


Behavioral Nature of the Problem

The kernel behavioral postulate of economics is that man is egois-

tic, rational and a utility maximizer. Even though the basic behavioral

force of increasing well-being is what induces a group of farmers to

"cooperate" by forming a cooperative association, individually they are

likely to engage in independent noncooperative behavior. The resulting

behavior, from a conceptual standpoint, is the analogy of the prisoner's

dilemma.5 Such behavior results from a member's dilemma when he has the

incentive to "free ride" (and thus capture gains when other members are

behaving for the cooperative welfare) or to "protect" himself when other

members are attempting to free ride. The so-called dilemma arises

because what appears to be best for an individual member, given the

behavior of other members, produces a result that can be improved by

"cooperation" or coordination, even if every individual prefers the

mutual cooperation outcome.

Still in the twilight zone of behavioral theory is the dilemma of

whether the achievement of the preferred outcome in the Prisoner's

Dilemma Game is compatible with individual incentives. Hobbes' theory

(1909) suggests that the only way to insure that the preferred outcome

is obtained is to establish a government with sufficient power to ensure

that it is in every man's interest to choose the cooperation outcome.

This suggests that coercion is necessary (or that the individuals agree

to be coerced) in that regard. In terms of the above problem, this

would indicate a centralized management that coordinates members' deliv-

eries so that the coordination outcome results. Coercion, however,

implies the loss of members' sovereignty while tailoring of arrangements

may provide a coordination mechanism among cooperative members without

resorting to coercion.

5Luce and Raiffa (1957) present a discussion of the classical
prisoner's dilemma game.

By its nature, an arrangement is a contract, and contracts govern

or regulate the exchange between parties, thus constraining their behav-

ior. Alchian and Demsetz (1972) argue about the possibility of individ-

uals "shirking" contractual responsibilities if benefits of doing so

exceed the costs. As a case in point, they consider that mutual shirk-

ing is more likely to occur in the case of common ownership.

The problem of scanning arrangements among cooperative members is

analogous to problems faced by policy makers who must account for the

actions of a myriad of decentralized decision making units which take

policy variables as given, but also have their own objectives. Thus,

setting arrangements scenarios to scan alternative arrangements can be

viewed as a hierarchical decision problem.


The overall objective of this research is the assessment of the

implications of alternative arrangements among the members of processing

cooperatives through the structure-behavior-performance paradigm. More

specifically, the objectives are

1. To provide a conceptual framework to investigate the behavior of

processing cooperative members, and to assess the performance

implications of alternative coordination arrangements among the

members that may induce compliance to attain coordinated cooper-

ative equilibria.

2. To develop an empirical harvest-processing model as a con-

strained optimization problem suitable to represent the arrange-

ments among the members.

3. To illustrate the impact of alternative pricing policies, volume

regulation and processing arrangements for processing coopera-

tives by accommodating the above models to the case of Florida

sugarcane processing cooperatives.


The intended scope of this research is confined to the determina-

tion of the economic effects of alternative arrangements on the perfor-

mance of processing cooperatives. This is not, however, an attempt to

find the "best" arrangements for these farmer-owned organizations. The

lack of any universal set of value judgments, of accurate relevant data,

and the impossibility of a fully satisfactory partial solution, will

prevent that.

The term "alternative" rather than "optimal" arrangements implies

discretion on the formulation of arrangements scenarios. Thus the

present analysis is limited to a set of policy variables in the spectrum

of arrangements possibilities, to provide, perhaps, a heuristic answer

to the problem. In actual situations, other considerations (e.g.

social, ethical or political) may be decisive, regardless of the

economic outcome. If, however, the study succeeds in making some of the

central issues involved in the formulation and implementation of alter-

native arrangements any clearer, the scope of it is not fruitless in

this unexplored area of research.

Organization of the Study

This chapter has presented an introduction to the problems posed by

cooperative arrangements and has listed the objectives of the study.

The following chapter describes the economic nature of cooperative

associations, emphasizing the organizational characteristics of proces-

sing cooperatives. The heritage of economic theories of cooperation is

also reexamined. Then, the chapter addresses the underlying rationale

and identification of alternative cooperative arrangements.

In Chapter III, the concepts behind the operational procedures of

cooperatives provided in Chapter II are integrated into a conceptual

processing cooperative model to explain the behavior and functioning of

the cooperative and its members. The evaluation of different practices

through their impact on performance is also provided.

The conceptual model developed in Chapter III is modified in Chap-

ter IV to set up a mathematical programming model for the simulation of

alternative coordination arrangements. The empirical model is applied

to Florida sugarcane cooperatives for which the parameters are esti-

mated. The model is implemented as a network flow problem.

Chapter V presents the performance results of the simulation of

different arrangements such as payment based on the amount of sugarcane

(raw product) delivered, payment based on the amount of sugar (finished

product) delivered, coordinated (maximum total profits) cooperative

operation, delivery quotas and volume regulation schemes. Performance

(allocative efficiency and equity) comparisons are made, and a general

assessment of results is provided.


In the last chapter, the findings of the study are summarized.

Conclusions, limitations and suggestions for further research are pro-

vided for both the theoretical and empirical expositions of previous




Despite the important and increasing role of cooperatives in the

share of agricultural output, relatively few theoretical or empirical

studies, and no specific studies, have been done on sugarcane processing

cooperatives to date. This chapter discusses the basic concepts of

cooperation. The primary objective is to aid in the understanding of

the issues involved and to clear the avenues for subsequent theoretical

and empirical developments.

The Cooperative Association

A cooperative association is a coalition of firms or individuals

that pursue economic activities for the benefit of its members. Farmer

cooperatives are usually classified in two categories according to the

vertical position of such services: (1) marketing cooperatives, where

the cooperative provides marketing and/or processing services to the

patrons for the commodity they produce, and (2) supply cooperatives,

where the cooperative provides members with one or more of the produc-

tion inputs they need for their farm operations. In accordance with

their horizontal nature, cooperatives can be classified as having closed

or open membership depending upon whether new entry of members is

restricted (closed) or not (open).

The possible configurations of cooperatively-structured businesses

are summarized in Figure 2.1. Let Xij and denote a variable input

-- 4

X = Set of Variable Inputs

Y. .= Set of Outputs

i,j= Source and End Node
= 1,2,3,4 but irj

Figure 2.1.

Inter-flows of Inputs and Outputs in a Generalized
Hypothetical Cooperative Association Environment.

and a particular output flowing from node i to node j, where the nodes

1, 2, 3 and 4 are the cooperative, its members, nonmembers, and outside

markets where the cooperative and producers buy or sell commodities,

respectively. In a larger time span, membership adjustments can be

viewed as a conceptual two-way flow: members enter (Y42) and members

exit (Y24) from the cooperative. A closed membership cooperative would

be represented by deleting Y42. Marketing cooperatives operate with

little or no flow along X32 and X34, while supply cooperatives operate

with little or no flow along Y23 and Y43. X12' Y23' Y31, and X13 con-

stitute the organizational scheme of a typical processing cooperative

whose structure description is given in the next section. These flows

are also indicative of the flows of costs and revenues in the micro-


One way to discern the characteristics of a cooperative association

is by comparing it with noncooperative firms. VanSickle (1980) presents

a series of features that distinguish cooperatives from noncooperative

corporations. These are summarized in Table 2.1. The role that a raw

product plays in decision making by noncooperative firms and marketing

cooperatives differs. In the former, the raw product is just an input

in the vertical operation while for marketing or processing cooperatives

the raw product is also the vehicle of return of the members' operations

with the cooperative.

Another way to discern the characteristics of cooperative associa-

tions is by considering the principles that govern the interrelation-

ships between a cooperative and its members. Abrahamsen (1976) states

three principles: (1) service at cost by the cooperative, (2) member

control and ownership, and (3) limited return on capital. These

principles make the conventional or neoclassical theory of the firm

neither appropriate nor directly applicable to the study of cooperative


Table 2.1. Differences Between Cooperative Associations and Noncooper-
ative Corporations.

Feature Cooperative corporation

1. Benefits flow basis Patronage Investment
2. Ownership and control basis Members Investment
3. Return on capital Limited Open

4. Benefit form As patron service As returns
Stocks and deferred
5. Capital source Stocks
patronage refunds
6. Stock price Fixed Market determined

Source: VanSickle, 1980, pp. 1-4.

Processing Cooperatives

The agricultural economics literature has not distinguished between

processing cooperatives and pure marketing cooperatives. In addition to

buy-sell and first-handler operations, processing cooperatives inter-

nalize the processing of the raw product supplied by the patrons by

altering its form. This encompasses a greater dominion of a value-added

system than pure marketing cooperatives. Since integration is costly

and capital intensive, by extending the downstream boundaries these

cooperatives involve higher capital investment, which increases the

likelihood of limited processing plant capacity and of inflexibility in

membership, financial, marketing and organizational policies. In terms

of Figure 2.1, this type of organization implies that Y23 A Y13 A Y43'

The organizational implications associated with processing cooper-

atives point toward the need for a more detailed distinction from pure

marketing cooperatives. To some extent, one can presume that these

distinctive characteristics are linked to the nature of integration, to

economic characteristics of the agricultural commodity involved and to

the structure of markets both in the buying and in the final demand side

of particular situations. Some distinguishing organizational charac-

teristics of processing cooperatives are summarized in Table 2.2 and

discussed below.

Table 2.2. Differences Between Pure Marketing and Processing Cooper-

Marketing Processing
cooperatives cooperatives

Degree of vertical integration +c ++
Alteration of raw product form 0 ++
Perishability of raw product + ++
Capital requirement + ++
Restriction of membership likelihood + ++
Members interdependence + ++
Payment scheme complexity ++ +++

aThese differences have not been directly observed, but derived in a
hypothetical fashion in the text of the foregoing section.
bAs measured by the share of the value-added system.

CThe "+" sign indicates "High," "-" low, and "0" neutral.

Since processing cooperatives are a more integrated form of organi-

zation than pure marketing cooperatives, their boundaries encompass a

greater dominion of the value added system of the agricultural and food

industry. Marketing cooperatives, in a pure sense, engage in buy-sell

operations for the members with little or no further service, other than

centralizing the marketing of an agricultural commodity on behalf of

their patrons. The grain cooperatives in the northern United States,

for example, provide their members with the services of storage (ele-

vators), and coordination and transfer of product to processors or

wholesalers. Processing cooperatives advance to the next pricing point,

by internalizing the processing of the raw product supplied by the

patrons and marketing the finished commodity or commodities. However,

most agricultural commodities require at least some transformation that

cooperatives may undertake in the future.

Processing cooperatives are also more likely to handle a more

perishable commodity than exclusively marketing cooperatives. The

perishability of the product increases the propensity to forward inte-

grate into processing to control or assure an outlet for the product, or

to transform the commodity into a less perishable form.

Since integration is costly and capital intensive, processing

cooperatives involve a higher amount of capital investment. This

entails a greater commitment and possibly more inflexible membership

policies. Restriction of membership due to a plant capacity constraint

was found by Youde and Helmberger (1966). Too little volume may not

allow the coverage of a high overhead cost. Too much volume, a result'

of the influx of new members, results in a purge of profitability of

already existing members.

Since processing capacity is costly and therefore possibly limit-

ing, the arrangements among members for sharing the plant capacity is

more binding than in marketing cooperatives, especially when the commod-

ity has a time-dependent use value and is highly perishable. Payment

issues are more crucial in the case of processing cooperatives since

adding the processing dimension has the implication of expanding the set

of delivery attributes and variables that affect the value of the

members' deliveries.

Cooperative Theory Development

The earlier studies of cooperation were of a socio-reformistic,

descriptive and philosophical nature, leaving little or no room for

criticism. More recently, cooperative theory has evolved in the frame-

work of formal economic analysis, reorienting its treatment toward

scientific interpretation. This section reviews the latter phase.

The pioneer study of Emelianoff (1948) portrays the cooperative as

"an aggregate of economic units" with no decision making role. The

cooperative, then, only coordinates the activities of the units which

are directed by no central authority. Each unit retains its economic

individuality and independence, which in turn leads to conflicting

interests. He paved the road for posterior theory development, partic-

ularly by influencing Phillips.

