THE IMPACT OF ALTERNATIVE MARKETING ARRANGEMENTS
ON THE PERFORMANCE OF PROCESSING COOPERATIVES
RIGOBERTO ADOLFO LOPEZ
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
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.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................................... iii
LIST OF TABLES ...................................................... vi
LIST OF FIGURES .................................................... vii
I INTRODUCTION ............................................. 1
The Problem ............................ ............... 3
Behavioral Nature of the Problem ..................... 5
Objectives ........................................... 7
Scope ................................................. 8
Organization of the Study ............................ 9
II PROCESSING COOPERATIVES AND ARRANGEMENTS STRUCTURES ...... 11
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
III A CONCEPTUAL FRAMEWORK FOR COOPERATIVE BEHAVIOR
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
Heterogeneous Membership ............................. 53
The Coordinated Case .............................. 54
Payment Based on Raw Product ...................... 56
IV EMPIRICAL PROCEDURES: AN APPLICATION TO SUGARCANE
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
A COOPERATIVE PLANT SIZE IN THE LONG RUN ................... 109
B VARIABLES IN THE YIELD MODELS ............................ 115
C THE PROCESSING COOPERATIVE PROBLEM AS A NETWORK
FLOW PROBLEM ............................................. 119
D THE COMPUTER PROGRAM ..................................... 127
REFERENCES .......................................................... 137
BIOGRAPHICAL SKETCH ............................................... 141
LIST OF TABLES
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
LIST OF FIGURES
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.
THE IMPACT OF ALTERNATIVE MARKETING ARRANGEMENTS
ON THE PERFORMANCE OF PROCESSING COOPERATIVES
Rigoberto Adolfo Lopez
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
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 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
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
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-
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
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
PROCESSING COOPERATIVES AND ARRANGEMENTS STRUCTURES
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
x 3 Y24 PRODUCERS
X = Set of Variable Inputs
Y. .= Set of Outputs
i,j= Source and End Node
= 1,2,3,4 but irj
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-
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
6. Stock price Fixed Market determined
Source: VanSickle, 1980, pp. 1-4.
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
Table 2.2. Differences Between Pure Marketing and Processing Cooper-
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
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.
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
(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.
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
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.
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-
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.
A CONCEPTUAL FRAMEWORK FOR COOPERATIVE
BEHAVIOR AND PERFORMANCE
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
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
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
mPAY = CS
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)
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)
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-
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
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)
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)
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
y acm. (3.14)
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
1iyopic and Coordinated Equilibria.
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
-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
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
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
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
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
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
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
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
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
= 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)
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-
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
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
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.
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
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
11 r- -- -- -- O
- O (
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
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)
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
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)).
EMPIRICAL PROCEDURES: AN APPLICATION TO
SUGARCANE PROCESSING COOPERATIVES
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
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
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.
Notation Used in the Mathematical Programming Model for Sugarcane
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
= 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
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__ _ __ _~ ____ _
E E E
p if t
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 < 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)
(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)
(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.
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
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
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.
Age = Age of cane in periods of two weeks up to November 1 of foregoing
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
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
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
V = Variety p of sugarcane.
Y = Year of crop cycle.
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)
MAN4 MAN6 MAN7 MAN9 MAN10 MAN11 MILE
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)
MODE SUN t t2 t3 TEMP TREND
-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
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.
Estimated Coefficients and Selected Statistics for Predicting Net
Tons per Acre.a
Dependent variables: NT
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$
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
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
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)
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
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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.
EMPIRICAL RESULTS AND DISCUSSION
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-
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
Y. CS. I CS. PAY.
PA = 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.
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