Phillips (1953), who embraced Emilianoff's economic morphology, can

be considered to be the first to present a formal and explicit

cooperative model in a strict sense. He visualizes the cooperative as a

multiplant operation in which the participating firms agree to function

coordinately with respect to their joint activity. In this multiplant

environment, a cooperative member maximizes profits by equating the sum

of the marginal cost in its own plant and the marginal cost of the coop-

erative plant, with the marginal revenue from the output sold by the


Aresvik (1955), criticizing Phillips' analysis, proposes that

equilibrium is based on the average cost and average revenue curves of

the cooperative and not on the cooperative marginal curves as stated by

Phillips (1953). He criticized Phillips for inferring about institu-

tional arrangements exclusively from equilibrium conditions while over-

looking normative premises. On this perplexing problem, he suggests


Making group decisions in the group of cooperating persons
is, from a formal standpoint, exactly the same problem as
making social choices based on individual ordering, which is
intensively discussed in the literature of welfare eco-
nomics. Today, I think, it is the consensus among the econo-
mists that it is impossible without value premises to make
the step from individual orderings (preferences) to group
(Aresvik, 1955, p. 143).

Trifon (1961) modified Phillips' equilibrium conditions, arguing

that neither Phillips' nor Aresvik's conditions were appropriate. In

his analysis, each member has to reconcile his own self-centered pursuit

of profit with that of other members. He remarks that under the rule of

patronage dividends, the inter-relationship of interests in a production

or processing cooperative relative to marginal changes in total volume

is as follows:

Complementarity will prevail over phases of diminishing unit-
costs. . Supplementarity will prevail over phases of constant
unit-costs, and conflict will prevail over phases of rapidly rising
unit-costs (resulting from exhaustion of inflexible capacity,
especially under a severe resource restriction).
(Trifon, 1961, p. 217)

Furthermore, Trifon's analysis shows that a member, by expanding

his patronage, obtains only a fraction of the additional revenue and

costs resulting from the adjustment by the cooperative, while his shares

of initial total revenue and costs increase.

Kaarlehto (1956) initiated another line of thought by visualizing

cooperation in the context of economic integration. His basic idea of

cooperation relies on the integration of production and ordinary busi-

ness activities. The relevant returns curves are then the average

returns to each individual member and a joint (cooperative) average

revenue curve. The joint average revenue is obtained as average returns

of output less average marketing costs, and from this the members'

marginal revenue product function is derived. To maximize profits

members equate the joint marginal revenue product to their own marginal

costs of production.

A very influential approach in the most recent vintage of cooper-

ative models was developed by Helmberger and Hoos (1962). They con-

ceived the cooperative in the framework of organization theory. In an

organization, they argued, "the participants must adopt those decisional

premises in choosing among alternative courses of action which will give

rise to consciously coordinated activity" (p. 278). In their model, the

cooperative is recognized as a single decision unit that strives to

maximize the price of raw material to the members, or equivalently, to

maximize the surplus resulting from "processing" members' (homogeneous)

raw product and selling the finished commodity. The objective is

inspired by the assumptions that physical patronage of each and all

members is fixed and that members view the price received as fixed.

According to Helmberger and Hoos (1962) the objective of the coop-

erative is to obtain a maximum surplus of cooperative net savings cor-

responding to each level of members' output. This relationship depicts

an average revenue product function, whose value is the per unit price

paid to the members. Equilibrium is established where this curve inter-

sects the members' supply function.

Hardie (1969) extended the Helmberger and Hoos model to a multi-

product case formulated as a linear program. He proposes to consider

the shadow price of each product of the cooperative as the per unit

return paid to the members so that each member receives the cooperative

surplus earned by his products. This model allows for various types and

grades of raw material and makes it the first to put the finger on the

quality issue of the members' raw product.

Another extension of the Helmberger and Hoos model is the bargain-

ing cooperative model presented by Ladd (1974). His model considers a

multi-service cooperative of raw material producers which sells input to

producers,. provides a "free" service to producer members and nonmembers

(unspecified though), and bargains with a processor for raw material

price. His analysis shows that the cooperative objectives of maximiza-

tion of quantity of raw material cooperatively marketed and the maximi-

zation of the raw material price paid to members, resulted not only in

different optimality conditions but also that neither objective was

equivalent to the total profit maximization conditions (marginal revenue

equals marginal costs). These findings elicit the sensitivity of the

cooperative operation to different objectives.

In the landmark work of Eschenburg (1971), the goal of the cooper-

ative is the maximization of the sum of members' profits. He concludes

that a simultaneous equilibrium of all the members is generally unat-

tainable since the level preferred by the members is not harmonious with

the level preferred by management. Presaging the approach to coopera-

tive theory and empirical work, he remarks:

Since the results of cooperative activity depend upon the
behavior of the participants, and since the behavior is
largely, but not entirely determined by the organization
structure (of the cooperative), it follows that the problem
of optimal organization and operation can only be dealt with
for specific organizations operating in particular environ-
ments. . The consequences for (cooperative) theory con-
struction are that one can and must derive as many different
theories as there are different (cooperative) organizational
(Eschenburg, 1971, pp. 84-85)l

Perhaps many issues can be best dealt with by specialized

theories of cooperation as suggested above by Eschenburg (1971).

On the same issue, Ladd (1982) stated

The price we would have to pay for a general theory of coop-
eration is too high. We need a number of different special
cooperative theories because no general theory can be small
enough to be useful and manageable while being large enough
to incorporate existing variations in cooperative objectives,
environments, and problems.
(Ladd, 1982, p. 2).

The above problem, indicated by Eschenburg (1971) and Ladd (1982),

is not peculiar to cooperatives. However, the conventional theory of

the firm is much more developed than cooperative theory to deal with

specific situations and environments. Thus, there is a need to develop

a theoretical framework for processing cooperatives and for individual

and cooperative behavior under alternative arrangements among the


1Vitaliano's (1977) version from the original in German.

Cooperative Arrangements

It is reasonable to expect that the structure of the coop, the
mechanism of control, the extent and nature of vertical integra-
tion, voting rules, and the standard operating procedures would be
among the most important characteristics of cooperators related to
their performance.
(Shaffer, 1977, p. 168)

As the objective of the cooperative should be to benefit the

members, different arrangements (instruments) may aim to achieve this

objective but would generate different performance results in terms of

the well-being of the members.

The preceding section has shown that a conflict-free or harmonious

unconstrained cooperative operation is rarely, if ever, the case.

Furthermore, the likelihood of conflict increases as the degree of

downstream integration increases, making conflict issues of foremost

importance to processing cooperatives. The conflicts in the joint

operation of the cooperative, which introduce elements of dissociation,

may be due to interdependence among the members. This may take the form

of cross-externalities regarding the quality of raw product delivered

and the use of restricted processing capacity. Since members are inter-

dependent in the operation of the joint plant, agreements or arrange-

ments are essential for workable guidelines of mutual share benefits and


In this study a marketing arrangement is referred to as a formal

commitment between the cooperative and its members, in which the rights,

duties and rules of operation for both the members and the cooperative

are explicitly stated, with respect to the marketing of the members'

commodities through the cooperative for services of processing and

marketing. Along these lines, arrangements can be considered "instru-

ments" of coordination of the members to achieve their objectives.

The principle of proportionality is the epitome of the organiza-

tional and financial policies established by the members. In theory,

this principle provides equitable treatment of members. The operation-

alization of this principle is one of the most perplexing problems that

cooperatives face. In this presentation arrangements are broken down

into the areas of payment, financing, and processing.

Payment Arrangements

These arrangements refer to the computation of payments to members

for their deliveries. Payments are made from the net savings of the

cooperative operation. Alternatively, they refer to the allocation of

net savings to the members for the contribution of their patronage. The

first step in establishing these arrangements is the determination of

the basis for patronage, i.e., what unit is to be used as the criterion

to allocate payment (or charge in a supply cooperative) to the

members. Some alternative methods are

1. The amount of service provided to the patron. This approach

views the cooperative as a utility plant, where members are charged for

the use of the services, and thus a "service" unit is the criterion of

allocation when such service is subtracted from the savings.

2. Amount of raw material delivered. This provision ignores

recognition of quality differentials. It is, however, an easy method to


3. Use value basis. Each member is compensated by their contri-

bution of their deliveries to the net savings of the cooperative.

The objective in selecting a payment scheme is to provide incentive

and equity to the members who individually are attempting to maximize

profits. In establishing an adequate payment norm, members must first

identify the raw product characteristics that affect the "actual" con-

tribution of each member. Some of these characteristics are (1) volume

delivered, (2) quality of the products delivered, (3) time of delivery,

(4) producer location, and (5) services required from the cooperative.

Ideally these factors should be taken into account for payment to the

patrons. In one extreme, a truly equitable method of payment may prove

disadvantageous to the members because of high implemention costs. On

the other hand, a complete pooling in favor of a flat price for the raw

product may distort the price signal sent to the members, and ultimately

result in inefficiency in the cooperative operation.

Cooperatives resort to pooling, a process of averaging costs and

returns, in establishing payments. The degree of pooling, then, refers

to the extent of boundaries in characteristic space in which average

costs and returns are applied, thus establishing a price for products

contained in a given boundary. Commonly, grades are established in

marketing cooperatives for payment purposes (Sosnick, 1963). Sosnick

(1963) proposes four evaluation criteria for a pooling program:

1. The program should provide appropriate incentives to contract

or expand the production of commodities and for grades or

quality of a given commodity (adjustment in volume and


2. The program should be equitable so that payment to the patron

for his deliveries should not diverge from the net resale value

of his deliveries;

3. The program should minimize the share of market risks borne by

individual market lots; and

4. The program should minimize the costs of operating the pooling


Financial Arrangements

The ability of cooperatives to cope with challenges encountered

when forward integrating, especially into the processing segments, is

conditioned to the financial structure they possess. The spirit of

proportionality dictates that capital should be supplied by the members

proportionately to their volume of business. Some important financial

structural parameters determined by arrangements are

1. The equity structure of the cooperative.

2. The pattern of retention of patron savings. Usually cooper-

atives pay an initial amount to patrons for deliveries and later refund

the rest when the cooperative net saving has been determined. Different

patterns of retention affect their members, especially if they have

strong liquidity preference.

3. The determination of debt-equity of the cooperative, i.e., the

degree of resorting to loans from outside sources (debt) to the capital

provided by the member (equity).

The potential conflicts associated with capital share in proportion

to patronage is that members may have different productivity of own

capital, and thus, different reservation rates of return. As important

as they are, the analysis of alternative financial arrangements and the

search for sound financial strategies for cooperatives are set aside.

This abstraction will allow more concentration on the issues surrounding

the objectives of this study.

Processing Arrangements

These arrangements refer to the share of a fixed processing capac-

ity that results from high capital cost of the cooperative plant. An

additional factor that leads to processing arrangements is the specific

pattern of use value over time, which is reflected in a pattern of

perceived revenues by the members under a given payment scheme. Some

arrangements associated with processing include

1. Temporal-related quotas. This arrangement would bind members

to send deliveries during any period of the processing season, in such a

way that deliveries of all members are scheduled proportionally across

members and over time.

2. Production quotas. Minimum quantity requirements may be neces-

sary to protect the cooperative from high operating costs due to inade-

quate volume.

3. Production ceilings. A symmetric argument holds for the impo-

sition of upper bounds in the deliveries of raw material to the members,

to protect the members of autopenalizing when operating beyond overall

optimal cooperative capacity. To the knowledge of the author, these

arrangements have not been explored. Such arrangements, however, would

appear to be controversial.

Control and Cooperative Objective

The settlement of arrangements are conditioned by the manner in

which control and decision making are shared by the members. Abrahamsen

(1976) recognizes two types of voting policies used by cooperatives:

equal voting (one man-one vote) and patronage voting (voting power

relative to patronage). As most cooperatives have been identified with

the first voting system, traditional ideas of what constitutes equitable

participation may need to be revised when cooperatives increase in

complexity of operation and when member patronage varies greatly.

The internal power structure of the cooperative can be character-

ized by a pyramid of control composed of three levels: the members, the

board of directors, and the management team. The decision making domi-

nance of one level over another affects the type of arrangements gener-

ated to achieve the objectives of the dominant element. The causality

paradigm appears to indicate that, in general, decision making flows

from the members toward management, ending in a bottle-neck in discre-

tionary decision power.

As suggested by Aresvik (1955), decisions in cooperatives appear to

be analogous to social choices. Economists, however, can only indicate

a partial ordering of decision, without normative premises, with the

Pareto criterion. Each member is visualized as a rational individual

that would join the cooperative to increase his utility, and any voting

side chosen is an attempt to enhance his satisfaction. The cooperative

then is viewed as an institution to increase utility or well-being of

the members by increasing profits, decreasing (price, quantity, quality)

risks, and possibly providing some public-type goods. Given that profit

and risk are the primary argument of a member's utility function, the

member in isolation would strive to maximize a weighted average of

profits and (negative weight for risk aversion) risks. An oversimplifi-

cation of members' behavior is that they attempt to maximize profits.

As all members try to do so, conflicts emerge which are settled accord-

ing to the power of members, directors or management. The outcomes from

the exercising of power in the cooperative groups are arrangements to

delineate the rules of marketing the members' product.

Earlier work has not recognized the role of decision making by the

cooperative (e.g., Emelianoff, 1948; Phillips, 1953), and thus contain

no explicit cooperative objective. More recent work, however, has

stressed an active decision making role, while possessing a single

objective. The sensitivity of the cooperative outcome to the assumed

objectives was illustrated by Ladd (1974), where he shows that an effi-

cient quantity maximizer differs from an efficient price maximizer (as

in Helmberger and Hoos), and both differ from profit maximizers. Plau-

sible cooperative objectives are

1. Minimization of costs. This objective appears to be plausible

only if the cooperative had fixed or zero (supply cooperatives) revenue,

which is equivalent to maximizing profits, or better said, it would be a

subcase of the profit maximization objective.

2. Maximization of cooperative surplus or price. This objective,

stated by Helmberger and Hoos (1962), seems plausible when patronage is

fixed (e.g., the very short run). This is indeed a subcase of the total

profit maximization case, where the level of output of the members (and

thus their production costs) is fixed. Then the only viable way to

maximize members' profits is to maximize net cooperative surplus.

3. Maximization of total members' profits. In the Helmberger and

Hoos framework, this would imply at least that the volume of deliveries

of the members is not fixed, and thus there is flexibility to adjust to

the point of maximum profits. Ladd (1982) and Eschenburg (1971) have

supported this objective on the grounds that it better resembles the

individual objective of maximizing profits. Indeed, why should the

cooperative maximize its net surplus instead of maximizing the sum of

"members' surplus" which is total profits?

The use of a single objective in cooperative models is a gross

oversimplification of the plurality of objectives a cooperative con-

siders. An illustration of this is provided by Jacobson (1972) who

found four primary objectives that describe the service role of milk


1. To guarantee their producers a market,

2. To bargain for the best possible terms,

3. To assemble and market the milk as efficiently as possible, and

4. To help achieve higher quality levels in incoming milk markets.

The last three objectives aim directly to increase the total

profits of the members. At this crossroad a controversial question

is: can the cooperative achieve the total profits maximum through

alternative arrangements? These issues are the ones that this study

attempts to explore. The extent that alternative arrangements can

improve the performance of cooperatives depends upon the behavior of the

members under those arrangements. Such behavior, along with its under-

lying rationale, is explored in the following chapter.



Perhaps the most basic behavioral postulate of economics is that

man is egoistic, rational and a utility maximizer. Even though the

basic behavioral force of increasing well-being is what induces a group

of farmers to "cooperate" by forming a cooperative association, individ-

ually they are likely to engage in independent noncooperative behav-

ior. The resulting behavior, from a conceptual standpoint, is analogous

to the prisoner's dilemma.1 Such behavior results from a member's

dilemma where he has incentive to "free ride" (and thus capture gains

when other members are behaving for the cooperative welfare) or to

"protect" himself when other members are attempting to "free ride."

The purpose of this chapter is to provide a conceptual framework to

investigate the behavior of processing cooperative members and to assess

the welfare implications of alternative coordination arrangements among

the members that may induce compliance to attain cooperative coordinated

equilibriums. The model structure and analysis incorporate coordination

mechanisms, membership adjustments and open market purchases strate-

gies. The model allows analysis of a broader class of group behavior

problems, in particular free riding and the cooperative analogy of the

prisoner's dilemma.

1Luce and Raifa (1957) present a discussion of the classical
prisoner's dilemma game.


A Mathematical Model of Processing Cooperatives

Consider a processing cooperative which purchases a homogeneous raw

product, y, and transforms it into a finished product Z. The coopera-

tive sells Z in a competitive market at price P. The net revenue of

the cooperative, called cooperative surplus (CS), is

CS = Pz Z C(Z,P) FCC, (3.1)

where C(Z,P) is the variable cost of transforming y into Z, P is a

vector whose elements are the prices of other inputs, and FCC is the

fixed cost of the cooperative.2

Let yi denote the delivery of raw product by member i. Assume

there are m growers and the membership is closed. Then the total raw

product to be processed by the cooperative is3

Y = E . (3.2)

Since the cooperative is organized solely for the benefit of its

members, it must distribute all the cooperative surplus (CS) back to the

members. Thus,

2At this juncture, we assume that the cooperative is technically
efficient in the sense that it produces a given output at minimum cost,
or by duality it maximizes output for a given expenditure level. For
the remainder of the analysis it is assumed that the fixed cost of the
cooperative is the same for the time spans implied. This is not an
innocuous assumption when one considers the relatively extensive capital
longevity associated with processing assets. A complementary analysis
with fixed and variable cooperative plant size in the long run is pre-
sented in Appendix A.

3So far we are assuming that the cooperative does not buy outside
in the open market. This assumption is relaxed later.

E PAY. = CS, (3.3)

where PAYi denotes the payment to grower i for the delivery of yi.

Assume that the members are homogeneous (identical), then yi = yj,

for all i and j. For notational convenience, let yi = y, so that (3.2)

becomes my = Y. Under the assumption of member homogeneity PAYi = PAY.

for all i and j, and letting PAYi = PAY, (3.3) becomes



A relationship exists between y, individual production, and PAY,

individual payment. Define P to be the "price" per unit of member

output,4 the average net revenue product (ANR) of the cooperative, then

PAY = P y (3.5)

y my

Cooperative Behavior and Optimal Volume


Myopic and Coordinated Behavior

In the short run, the member's production function and the corre-

sponding cost-function are constrained by the existence of fixed inputs

which are linearly weighted by their prices to constitute the fixed cost

of producing the raw material in the time span considered.

This input fixity may not only arise from asset fixity in the short

run (e.g. land, machinery and multi-period crops) but also from

4The price definition given in (3.6) is basically the same as the
one given by Helmberger and Hoos (1962). The differences are that they
treated members' total raw product as fixed and they did not distinguish
the raw product of each member.

contractual obligations or other business arrangements. Given some

fixed inputs, a typical cooperative member strives to maximize net

returns,5 that is to maximize

T = P y c(y,W) FC, (3.7)

where c(y,W) is the variable cost of producing y with variable inputs

whose prices are denoted by a vector W, FC is the fixed costs of the

grower and P is defined as above.

Total profits of the members are

Te = miT = P my m c(y,W) mFC = m(P y c(Y,W) FC) (3.8)
y y

which is simply m times each member's maximand. Thus, the value of y

which maximizes individual maximum profits is the same value which

maximizes total profits. The first order condition for profit maximi-

zation is

SPy + y y 0. (3.9)
ay y ay ay

Equation (3.9) says that the individual grower should equate marginal

revenue and marginal costs. Two subcases arrive with respect to the

member behavior. These cases are myopic and coordinated cooperative,

depending on how the members regard 3P /3y, the slope of the average net

revenue function.

In the myopic case members are driven by strategic individual

rationality and thus behave solely as quantity adjusters, regarding Py

5A single objective of profit maximization is assumed. However,
the member may receive nonpecuniary benefits from its cooperative
membership which increase his utility but not his net returns.

as invariant, i.e., as if 3P y/y is zero. The likelihood of this case is

increasingly plausible as the members are "atomized" with respect to the

scale of the cooperative since the price a member receives is largely

independent of his delivery. This suggests the potential for myopia as

individual members' share of the operation decreases. In this case, set

Py /Dy equal to zero and solve (3.9) for y to obtain a member's supply

function. The aggregation of these functions is the members' supply

function. In inverse form6

PS = P (my,W). (3.10)
y y

Analogous to the result of Helmberger and Hoos (1962), cooperative

equilibrium is established where (3.10) intersects (3.6).

Consider the case of a coordinated cooperative in which the members

behave in a collectively rational way. If the members recognize their

interdependence and react in a coordinated way such that they fully

recognize the impact of their output level on the price they receive,

each would attain a higher level of profits. Differentiating (3.6) with

respect to y gives

y ( OCS/ay)y CS (3.11)
Sy 2

Substituting (3.11) into (3.9) yields

+ [(CS/S ]y = 0. (3.12)
Dy y 2 Dy

6It is assumed that aggregate supply embodies a monotonic function;
thus, it can be inverted while retaining a one-to-one mapping of quan-
tity and price.

Using (3.6) gives

CS 1 3CS CS 3c
-- + my 0. (3.13)
my m dy my dy

aCS ac
y acm. (3.14)
ay ay

Equation (3.14) implies that for maximum total profits the members
should produce at the intersection of their supply curve (-L- m) and the

cooperative marginal surplus or marginal net revenue curve (MNR). This

represents a coordinated equilibrium. Equation (3.14) also implies that

for a coordinated solution the marginal cost of producing y incurred by

each member (3c/8y) must equal their share of the marginal cooperative
surplus (3CS/3y) -.

Substituting (3.14) into (3.9) for 3c/3y, the marginal net revenue

for a grower is

I 3CS v
=- y + P (3.15)
m ay 3y y

Thus, if members regard Py as beyond control, the individual will act as

if marginal revenue is P To determine the sign and magnitude of

aP /3y, manipulate equation (3.15) to obtain

ap- /y= ( ). (3.16)
dy dy m y

If Py (ANR) exceeds the member share of the marginal revenue (ANR >

MNR/m), then 3P /yy < 0 and myopia would have implicit cost. Thus,

there would be pecuniary advantages of increasing the sophistication of

the cooperative toward the coordinated case.

Differentiating equation (3.1) gives

-CS P 3 C 3Z (3.17)
ay 3y 3Z 3y

Substituting (3.17) into (3.14) and rearranging gives

(p C >Z 3c
(P ) m (3.18)
z az 3y ay

Similar to equation (3.14), equation (3.18) says that for a coordinated
solution y is adjusted until the aggregate supply of the members (m -1 )

equal the marginal net revenue of the cooperative (MNR) on the left hand


In a situation of myopic equilibrium and 3P y/y negative, then it

is advantageous for members to jointly reduce deliveries to the point

where the raw material price increase plus the grower's cost reduction

balance the foregone revenues associated with the lower volume of deliv-

eries; that is, to move to a coordinated equilibrium. If positive, then

the cooperative may increase its membership (m* > m), buy in the open

market or encourage members to increase their deliveries.

In Figure 3.1, myopic and coordinated equilibrium are depicted.

Myopic equilibrium occurs at point e where the members' supply function

(S) intersects the average net revenue function (ANR) of the cooper-

ative. Coordinated equilibrium occurs at point c, where the members'

supply function intersects the marginal net revenue function (MNR) of

the cooperative. The myopic cooperative produces mye and receives pe
(point e) while the coordinated cooperative produces my* and receives P

(point c). Note that at point e 3P /ay < 0, and point c is Pareto

superior in the sense that individual and total profits are greater than

under noncooperative myopic behavior at point e. From the concavity


myP mye

1iyopic and Coordinated Equilibria.

Figure 3.1.

condition for profit maximization at point c, total profits decrease as

the cooperative operates to the left of c. In this fashion one finds a

point where cooperative profits are identical to the myopic cooperative

profits but the delivery volume is even smaller than in the coordinate


Rationale for Myopia

A rationale for myopia can be derived in terms of the above

results. Under the prevailing arrangements, a member has an incentive

to increase his individual delivery, for example, from a coordinated

cooperative position. To illustrate the last point, combine equations

(3.14) and (3.15) to obtain the following expression of a coordinated


ac ap
-a y ay + P .
dy dY y

At a coordinated solution, such as the one depicted at point c in Figure

3.1, Py / y < 0. Thus, at that point, a myopic member perceives 3P /ay

= 0 and therefore perceives ac/ay < P If he behaves individualis-

tically then he would increase his deliveries of raw material. This

incentive arises from the fact that marginal return to a member in

isolation is greater than its marginal cost of producing y. If all

members react in the same way, they would gradually move from point a

toward point e. P would simultaneously be decreasing up to where

further increases in deliveries are no longer desired, at point e, in

myopic equilibrium. This equilibrium position would be stable as long

as members retain myopia, or as long as no arrangements are tailored to

induce them to produce at point c.

Such behavior results in a member's dilemma where he has incentive

to "free ride" (and thus capture gains when other members are adhering

to coordinated cooperative behavior) or to "protect" himself when other

members attempt to "free ride." The group behavior result, from a

conceptual standpoint, is the cooperative analogue of the prisoner's

dilemma. The pursuit of self-interest (individual rationality) produces

an outcome that is collectively irrational. Point e in Figure 3.1

(myopic equilibrium) coincides with the cooperative equilibrium of

Helmberger and Hoos (1962). The foregoing analysis has identified the

source of "myopia" and a coordinated equilibrium.

One can notice the similarity of this analysis with that of car-

tels, although in a closed processing cooperative unnoticed cheating is

less likely because the cooperative management monitors and knows the

activities of each member.

Cooperative Surplus and Price Sensitivity

Rearrange equation (3.11) to yield

y 1 CS CS
ay my 9y y

Use the payment definition given in equation (3.6) to multiply the

right-hand side by P /(CS/my) (which equals one). Then multiply and

divide by y and eliminate my from the resultant expression to obtain

ap P
S= -.S [ c CS ]. (3.19)
ay CS y y y

After multiplying both sides of (3.19) by y/P and manipulating the

result, one obtains

,P y CS,y 1 (3.20)

where = -= Y- is the elasticity of raw material price with
y Y CS p
respect to members' deliveries and nCS,y L is the elasticity of
CS, y =y CS
the cooperative surplus with respect to members' deliveries.

Equation (3.20) depicts the relationship between the sensitivity of

cooperative surplus and member price to changes in deliveries. If nCS,y

equals one, then up equals zero and myopic equilibrium and coor-

dinated equilibrium coincide. The more inelastic cooperative surplus is

to raw material deliveries (nCS,y close to zero), the greater the impact

of coordination and the greater the amount of raw material reduction

required to achieve the state of maximum total profits. This follows

since small nCS,y implies cooperative surplus changes little as total

deliveries are reduced; however, the value of P increases, since P =


The above statement implies that with higher capital investment of

the cooperative (which generates higher cooperative fixed outlays), the

more crucial it becomes for the cooperative to assure adequate supplies

of raw material for its survival and to return an adequate payment to

its members. Thus, if fixed costs dominate, the price received by

members is more sensitive.

A vertically integrated firm facing the same cost structure as the

foregoing cooperative would produce at the coordinated output (point c,

Figure 3.1). However, as nCS,y becomes nearly one the performance

difference between a myopic cooperative and a noncooperative vertically

integrated firm vanishes.

Arrangements to Ensure Coordinated Behavior

Three approaches are envisioned as potential instruments to ensure

a coordinated equilibrium:

1. Given m members, impose a quota of y=y* to each member. In

this case the members supply curve becomes vertical at an aggregate

supply level of my*. The cooperative will only accept deliveries con-

sistent with the optimal capacity use. An equivalent but analogous

instrument is the institution of processing rights to be sold by the

cooperative. In the context of our model, the coordinated state would

be achieved if the cooperative sells each member the right to process

y*. This arrangement is a cooperative-mapping of coercion as the only

way to ensure that the preferred outcome is obtained, as suggested by

Hobbes (1909).

2. Educate the members as to the effect of 3P y/y. However, if

such optimal volume is not enforced, a conscious-raising program seems

rather utopic since members will always have an incentive to cheat.

They would free ride at the expense of other members that are cooper-

ating in attaining the coordinated solution, and subsequent retaliation

would establish myopic equilibrium.

3. Impose an internal tax on deliveries exceeding y*, a penalty at

least equal to the difference of P received at optimal capacity use and
the grower's marginal cost of producing y (point c, Figure 3.1). In

this way no individual marginal gains would occur beyond y*, and incen-

tives to cheat would be eliminated.8

The use of a point quota is only for pedagogic purposes. It is,
of course, more realistic to impose upper and lower quotas (interval

8The problem here is similar to the problems of maximizing cartel
profits; however, here the delivery level can be directly observable,
and thus penalized.

Benefits from Coordination

Consider the benefits of the coordinated equilibrium as compared to

the myopic equilibrium. Total profits are cooperative surplus less

members' total costs. Cooperative surplus equals the members' gross

revenues. Following Just et al. (1982) in measuring producers' welfare

changes quasi-rents are given by profits plus the members' fixed

costs. At myopic equilibrium cooperative surplus (gross revenues to the
e e
members) is given by P ymy in Figure 3.1. The area below the supply

curve represents the total variable costs of the growers. Thus the area

above the supply curve and below the price measures the total quasi-

rents that accrue to the members. The change in total profits or

producers' quasi-rents from moving into a coordinated equilibrium is

given by the cross-hatched area less the solid shaded area in Figure


Underutilized Cooperative Plant

This situation arises when myopic equilibrium occurs in the rising

region of the ANR function, and thus there are yet size economies of the

cooperative processing plant to be exploited (to the left of point e in

Figure 3.2).

One can reasonably postulate that membership size (m) is sticky

downward in the short run, i.e., membership expansion is more likely to

occur than membership contraction. Note that coordinated equilibrium at

point c, Figure 3.2, with membership ml is not attainable since the cost

of producing such output exceeds the revenues received by the members.

A noncooperative firm buying solely from ml independent growers and

having the same cost structure as the foregoing cooperative, cannot stay




mly1 m2Y2
m1 Y2


Figure 3.2.


Alternative Membership and Open Market Purchase
Policies for an Underutilized Cooperative Plant.

mi Yl *

in business at point c. This provides a rationale for the formation of

cooperatives to protect markets where there is lack of profitability in

the processing stage. The cooperative subsists at myopic equilibrium

with mI members, each producing yl and receiving price PI.

If the cooperative is operating below optimal capacity, two choices

may be available to allow cooperative volume expansion: increasing mem-

bership size, and buying raw material in the open market. These situa-

tions are compared in Figure 3.2.

An influx of m2 mI new members shifts the raw product supply from

S to S' and increases the price received by already existing members (to

P2), and therefore the amount supplied by each member (to y2). With

membership adjustment only, this corresponds to the optimal membership--

profits of the mI already existing members are increased by abPiP2.9

Holding each member output constant (y = y), and differentiating

(3.7) gives

ar- = y (3.21)

Further, differentiating (3.7) and using (3.6),

i C S S ) 1 (3.22)
nm 2m m m

Setting (3.22) equal to zero we find that with each member provid-

ing y=y, optimal membership level is where the marginal cooperative

surplus contribution of the last member equals the average surplus that

accrue to all members (CS/m = aCS/3m).

Optimal membership size here is referred to as the one that maxi-
mizes per capital profits, that is, the value of m that an individual
cooperative member would prefer, assuming no altruism and that m is

If the open market price of the raw product is lower than that

received by the members at equilibrium, it is more advantageous for the

cooperative to buy in the open market rather than expanding member-

ship. To illustrate, assume that in the open market raw product may be

acquired at price P If the cooperative buys in the open market it

would not only capitalize on scale economies of the cooperative proces-

sing plant, but also on marginal value of raw material bought outside

which exceeds its marginal cost of acquisition (P ). Thus, the relevant

average net revenue curve is above ANR because of the exploitation of

nonmembers' raw material from generating surplus that they do not pay

back to the sellers (ANKR' in Figure 3.2). Members supply mlyl, and the

cooperative would buy y in the market to receive price PI, while stick-

ing to membership mi. Profits to the mI members would be higher than

when they expand membership since their marginal cost given by S is

higher than their marginal cost of buying in the open market (P ). The

potential instability of P however, may invalidate these conclu-

sions. In the case of fluctuating P c it may be preferable to increase

membership to assure adequate raw material supplies.

Payment for Quality

In the foregoing discussion, the complications that may arise if

variations in raw product quality are taken into consideration have been

disregarded. The volume (quantity) is but one dimension of the raw

product delivered by the members. Many problems, however, are derived

from the heterogeneous characteristics of the commodity involved where

the homogeneous product case is neither convenient nor appropriate.

Probably the most important problem related to product characteristics

is the appropriate payment or compensation to the grower for the objec-

tively measurable characteristics of his product.

The final commodity produced by the cooperative is assumed to be

homogeneous (Z), so that we abstract from the effects of quality varia-

tion on the final demand side. This allows quality to be determined

solely by the decisions of the cooperative members, affecting the cost

or supply side of the operation where the payment of the growers is

generated.10 Let the raw product possess a set of characteristics, and

let A be a 1 by k vector of continuous and unambiguously measurable

characteristics A=[al, ..., ak], where each characteristic is indexed by

i. The vector A contains only the relevant characteristics of the raw

product; that is, the ones that affect cooperative surplus. Assume that

the level of characteristics can be influenced by the members and that y

is the amount of raw material produced by the members. Let the growers'

cost function be given by c = c(y, A; W), where W is the vector of

factor prices and the marginal costs of the arguments in c are positive

and increasing.

Assume that the characteristics are such that the higher a., the

more the contribution to cooperative surplus (characteristics measured

as "goods"). Normally the level of each characteristic would have

bounds that define the technically feasible set or institutional regula-

tions. Define an arbitrary payment function that the cooperative

10Implied in the analysis that follows is that the raw product
identity, in terms of the relevant characteristics, is kept throughout
its processing. This excludes the case where the raw product undergoes
a blending process in which the product identity is lost since the
nature of the finished product depends also on the choice of charac-
teristics of other materials that are mixed with the members' raw

utilizes to distribute the cooperative surplus back to the members. The

payment per unit of y is defined to be P = P(AA), where X is a diagonal

matrix whose diagonal elements are the pooling parameters that define

the payment scheme. If characteristic a. is pooled, then Xi is zero, if

not X. = 1.

Below, the behavior of the members is analyzed under two payment

schemes: fully accurate pricing, when no characteristics are pooled,

and pooling or imperfect pricing, when at least one characteristic is

pooled.11 The effect of pooling schemes on the location of the ANR

function can be translated into allocative efficiency issues since it

distorts the signal sent to the members, and under individualistic

behavior it modifies the maximand of individuals. It must be kept in

mind that under the assumption of member homogeneity, raw product supply

(y) and characteristics will be the same across members; however total

raw product and characteristics levels may be different across payment


Fully Accurate Pricing

If payment is not distorted in the sense that it fully accounts for

the contributed cooperative surplus, no characteristics are pooled.

This case implies that X = Ik, a k-dimensional identity matrix. Thus, a

typical member maximizes

T = P(A)y c(y, A; W) FC. (3.23)

11ln this model the term "pooling of characteristics" is intended
to denote the pooling of cooperative costs and revenues associated with
the characteristics.

Assuming an interior solution, the first order conditions are given


p + y c 0 (3.24)
dy +y -dy

a ^= y 0. i = 1, ... k (3.25)
@a. da. -a a.
1 1 1

Equation (3.24) states that maximum profits are reached when the

physical quantity of raw material (y) is set where its marginal revenue

equals the marginal cost of producing it incurred by the members.

Equation (3.25) indicates that it is also necessary that the level of

characteristics be set where their marginal revenue equals the marginal

cost of producing them incurred by the members. Even though under fully

accurate pricing members are coordinated with respect to characteristics

of the raw product, myopic behavior with respect to the volume of deliv-

eries (y) is likely if there are no discriminatory pricing or quota

schemes to control the supply of raw material.


With imperfect pricing accuracy X-Ik is a negative semi-definite

matrix and at least one Xi equals zero, implying some pooling. Further,

assume P is homogeneous of degree one in Xi so that 3P/3(Xa.) =

Xi(3P/a i). When some characteristics are pooled, an individual has the

incentive to set it at minimum cost level. Let a? be the lower limit on

21In what follows it is assumed that the production technology is
characterized by nonjointness in characteristics and quantity of the raw
product. This implies that 3y/3a. = 0 and Ba./3a. = 0 (i # j). This
assumption is questionable if the production technology is such that the
choice of one characteristic is not independent of other characteristics
or of the amount of raw material. For the sake of simplicity, however,
nonjointness has been assumed in the production of raw material.

the ith characteristic whose imputed value is given by 8i. Then, a

typical member strives to maximize

= P(AA)y c(y, A; W) FC + ZS.(ao a.) (3.26)
i 1 1

The Kuhn-Tucker conditions are

ST;c 37T
= P + -y y --- 0; -y y = 0 (3.27)

S7-. y B. a 0 a. = 0 (3.28)
1. 1 1 1

a. a. 0; 7. =7 0 (3.29)
1 1

Assume an interior solution for y and for nonpooled character-

istics. If the ith characteristic is pooled then .i = 0 and the myopic

member produces at a = a? at minimum cost level since there is no

direct perceived pay-off of producing higher levels of ai. The above

system of equations is the heterogeneous raw product analogy of equation


Assume an interior solution for y and for nonpooled character-
o o
istics. 8. is the imputed value of ai = ai; that is, &i = 3-i/;a..
Thus, i is the change in i that results when a. is increased and there-

fore, for an individual member, it is negative. Following the argument

used earlier, one can derive the expressions below

1 3CS _
m ay y ay

1 3CS aP
m a. i a. y
1 1

X. = 0 says that the grower perceives 3P/3aa = 0, i.e., he does not

perceive any impact of a change of a. on the price he receives. If Xi =
0, (3.28) becomes a. = 0 (if a. > 0), which implies 3C/3aa =
-Bi. With pooling and lower limits on characteristics, the marginal

cost of producing a. is equated to its imputed value. If minimum levels
o *
of ai were set such that ai = ai of a coordinated solution, a coor-

dinated solution can be attained solely with the imposition of appro-

priate minimum levels of acceptable characteristics.

Equilibria Location

With k characteristics, the location of the average revenue func-

tion of the cooperative and the location of the members' supply function

is in a k+l dimensional euclidean space. Take the ratio of the marginal

conditions for two characteristics a. and a. (i j).

From equation (3.28)13

i aa. ac/aa. + B.
- > or < 1 1 (3.30)
ap 3c/3a. + B.
j 3a. J J

Hold the assumption of unique interior solution for nonpooled

characteristics. If no pooling occurs, then Xi = 1 and Bi = 0 (i=l,

..., k). Then the left-hand side of (3.30) can be derived from the

payment function and the right-hand side from an isocost function.

Optimality requires that the slope of the payment function (per capital

13The inequality signs in (3.30) stand for the cases where pooling
occurs. If a. is pooled (X. = 0) then the left-hand side of (3.30) is
1 1
zero and therefore smaller than the right-hand side. If a1 is pooled
(X. = 0) then the left-hand side is infinite and therefore greater than
the right-hand side.

cooperative surplus) be tangent to the slope of the grower's cost func-

tion. For maximum net returns to occur, the increase in payment per

marginal increase in cost must be equal among all characteristics. If

a. is pooled and aj is not, then X. = 0 and i. is positive while X- = 1

and a. is zero. For a nonpooled ai, a myopic member perceives a flat

marginal revenue function in a.'s dimension, however it is not flat if

a. affects cooperative surplus.

To analyze further the quality and quantity locations of equilib-

rium, let a single variable characteristic be denoted as "a." An

increase in "a" implies an upward shift of the ANR function ("a"

measured as a "good") and a leftward shift of the members' supply func-

tion (since the marginal grower's cost is a positive and increasing

function of its arguments). With the amount of raw material held con-

stant (y = yo) members will supply higher quality only at a higher per

unit price of y. Alternatively, they will supply more y only if quality

is inferior for a given price of y. When quality is improved, say from

a stimulus to produce higher quality, supply shifts to the left while

average revenue shifts upward. Whether the members produce more or less

quantity of raw product after producing higher quality is indeter-

minate. The outcome depends upon the sensitivity of the average net

revenue function (or cooperative surplus) to quality relative to the

sensitivity of the supply function of the members. Figure 3.3 illu-

strates two cases of the amount of raw product responsiveness to

increases in characteristic "a." For a supply function that is rela-

tively insensitive, equilibrium occurs at point 2 and the amount of raw

product increases. For a very sensitive supply function equilibrium

occurs at point 3 and the amount of raw product decreases. One result

- 0
0 0 0

11 r- -- -- -- O
0 z

- O (






i -4


is consistent: the raw material price must increase. This result is

consistent with the fact that when the quality of raw product is

improved, the raw product is worth more.14

Heterogeneous Membership

Membership structure is an important determinant of the performance

of agricultural cooperatives. So far, the foregoing conceptual frame-

work has disregarded differences among the members that compose the

cooperative association. The assumption of membership homogeneity has

sidestepped equity and redistributional effects that alternative

arrangements imply when members are unequal.

Let Z denote the final product, Y the raw product, and let the

relationship between Z and Y be given by15

Z = aY, (3.31)

where a is "the yield of Y," so that 0 < a < 1. Let yi denote the

output of grower i, and as before, Y = Zyi. Then (3.31) becomes

Z = aZyi. (3.32)

14Even though the present discussion has been limited to the case
of nonjoint production (in characteristics and quantity), whether a
coordinated case unidirectionally produces higher or lower levels of a
characteristic depends on jointness of characteristics and on the
importance of each characteristic on both the cooperative surplus and
the members' cost.

151n many agricultural processing cooperatives, the role performed
by the cooperative is the extraction of some characteristics from the
raw product supplied by the members. Some examples are the extraction
of raw sugar from sugarcane, oil and meal from soybeans, fat from milk,
and juice from citrus crops. The mathematical form presented below is
suitable to conceptually represent these processes.

Recall equation (3.1) where C(Z) is the variable cost of processing

Z and FCC is the fixed cost of the cooperative. Assume the processing

cost function is separable, so that the cost of processing each member's

delivery can be allocated to that grower. Furthermore, since Z = aY

then C(Z) = C(aY), and separability implies that

C(aY) = C[a Eyi] = EC(ay.). (3.33)
1 i

Let the fixed cost component of CS be apportioned to the members in some

fashion. Allow for different "a" across growers so that Zi = aiyi and

equation (3.33) becomes

C(Z) = EC(a.y.) (3.34)

In the case of member heterogeneity, cooperative surplus is

CS = P EZ. EC(a.y.) FCC. (3.35)
Z. 1 1 1
1 1

Assume that the marginal processing cost is nondecreasing in its argu-

ments so that 3C/aZi = 3C/Daiyi > 0. Based on the above framework where

the raw product of the members is differentiated and a functional form

for the cooperative processing is assumed, the impact of two payment

schemes are analyzed below.

The Coordinated Case

For the coordinated case let the fixed cooperative cost be shared

in a predetermined way. Given the assumption of separability, a coor-

dinated system would pay PAY. to member i for his deliveries. Then

PAY. = P Z C(a.i.) .FCC,
1 Z 1 1 1 1


where E. is the share of cooperative fixed costs charged to member i.16

Note that using equations (3.35) and (3.36), SPAY. = CS. Grower's net

returns are given by

7. = PAY. c.(y., a.) FC. (3.37)

where ci(yi, ai) is the grower's variable cost of producing yi with

attribute a. and FC. is the fixed grower's cost. The grower's marginal

cost is assumed to be nondecreasing in its arguments 3ci/3yi, 3ci/@ai >

0. Under a coordinated system (using payment defined in (3.36)) the

grower's maximand (equation (3.37)) becomes

it. = P a.y. C(a.y.) 5.FCC c.(y., a.) FC. (3.38)

To find the optimum level of production for grower i under a coor-

dinated payment scheme, set the first partial derivatives to zero,

3i./y.i = P a. 3C/3(a.y.) ]a. 3c./3y. = 0 (3.39)

3i./3a. = Pz y [aC/3(a.y.) lv. 3c./aa. = 0 (3.40)

These partial derivatives have the usual interpretations. Assuming that

the second order conditions are satisfied and that the system possesses

a unique interior solution, solving (3.39) and (3.40) the optimal amount

of raw product and quality level for each member is found at yi =

Yi(Pz,U,W,FCC) and al = ai(Pz,U,W,FCC), where U and W are parameters in

the cooperative processing cost function and grower cost function


16The assumption that every member has a predetermined cooperative
fixed cost share, Ei, is for simplicity. Ei based upon each member's
share of raw material is one particular criterion.

Payment Based on Raw Product

If payment is based on raw product, then define P = CS/Y and

PAY. = P y. = (CS/Y)y. (3.41)

Using the payment definition given above, the grower's net revenue is

7. = P y. c.(y a.) FC. (3.42)

The grower takes P as a fixed, exogenous variable. Furthermore, since

Yi is his only direct variable of interest, the grower will optimize

only on yi. Thus

a 7Tr. ac.
I = F I = 0. (3.43)
i P = const Y -Yi

It is instructive to compare this first-order condition to the

first order condition for the grower under a coordinated payment

system. Recall (3.39) and (3.40) and note that

=NR(y.) = P a. a., (3.44)
1. 33. I @a.y. 1
i .i i

MNR(a.) = = P y. y.. (3.45)
i da. z i a.y.
I i@ i

In the case of a single attribute, one can see the similarity

between the heterogeneous member and the homogeneous member cases. In a

myopic cooperative, members equate average revenue with marginal cost

(equation (3.43)) and in a coordinated cooperative members equate mar-

ginal revenue with marginal cost (equation (3.39) and (3.40)).



This chapter presents a model to empirically test the theoretical

model of the preceding chapter. A mathematical programming model is

developed for sugarcane processing cooperatives which empirically

describes the structure of a processing cooperative and the arrangements

among its members.

Since straightforward maximization of members' profits would only

provide the "coordinated" solution, it is necessary to advance beyond

the total profit maximization objective. Particularly, the cooperative

maximand must capture individual behavior given a set of structural


The problem of scanning arrangements among cooperative members is

analogous to problems faced by policy makers who must account for the

actions of a myriad decentralized decision making units which take

policy variables as given but also have their own objectives. Candler

et al. (1981) have identified a potential and promising approach--

multilevel programming--to deal with this class of problems. In the

first level (higher hierarchy), policy makers optimize their utility

function which depends on controllable variables (policies) and

noncontrollable variables that are set at a second level. Then the

units in the lower hierarchy try to select the level of variables in

order to optimize their own objective. This nested optimization

approach is analytically propriate for the selection of "optimal"

arrangements (policies) of cooperative members (second level), but its

data requirements are beyond the scope of this study. Even the approach

taken in this analysis is data intensive. The approach taken below is a

subcase of the class problem discussed by Candler et al., where arrange-

ments are set at a first level in a discretionary manner and members

react in the second level where they make production decisions.

Florida Sugarcane Cooperatives

Sugarcane cooperatives offer a classical example of processing

cooperatives for which data are reasonably available. In Florida,

sugarcane processing cooperative associations account for about 35

percent of all cane processed (Zepp, 1976),1 which is produced by mem-

bers who have complete autonomy over cane production but are interdepen-

dent at harvest time when the jointly owned capital renders services of

harvesting, hauling and processing the cane, and marketing the jointly

produced sugar.2 Quality of cane consists of extractable sugar and

processing quality or fiber content (Meade and Chen, 1977). Coopera-

tively produced sugar is sold in terminal outlets which are relatively

competitive, and thus the price of sugar received is exogeneous to the

iThe Florida sugar industry is located in the southern end of Lake
Okeechobee and comprises more than 340,000 acres which produced
1,121,490 short tons of raw sugar in the 1980-81 season, supplying some
10 percent of the nation's consumption (Alvarez et al., p. 1982).
20f much less economic importance, molasses and bagasse are by-
products of sugar production. The cooperative member receives some
additional payment from molasses sales, however, for the remaining of
the study, sugar is considered as the sole output of sugar production.

cooperative. The cooperative as well as the members purchase inputs and

services at given prices.

The core of arrangements of sugarcane processing cooperatives in

Florida consists of (1) payment based on the amount of sugar delivered,

adjusted with a fixed charge per ton of cane, (2) processing quota

throughout the processing season, (3) members sovereignty in determining

the volume and composition of deliveries, and (4) closed membership.

The prevailing payment arrangements among Florida sugarcane cooper-

atives entails the compensation of the grower by the amount of "net

standard tons" of cane delivered for processing. This is an attempt to

compensate for the amount of sugar, the final commodity, contained in

the delivered raw material.3 In brief, this payment method adjusts the

volume of cane delivered by a qualitative factor which depends on the

amount of sucrose (sugar) in the juice. Also, growers are charged a

fixed fee which is the average harvest and transportation cost per ton

of cane.

Pooling of processing costs that arise from differences in process-

ing quality of cane does not provide equity because some members are

overcompensated at expense of the others; such pooling does not provide

stimuli to produce high processing quality cane either. Since sugarcane

is perishable, storage can not be utilized and deliveries must be pro-

cessed soon after harvesting. Therefore, the terms processing and

3Cane delivered to the mill includes sugarcane, field trash and
water. Field trash and cane tops are subtracted to obtain "net tons" of
cane. "Standard tons" of cane are net tons of cane adjusted with a
quality factor which is determined upon analysis of the sucrose content
in the cane juice (Meade and Chen, 1977).

harvesting period can be used interchangeably. Processing time sharing

is arranged by imposing delivery quotas upon each member so that the

pattern of deliveries from each member is regulated on an equitable

basis. Since sugar content increases as the season progresses, members

would prefer to deliver their sugarcane as late as possible to obtain

higher revenues. When the limited processing capacity forces the coop-

erative to extend the processing season, potential conflicts among the

members regarding preferred delivery time are settled via quotas based

on the weight of sugarcane.

Even though the flow of deliveries is regulated with processing

quotas, the cooperative must process all members' deliveries. The

members' sovereignty or discretion in determining the volume and compo-

sition of deliveries, under the prevailing arrangements, allows the

possibility of individualistic strategic behavior and thus of a "myopic"


Production Environment and Value Added

The members of the cooperative have three tools to influence the

character of their deliveries. First, they vary the intensity of the

inputs used in a given area. Second, they adjust the area under culti-

vation for a given package of other input combinations. Third, they can

select from an array of varieties of sugarcane which offer alternative

packages of potential tonnage and qualitative values.

There are a number of alternative varieties that a grower may

select for planting. Different varieties imply different strategies

available to the grower with varying effects on the performance of the

individual and the cooperative. It is useful to look at this problem as

one of choosing among alternative techniques of production.

There are at least four reasons for variation in the value added

(surplus) generated by each variety. Varieties differ by (1) tons of

cane produced per acre, (2) sugar content, (3) time to process, and (4)

growing cost. All other factors can be computed from these four.

When one considers other crops that involve processing coopera-

tives, the production alternatives available to the grower may take

different forms. In dairy farming, for instance, it may be a choice

among different breeds of cows that involve varying production of raw

milk, fat content, and costs. Choices may involve entire systems of

production. One must bear this in mind in order to guard against gener-

alizing too much.

A Mathematical Programming Model

The following discussion presents a mathematical programming model

to provide solutions for a processing cooperative operation under alter-

native payment and processing arrangements. As suggested by Eschenburg

(1971) and Ladd (1982), each cooperative structure is shaped by its own

biological and economic environment. To empirically analyze the outcome

of alternative arrangements then, it is appropriate to limit the discus-

sion to a specific case--sugarcane processing cooperatives. The anal-

ysis does not fit all processing cooperative cases but it provides a

framework for the central issues involved in the problem that this study


In this section, it is assumed that the time span for decision

making allows for the selection of varieties of sugarcane for the fields

to be planted. These are considered as the sole instruments that a

grower uses to regulate volume and composition of deliveries. This is a

simplication of all the agronomic tools that a grower uses to affect his

deliveries. To formulate the problem mathematically and to include its

temporal dimension, let the processing season be divided into T time

periods of equal length (t=l,...,T). The characteristics that determine

yields, costs and processing capacity use are unique to each field.

Cooperative surplus (CS), the net surplus available for payment, is

generated by the revenues from sugar sales less the cooperative costs

incurred in providing the marketing and processing services to the

members. Letting the cooperative surplus be separable in terms of the

members' deliveries, CS can be written as

CS = I (Z.) (4.1)

where CS, is the cooperative surplus generated by grower i. The above

equation implies that the cooperative processing cost is also separable

in each members' deliveries. That is

C(Z) = E C(Z.) (4.2)

where Z is the output sold by the cooperative (sugar) and Zi is the

output extracted from the delivery of raw material of member i. This

equation in term implies that the fixed cooperative cost is apportioned

4In Florida, a field is a well defined area (usually 40 acres). It
is also the unit which the members use for decision making.

among the members. However, a payment scheme considered below departs

from this to use amount of finished commodity as criteria to apportion

fixed costs.

Consider fields, varieties of sugarcane and time to harvest as the

sole instruments that a cooperative member uses for quantity-quality

locational decisions. Cooperative surplus is given by

CS = P E E E E Fpft L Z Sugar sales (4.3)
z i f t pft f pfti
p i f t
-E E E E Fpft L C (Y .) Less harvest cost
p i f pft f 1 pft
E E E F L C (Yfti D ) Less transportation cost
pft f 2 pfti f

-E E E E Fpft Lf C (Y .) Less processing cost
p i f p pft
FCC Less fixed cooperative cost

The notation and symbols used throughout this section are defined

in Table 4.1. In other words, (4.1) and (4.3) imply that the marketing

services are disaggregated into independent stages of production that

are vertically integrated, and the identity of each member delivery is

made in terms of generated costs and revenues.5

The payment problem for these cooperatives concerns the allocation

of the cooperative surplus among the members. Because of the nature of

cooperative associations, CS is entirely paid back to the members.

Given the quality dimensions of sugarcane, three possible payment

51f stages of production are appropriately defined so as to be
independent except for the flow of raw material between them, each can
be thought of as having its own production function (French, 1977). By
duality and given input prices, each stage can have a "separate" cost
function. The implication of staged cost structure is that total
cooperative cost is the aggregation of costs incurred at each stage.

Table 4.1.


Notation Used in the Mathematical Programming Model for Sugarcane
Processing Cooperatives.











i = 1,....,m members

= Number of fields that belong to member i

F = 1 F. = total number of fields

t = 1 if field fi that belongs to member i is planted with variety p anc
harvested in period t, 0 otherwise.

f = 1,...., F. fields that belong to member i.

t = 1,...., T processing periods.

p = 1,...., P varieties of sugarcane.

= Per ton price of sugar net of marketing cost

= Area of field f in acres.

= Tons of sugar produced per acre in field f with variety p delivered
in time period t by member i.

-i Tons ofsugarcane per acre produced in field f with variety p
delivered in time period t by member i.

= Distance in road miles from field f to processing plant.

S = Mill upper capacity in period t defined in ton of sugarcane.

-t Maximum volume of deliveries to be processed in time period t for
member i.

= Variety p of sugarcane.

1 = Harvest cost per ton of sugarcane.

'2 Transportation cost of a ton of sugarcane from a given field to the
processing plant.

3 = Processing cost per ton of sugarcane of variety p.

i = Cost per acre of growing cane of variety p in field f by member i.

M = E Z E Fp L FCf, i.e., members' total fixed costs.
p i f t




I__ _ __ _~ ____ _






4.1 (Continued)

p if t

p ift

p ift


F pf L Z pfti i.e., total cane produced by the

F L Z pfti, i.e., total sugar produced by the

F L Y fti i.e., total cane processed for the member
pft f pfti
in period t

F L C pfi, i.e., members' total variable cost.
pft f pfi

systems seem plausible: (1) payment based on raw product weight, (2)

payment based on weight of the finished product extracted, and (3)

payment on recoverable finished commodity adjusted for the cost of

marketing and processing the cane. The foregoing model allows more

complex payment schemes, such as partial pooling of harvesting, trans-

portation and processing costs, but to avoid confusion only the above

payment systems are operationalized. Given that a payment system has

been defined, the next step to develop in the model is to state the

cooperative maximand under a given payment system. Under the payment

systems considered, the cooperative strives to maximize total net

returns in all cases. However, nested in the cooperative maximand is

the member maximand in which a payment scheme is regarded as exogeneous

in the decision to plant a field, with what variety and in what period

to make the delivery. Because the price or payment is endogenous to the

cooperative but the individual member regards it as exogeneous when he

evaluates the fields of sugarcane, the problem is a subcase of the bi-

level programming problem presented by Candler et al. (1981). Even

though the payment policies are discerned as discrete, the individual

member behavior is simulated as a nested optimization taking the pricing

policies as given. However, the actions are recursive and interactive

among the members until equilibrium is reached.

Payment Based on Raw Product

Consider the first payment system where members are paid based on

tonnage of raw material delivered (Y). A price (P ) per unit of Y is

P = CS/Y


and the payment to grower i for the delivery of yi is

PAYi = Py Yi (4.5)

Notice that P is the same for all growers.

This payment implies the pooling of the qualitative dimensions of

sugarcane delivered and of all cost components of CS (equation 4.3). In

a myopic cooperative, P is viewed as given at the individual member

level. However, P is endogeneous to the cooperative system.

Processing plant capacity is defined by the amount of cane that can

be economically processed in every period of the season. There are two

limits to be considered: a lower limit which specifies the minimum

amount of cane that justifies an economic operation of the mill, and an

upper limit which specifies the maximum amount that can be processed in

a given period.

Given that the members behave myopically, the cooperative strives

to maximize total net returns subject to the mill and quota constraint

and the myopic equilibrium condition. That is to maximize

P Y C FCM Total net returns (4.6)
y m

subject to

Y < Mu Mill upper capacity (4.7)

Y > Ml Mill lower capacity (4.8)

Mit > Q Member upper quota (4.9)

iM. < Qf Member lower quota (4.10)

CS/Y-P = 0 Myopic equilibrium (4.11

The notation is defined in Table 4.1. Equation (4.11), the last

constraint, guarantees myopic equilibrium and that the cooperative

surplus is exhausted (P Y = CS = total payment).

Payment Based on Finished Product

Next, consider the arrangement in which members are paid for the

amount of finished product (Zi) that is extracted from his delivery of

raw product (yi). The price is based on Z rather than on Y and it can

be expressed as

P = CS/Z (4.12)

and the payment to grower i is

PAY. = P Z. (4.13)
1 z 1

By defining Pyi = P (Zi/yi), a price per unit of Yi can be calcu-

lated. In this method, a constant per unit price of finished product is

determined for all growers but the per unit price of the raw product

differs. The term Z. is the "finished product equivalent." The struc-

ture of the maximand of a myopic cooperative using this payment system

is given by maximizing

P Z C FCM Total net returns (4.14)
z m

subject to

(4.7), ..., (4.10) Above constraints

CS/Z Pz = 0 Myopic equilibrium (4.15)

The notation definitions are given in Table 4.1.

The Coordinated Cooperative

Last, consider the case where the growers are paid on a use value

basis. Thus, they are paid the quantity of finished product extracted

from their delivery of raw product adjusted for the cost of processing.

The "use value" of delivery of a member is

Pz Zi C(Z.) (4.16)

Under fully coordinated behavior, the grower's payment PAY. is the

use value, hence,

PAYi = Pz Z. C(Zi) (4.17)

The mathematical structure of this problem is by maximizing

CS Cm FCM Total net returns (4.18)

subject to

(4.7) and (4.8) As above.

If each delivery is evaluated individually according to the cooper-

ative surplus it generates, the solution of the problem provides a

"coordinated" solution given the preceding assumptions.

Processing Arrangements

Nonquota arrangements can be simulated by releasing the members

upper and lower quotas constraints (equations 4.9 and 4.10) in any of

the above problems The performance implications can be evaluated from

the solution. More complex arrangement schemes can be simulated with

permutable combinations of quota arrangements and alternative payment


Estimation of Parameters and Data Management

To make the above model operational, its parameters must first be

estimated. Such parameters consist of the price of raw sugar, sugar

yields, cooperative and members' costs, and those concerning the struc-

ture of the cooperative such as the members relative and absolute size,

a measure of the processing capacity and usage, and the relevant

arrangements among the members.

Estimations of Yields

The first step to operationalize the mathematical model is to

estimate the quality, yields and raw product produced with the varieties

of sugarcane. These estimates are direct input into the cooperative

surplus to be generated. More specifically, the objective here is to

estimate Zpfti and Ypfti of equation (4.3).

In Florida, sugar content (the extractable characteristic) in the

cane generally increases as the processing season progresses due to the

progressive influence of cool temperatures. Given the relationship

between sugar produced and raw material, and following Alvarez et al.

(1982) for the specification of environmental variables to be included,

a conceptual model for the amount of sugar per acre (Z) is

Z = PRS NT (4.18)

PRS = PRS(B,Zx, Zprs) (4.19)

NT = NT(B, Zx, Znt) (4.20)

where B is a vector such that

B = (PAY, W, t, V, M, Y, MODE, Age, s, SUN, F, TEMP)

sA:az E-- IS -- -

X=- T C= _C3 ~ 7 -- 1 ZsIZ

I S mzc 1 -

=a 7- S- m s =- =:-7


Table 4.2. Notation Used in the Specification of Yield Models.a

Notation Definition

Z = Tons of sugar produced per acre.
PRS = Percent of recoverable sugar.
NT = Net tons per acre.
PAY = Payment scheme arranged by the cooperative.
W = A vector of input prices used in sugarcane production.
S = A subscript denoting the period of the season.
V = Variety P of sugarcane.

MANi = Management of the ith member.
Y = Year of crop cycle.

MODE = Mode of harvest (mechanical or by hand).
Age = Age of cane since planting or last harvest.
s = Soil quality.

SUN = Solar radiation.
F = Freeze.
TEMP = Teperature during growing season.
Zx = Other economic factors that affect sugarcane composition such as
members behavior, risk aversity, arrangements.

Zprs = All other variables that affect PRS assumed constant.

Znt = All other variables that affect NT. assumed constant.

aAlvarez et al. (1982) presents a detailed discussion for the inclusion of
the agronomic and environmental variables which was briefly summarized in
Appendix B.

Ordinary least squares was applied to pooled data to obtain the

estimated statistical models presented below.6 Given the large number

of regressors, a search for functional form is fruitless and it is

assumed that all statistical models are linear.

The regressors are defined in Table 4.3. Class variables are used

for the distinction of cooperative members, variety of cane and mode of

harvesting. The remaining variables are treated as covariates. Since

the PRS (percent of recoverable sugar) and NT (net tons of cane) equa-

tions have similar set of regressors, Zellner's seemingly unrelated

regression technique offers little advantage over ordinary least

squares. The specification of the statistical models is based on the

work of Alvarez et al. (1982).

The coefficients for the estimation of percent of recoverable

sugar, the extractable characteristic, are presented in Table 4.4. The

6The data collected for the estimation of the statistical models of
tonage and sugar yields contain information in both a time series and a
cross sectional form. A crucial decision is to determine how to combine
these two types of information in a statistical model in order to best
predict and to learn about the parameters generating the data. Thus,
the problem is whether or not to pool the micro samples of each field,
and if so to what extent. Ideally, data should be pooled only if the
cross sections (fields) were identical. If not, the choice of an
appropriate estimation technique depends on what assumptions are made
about the intercept coefficient of each cross section. If spherical
random errors are associated with the intercept of the cross sections, a
random effects or error component model should be estimated. If the
intercepts of the cross sections are assumed to be fixed parameters, the
dummy variable or covariance model should be estimated (sometimes called
fixed effects). Here, the model estimated is assumed to be a subcase of
the latter where the dummy variable coefficient are equal to each
other. In other words, to properly apply ordinary least squares to
pooled data, it is assumed that the data generate spherical distrubances
in the sense that they are homoskedastic, cross-sectional independent
and serially uncorrelated. Judge et al. (1982) address the issues and
implications of different pooling schemes.

Table 4.3. Notation Used in the Regressions for Predicting Percent Recoverable
Sugar and Net Tons of Sugarcane.

Notation Definition

Age = Age of cane in periods of two weeks up to November 1 of foregoing
processing season.
F = Freeze degrees defined as the number of hours times the number of
integer degrees at/or below 33"F during the foregoing processing

MAN = 1 if the field is controlled by member i of the cooperative, 0

MILE = Distance in miles from Lake Okeechobee to the field, a proxy for
soil depth.

MODE = 1 if the field is mechnically harvested, 0 otherwise.

NT = Net tons of cane per acre.

PRS = Percent of recoverable sugar.

SUN = Solar radiation as average langley units from April to October of
current year.
t = Harvest period in four-week intervals.

TEMP = Temperature in degree days defined as the number of degrees by
which the monthly average temperature exceed 60F from April to
TREND = 1 if observation occurs in 1971, and k + 1 if observation occurs k
years after.
V = Variety p of sugarcane.
Y = Year of crop cycle.

Table 4.4.

Estimated Coefficients and Selected Statistics for the Predicting
Percent of Recoverable Sugar.a

Dependent variable: PRS

Intercept Age F F Day Day2 MAN2
7.64 -0.146 0.004 -0.00002 -0.03 0.0005 0.18
(8.31) (-6.62) (-6.62) (-10.14) (-5.96) (12.94) (6.35)
0.24 0.36 0.44 0.21 0.16 0.12 -0.02
(4.94) (4.25) (5.60) (3.30) (1.98) (1.55) (-5.96)
-0.30 -.009 -0.65 0.30 -0.03 0.28 -.10
(-11.12) (-10.16) (-4.66) (6.45) (-6.78) (7.63) (-14.15)

V10 V1 V2 V13 V14 t*V2 t*V5
0.11 -0.45 -0.99 -0.17 -0.81 0.13 0.20
(1.64) (-2.84) (-2.71) (-1.41) (-3.08) (8.48) (3.06)
t*V6 t*V7 t*V9 t*V12 t*V13 Y*V14 Y
-0.05 0.12 -0.04 0.21 0.11 0.31 -0.02
(-1.90) (3.20) (-2.11) (2.60) (3.30) (4.09) (-1.01)

R2=0.33 F-ratio = 55.29 n = 4584
Mean Square Error = 0.53

aSymbols are defined in Table 4.3. Below the estimated coefficients the
corresponding t-ratios are presented in parentheses.

signs and magnitudes of coefficients conform with a priori expectations,

and are generally consistent with the results of Alvarez et al. (1982).

A relevant finding is the significant effect of the time of harvest (t)

on PRS and a well defined tendency of PRS to increase as the processing

season progresses. In general, varieties have significantly different

effect on PRS.

The coefficients for the estimations of net tons per acre are

presented in Table 4.5. The results are also consistent with the find-

ings of Alvarez et al. (1982). Varieties of cane and members are sig-

nificantly different in the way they affect net tons of cane produced

per acre.

Processing and Cooperative Structures

As pointed out by Eschenburg (1971), it is important to describe

the structure of the cooperative since the behavior of the members is

largely determined by the organization structure.

The cooperative under study processed sugarcane from 800 fields

with a daily processing capacity of 7,140 tons of cane operating 140

days of the 1979-80 processing season (or equivalently, processing

capacity is about 1,000,000 tons of cane for the season). To simplify

the structure of the problem, the membership of the cooperative is

assumed to consist of five growers, selected at random, and each owns

160 fields. The five most frequent varieties in the 1979-80 season are

selected as finite possibilities available to a grower face. These

varieties actually accounted for 98 percent of the area harvested in the

1979-80 season by the cooperative. The processing season is divided

into five harvest periods, each encompassing four weeks, within which

the quota and the mill capacity are defined.

Table 4.5.

Estimated Coefficients and Selected Statistics for Predicting Net
Tons per Acre.a

Dependent variables: NT















V 0*Y


V *Y

R2 = 0.54 F-ratio = 110.00 n = 4584
Mean Square Error = 45.21
Mean NT = 34.62

aSymbols are defined in Table 4.3. Below the estimated coefficients the t-
ratios are presented in parentheses.

The total tonnage (net tons) that accrues to each member is divided

into the number of periods to obtain a point estimation for the delivery

quota. An interval is defined by a lower and an upper limit in net tons

within which the member must deliver each period. The upper and lower

limits of the processing plant and members' quotas are specified such

that they remain the same throughout the period.7

Estimation of Costs

The next step to operationalize the mathematical programming model

is to develop a cost function for the cooperative. An informal approach

is taken to estimate the cost components of cooperative surplus (C1, C2,

and C3 in equation 4.3) and to estimate the grower's cost function.

Primary cost data were collected via a survey among cane factories and

researchers in the area. The responses were complemented with secondary

sources. All cost figures below are expressed in December, 1981,


The processing cost function is specified such that the marginal

cost of processing cane is equal to the average variable cost indexed by

a processing quality factor which depends on the variety of sugarcane.

Viewing a variety of cane as providing a specific grade of processing

quality characteristics, the specified marginal processing cost is

me = aC /aNT = a$
1 P

In reality these parameters are vulnerable to the influence of
stochastic variables (weather may delay raw material delivery) and
equipment breakdowns. For our purposes this abstraction presents no
serious problem.

where a is a constant, p a processing time index which depends on

variety p. Then total processing cost is

TC (NT)= f a 6 dNT = a NT + FC
0 P 1

where FC1 is the fixed processing cost by definition of TC(0) = FC1

(denoted previously as FCC). This specification implies a variable

processing cost function linear in the volume of sugarcane in any time


An estimate of a is obtained with the USDA (1981) estimate of

average variable processing cost for Florida. Fixed processing cost is

obtained by using the seasonal processing capacity of the cooperative

(1,000,000) tons and the USDA's (1981) estimate of fixed processing cost

per ton of cane in Florida.

Even though the importance of processing quality of the different

varieties was recognized in the survey, primary data were not available.

Some survey answers suggest that fiber content (processing quality) in

sugarcane is highly correlated with varietal correction factors (VCF's)

used in experimental milling tests which have been computed in South

Florida. The estimated 's for the selected varieties are presented

in Table 4.6.

The cost of (hand) harvesting, hauling and transloading a "gross"

ton of sugarcane was estimated by the cooperative manager to be $7.14.

8See Miller and James (1978) for an explanation of VCF's. Some
mills in the area use these VCF's in their decision of what varieties to
grow or when paying the independent growers for sugarcane.

Net tons predicted in Table 4.5 and 4.6 are adjusted to "gross tons" of

cane with a factor of 1.05.

Table 4.6. Comparison of Varieties of Cane in the Mathematical Programming

Cost index-- Sample mean
Variety Processing Growing NT PRS
(Bp) (Ep)

A 1.16 0.97 49 9.3
B 1.18 0.80 37 10.0
C 1.28 0.70 37 9.1
D 1.28 1.10 36 9.3
E 1.00 1.00 34 9.6

varieties A, B, C, D and E correspond to V1, V2, V7, V9, and V8, respectively,
in Tables 4.4 and 4.5.

Supplies of raw agricultural products handled by a cooperative are

usually acquired from dispersed points. There is a need to incorporate

the spatial components of marketing cost associated with the raw

material delivered by the members, especially when considering alterna-

tive arrangements that deal with schemes for regulating of the members'

volume. Though in the case of Florida sugarcane cooperatives the mem-

bers are located in a relatively compact geographic region, sugarcane is

a very bulky commodity. For the 1981-82 season, the cooperative under

study contracted transportation at a fixed charge of $0.35 per ton and

$0.15 per ton per mile travelled.

Recall footnote 3. What is harvested and transported is gross
tons of cane, not net tons of cane that are processed. A factor of 1.05
is applied for trash, tops, leaves, and water to adjust the predicted
net tons of sugarcane to gross tons of cane. A factor of 1.5 is applied
to convert air miles to road miles in estimating transportation cost.

Regarding the grower's cost the survey revealed that variable cost

per acre differs among varieties of sugarcane. Unfortunately, no con-

sistent data exist for the different varieties of sugarcane regarding

these costs. Assume that the growing cost function is

C = CPA*E (4.24)
p p

where CPA is the variable expenses of growing per acre of cane, and E

is the (survey average) cost index associated with growing variety p of

sugarcane whose estimates are presented in Table 4.6.

Summary of Estimations

The parameter estimates for the mathematical programming problems

presented in equations (4.6) through (4.17) are summarized in Table

4.7. In brief, statistical models are used to predict sugar yields and

tons of cane per acre on a field basis for the different varieties. The

cost components of the cooperative surplus and the grower cost function

are estimated for the varieties. The varieties, fields, size of the

cooperative and processing capacity are obtained from an actual coopera-

tive operating in South Florida.

Implementation of the Model

When confronted with large-scale problems, agricultural economists

soon learn about the limitations of traditional solution techniques that

are widely used in the profession. One example is the almost exclusive

use of linear programming (simplex method) which has characterized

several generations of agricultural economists. Here, the choice of a

co 0 0

S c c c C c cc co m
co( 0 0 0 0
-4 4-

w u o
ac o 1- *-1
( Eii > > E i c c
cc 4-4 W^ ac *- 2 2 2 2

cO o 0 C Q O O 4 c 0. 0 C
-4n c0 0
o 0 -4 0 c) c
S1 .0 -- U 4 -4 i r4 3. :C
c c a cc 04 c o 0. 0
Q a (o O 0 >. a Uo U lo do

S i u1 c e r_ o 0 34 .J Q C 3-

= C CLu 2 2 a (B > c -4c o =
.61 > (*-U w 0- Dc c C 4.J. -4I CO L w C Co 9 ca ca c
mS 4 0 w 01) 0 Co ( 0 ) 1 0 -. a*w-4C U -4 U () Q w u
4 C 4- 4 1: -4 3 a W -4 W S -0S .S a 2 2
ca c L" C m rC 4 3 o a .9 W -4 4 B t 4
.0 ca C )4-w IV o 0u c ou -'4u 0 u 40 u0
m > cc 0 -4 a0 4 ) 0) a) 4) w)
L a u-i o L 0 4-4 w 00 2 0 e m (1) 1) m W )Z
w ) ac (u cO 0 0 cc 4 -4 1 0 0 1 0 1 0
)) (>) o-4 > -ji-o 144-4 1-44-4
4 o 4 o o W cc o wo w-i w wr x xe w L

Sw 0 ca c cM 'o- 44 1 0 0a 1 0 C o
rn 9l > > O ZU 0 'O O 4 -- ., -, O C4
0) -4

20 z

co w c t *
,4 C/4 en C

a Ea-4 +C

ca = c* .
m2 W 0 0 4 )
a 0 -4 C 1 4 u o o

e- 4 4 u u n en II ; Z4 4-x O 0 C
cccc en o oi E-i Q c- a *o en .

E) p C CO ^ NU 2 - O S 0
cc >s a >. 4- 4-4 u c 1 E: r ~

solution technique is critical given the large dimensions of the


The problems stated in equations (4.6) through (4.18) are integer

programming problems (Fpfit integer) and the use of the simplex method

will not insure integer solutions. However, there are alternative

approaches to solve the above integer programming problems. Specifi-

cally, the problems can be viewed as two-stage assignment problems (see

Appendix C for an illustration). In the first stage, varieties are

assigned to fields on a single processing period basis. Then, variety-

fields are assigned to a harvest period. The assignment and assignees

are matched in such a way that the cooperative objective is maximized

while satisfying the constraints.

The problem also falls into the class of capacitated transshipment

problems. Regardless of the physical context of the application, the

transshipment problem and the assignment problem can be formulated as

equivalent transportation problems (Hillier and Lieberman, 1980). With

800 fields, five processing periods, five growers and five varieties of

sugarcane, the resultant transportation problem consists of some 20,000


The capacitated transshipment problem and its specialization (the

transportation problem and other related problems) can be expressed as

network flow problems (Bradley et al., 1976). The specific adaptation

of the above problem to a network flow framework is briefly explained in

Appendix C. The mathematical programming problem developed above was

solved as a network flow problem with the program presented in Appendix

D and the performance results in the following chapter.



This chapter presents the empirical results of the model presented

in Chapter IV which employs sugarcane processing cooperatives as a

specific example to test the conceptual model developed in Chapter

III. Unfortunately, there are no studies to compare with the results

presented below. The empirical results concerning the estimation of

parameters of the mathematical programming model were presented in the

previous chapter. The focus is on the results from the runs of the

various mathematical programming problems. First, performance concepts

and measures to evaluate the arrangements are briefly discussed and

defined. Then the performance results are presented, compared and

discussed for alternative arrangements among cooperative members along

with a sensitivity analysis for selected structural parameters. Last,

the implications of the results and their relation to the conceptual

developments are integrated into an overall assessment.

The Performance Measures

Performance is such an elusive term that any attempt to measure it

should be preceded by an attempt to define it. Helmberger et al. (1977)

defined the performance of a firm as the ex post value of choice vari-

ables appearing in the profit function of the firm as envisaged in

economic theory. Thus, output and price levels embody the performance

of a firm if they are influenceable. They define market performance as

the total performance of all its participants, including all prices that

vary with the level of output. Beyond its definitional problem, the

performance measurement problem remains even for well-defined perfor-

mance dimensions.1

To evaluate the performance impact of alternative arrangements,

norms of comparison are required. Clearly, the ideal norm is the "coor-

dinated" cooperative solution since conceptually it represents a poten-

tial Pareto optimal allocation. A necessary condition for a Pareto

improvement is an increase in total net returns under a given set of

arrangements relative to another set.

The allocative efficiency objective is the maximization of total

net returns to the operation of the cooperative. The results deal with

two aspects of equity. One is the distribution of net returns among the

members measured with the coefficient of variation (ratio of standard

deviation over the mean). The coefficient of variation (C.V.) measures

the degree of relative dispersion of net returns. However, it measures

the degree of inequality rather than inequity.2 The second aspect of

equity regards payment equity or how well members are compensated in

accordance with the value of their deliveries measured with a price

1Lang et al. (1982) identified two difficulties associated with
measuring performance: first, the difficulty of measuring performance
directly; second, the problem of comparing the importance of one
dimension relative to another remains even if all dimensions of
performance in a commodity subsector were quantified.

2Discerning between equal vis-a-vis equitable treatment of the
members is one of the most perplexing problem that cooperatives face.
Both terms can be regarded as equivalent only if members are indeed

accuracy index (PAI). This index, whose specification is original in

this study, is intended to measure the degree of distortion between

payment to the growers and the cooperative surplus that they generate.

The computed values will always be < = 1.0, where 1.0 is perfectly

accurate pricing. The index provides a measure of pricing equity and

the degree of free riding since PAI<1 implies that some members are

overpaid at the expense of others. The price accuracy index, then, is

measured as

Y Cs

where yi is amount of raw material delivered by member i, Y the total

amount, CSi is the cooperative surplus generated and PAYi is the payment

from the deliveries of member i. Thus, PAI is the weighted sum of the

pricing accuracy of each member's deliveries, where the weights are the

shares of raw product of the members. This study emphasizes allocative

efficiency, and although net returns and pricing equity are measured,

the definition of an optimal or ideal equity values and the weights

attached to the different measures of performance is not attempted.

Based on the definition of performance given by Helmberger (1977),

the average net revenue product or average price per ton of sugarcane

(P ) and the amount of (tons) of sugarcane and sugar produced are

measured. Many other measures can be computed from the solutions of the

model (e.g. net returns per acre, average price per tons of cane and

quasirents), but given magnitude of results, concentration is placed on

the above measures.

Baseline Results and Discussion

The focus of this section is the presentation and discussion of

baseline results with the parameters estimated in the preceding

chapter. The productivity coefficients of the five members that compose

the cooperative coorespond to those of MAN1, MAN6, MAN7, MAN8, and MAN10

of Tables 4.4 and 4.5. The performance measures computed from the

solutions are presented in Table 5.1. Differences in the performance

results under alternative arrangements are due to differences in the

pattern of deliveries, varieties grown and area of cane planted by each

of the members. The latter two are reported in Table 5.1.

The coordinated cooperative makes total net returns of $4,648,126

for a single processing season, the highest of all the scenarios con-

sidered. The coordinated solution does not utilize members' quotas

since it implies that members are perfectly coordinated in order to

achieve collectively maximum net returns with no regard to individual

net returns or quotas. The higher net returns of the coordinated solu-

tion are due to the collective selection of varieties, fields and

periods of delivery to maximize collective rather than individual net

returns. This result represents a favorable central test of the theo-

retical model. Payment based on sugar delivered with processing quotas

ranked second with total net returns of $2,304,719 which represents a

loss of $2,343,407 from the coordinated solution due to the invididual-

istic (myopic) behavior of the cooperative members. Payment based on

the amount of raw product (sugarcane) with processing quotas resulted in

$2,251,238 total net returns. This represents a loss of $2,396,888 from

the coordinated solution and it was due to individualistic behavior of

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the members. When looking at the individual members, some results are

interesting. Some members benefited positively with cane-based payment

rather than with sugar-based payment and vice versa. For example,

member 3 is better off with sugar-based payment than with cane-based

payment by $105,876, while member 4 is better off with cane-based pay-

ment by $53,969. The redistribution of impact of alternative payment

schemes is not surprising since individual members have comparative

advantages in producing cane or sugar. However, all the members are

better off under a coordinated payment scheme than any other scheme.

The coefficient of variation of net returns of the members under a

coordinated payment scheme was the smallest (C.V. = 0.49). Sugar-based

price with quotas offered the second smallest coefficient of variation

(0.64), and tonnage-based payment with processing quotas offered was

ranked as third in profits variation (0.65). The imposition of quotas

in the presence of myopic behavior of the members in both sugar-based

and cane-based payments, reduced the variation of profits among the

members. Thus, in the cases considered quotas represented an improve-

ment in equity (equality) in the distribution of net returns. With

sugar-based payment allocative efficiency increased slightly, however

its coefficient of variation went up dramatically due to the change in

the relative distribution of profits. For instance, note that member 1

and member 5 increased their net returns while other members decreased

theirs when quotas were removed.

The results also indicate that quotas, under individualistic

behavior of the members, can improve coordination among the members.

For instance, total net returns were $260,473 higher with processing

quotas than without them in cane-based payment. Though in sugar-based

payment the removal of quotas led to higher net returns, the design of

appropriate quality specification and volume quotas can induce coopera-

tion as in the case of cane-based pricing. The amount of raw product

delivered as well as the amount of sugar produced were higher with

members having processing quotas. The result of cooperation being

induced with quotas is supportive of Hobbes' (1909) suggestion about the

possibility of achieving a preferred outcome by coercion.

The difference in total net returns between cane-based and sugar-

based payments in the presence of quotas is $45,951. This difference is

not as dramatic as one could expect. Three reasons are envisioned to

provide, in part, an explanation. First, the variety-choice selection

used in the optimization runs may not allow larger variation in quality-

quantity choice. The performance implications with alternative quality

choice specification is explored later in the sensitivity analysis.

Second, the amount of sugar and the amount of cane are not indepen-

dent. However, higher amount of cane tonnage does not imply higher

amount of sugar, since sugar also depends on the sugar content of the

delivered cane. Third, even if at first glance sugar may seem a more

plausible payment unit, this perception appears increasingly inaccurate

when one considers that processing costs (as well as transportation and

harvesting costs) are directly dependent on the volume of deliveries and

not on the amount of sugar delivered. In the presence of myopia, highly

productive growers (high-sugar content, low-cane tonnage) are penalized

for their deliveries which in turn leads to underproduction as in the

case of externalities.

The results are generally consistent with the theoretical arguments

of Chapter III. The raw product prices increase as coordination

increases. The $20.68 fully coordinated average price per ton of cane

(P ) is higher than in any other scenario. The coefficient of varia-

tion, intended to measure the variation of net returns among the

members, was higher without quotas. This implies more inequality in the

distribution of profits. Under a given payment scheme, higher degree of

pricing accuracy did not mean higher profits or coordination. Note that

with sugar-based payment, PAI increases from 0.903 to 0.967 when quotas

are imposed but total profits, however, are lower. In summary, quotas

can increase equity in payment and in the distribution of net returns at

some possible efficiency loss. The coefficients of variation and price

accuracy indices moved uni-directionally in a parallel fashion in all

the scenarios. The magnitude of the difference between the performance

of alternative payment schemes and the coordinated solution points out

the importance of the internalization of the cooperative processing

costs and revenues at the individual level.

Sensitivity Analysis

The preceding section has left questions regarding the sensitivity

of performance to the structural parameters of the cooperative. In an

attempt to solve this empirical question, selected scenarios are opera-

tionalized under alternative membership structures, variety selection

and processing cost indices. Except for the coordinated cooperative

case, the following scenarios are implemented only with the use of

processing quotas. The model specifications are essentially the same as

in the baseline results except in the parameters where change is


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