Cooperatives and Payment Schemes : Lessons from Theory and Examples from Danish Agriculture [1 ed.] 9788763099868, 9788763001953

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Cooperatives and Payment Schemes

Peter Bogetoft & Henrik B. Olesen

Cooperatives and Payment Schemes Lessons from theory and examples from Danish agriculture

Copenhagen Business School Press 2007

Cooperatives and Payment Schemes Lessons from theory and examples from Danish agriculture © Copenhagen Business School Press, 2007 Printed in Denmark by Narayana Press, Gylling Cover design by Morten Højmark 1. edition 2007 e-ISBN 978-87-630-9986-8

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Content PREFACE

7

GUIDANCE FOR READERS

9

1 SUMMARY 1.1 The Danish pig industry as an example 1.2 The theoretical challenge 1.3 The practical challenge 1.4 The criteria 1.5 Payment schemes 1.6 Multiple-criteria evaluation 1.7 Conclusion

13 14 15 16 17 21 25 25

2 COOPERATIVES 2.1 What is a cooperative 2.2 Traditional cooperatives 2.3 New Generation Cooperatives (NGCs) 2.4 General problems of cooperative ownership 2.5 Coordination and motivation 2.6 The literature on cooperatives 2.7 Case: The Danish pig industry 2.8 Conclusions

27 27 30 33 35 44 47 51 56

3 ECONOMIC OBJECTIVES AND CONDITIONS 3.1 Efficiency 3.2 Equality and the integrated profit 3.3 Technical applicability 3.4 Balanced budget 3.5 Individual incentives 3.6 Group incentives 3.7 Robustness and dynamics 3.8 Holistic evaluations 3.9 Conclusions

59 60 63 69 71 72 77 87 96 105

6

PETER BOGETOFT AND HENRIK B. OLESEN

4 SINGLE PRODUCT PAYMENT SCHEMES 4.1 Technologies and markets 4.2 The traditional payment scheme 4.3 The wise chairman’s solution 4.4 Production of special pigs – an example 4.5 Optimal, under- or over-production 4.6 The problem of over-production and some possible solutions 4.7 Balanced budget and the allocation of profits and losses 4.8 Fair and ‘natural’ profit allocations 4.9 Information needs 4.10 Summary

111 111 120 122 130 133 140 146 157 164 171

5 MULTI PRODUCT PAYMENT SCHEMES 5.1 A general example 5.2 National pricing system: Equal gross margins 5.3 Payment scheme for piglets: Equal returns on capital 5.4 The premium-pig system: Quota and premium products 5.5 The ACA (Alternate Cost Avoidance) method 5.6 Nucleolus 5.7 Shapley 5.8 Summary

175 175 177 186 191 204 212 216 222

REFERENCES

229

GLOSSARY

237

INDEX

243

Preface Approach

Criteria

Cooperatives

Payment schemes

Compromise

This book describes a set of economic methods and results that can guide the choice of payment (profit and cost sharing) schemes in cooperatives. We establish an economic framework in which the choice of a payment scheme is looked at as a multiple criteria decision problem with multiple decision makers. This allows us to identify a number of criteria and desirable characteristics for a payment scheme. The criteria are arranged in a goal hierarchy. This gives a structure to the problem. We deal with the criteria under the headings of coordination, motivation and dynamic adjustment. Coordination is to ensure that the right members are doing the right things at the right time. Motivation is to give the members selfinterest in the coordinated actions that benefit the cooperative the most. Dynamic adjustment is to promote reasonable investments and adjustment of payments when market and production conditions change. Cooperatives are firms that are owned and controlled by its users (as opposed to its investors). Cooperatives and cooperative payment schemes are found in all sectors of society. Moreover, many firms have more in common with cooperatives than with investor owned firms, regardless of their legal form. This is for example the case with: a group of consultants or lawyers sharing offices, secretarial assistance and clients, a group of citizens setting up a joint water-supply, or households in a region owning and operating a common electricity grid. We will usually take examples from agricultural marketing cooperatives, but the analysis can be used directly in other sectors, and it can easily be modified to cover consumer cooperatives. The analytical framework is used to assess a number of actual payment schemes. We analyze existing payment schemes used in the Danish pig industry and a number of other payment schemes, both practical and theoretical. It is not possible to find one particular scheme that is superior in relation to all criteria and in all situations. Rather, a compromise is necessary between the different criteria taking into account their relative importance in the specific context. This book helps to clarify and structure the compromise, and to identify the context specifics that are particularly important.

8

Thanks

PETER BOGETOFT AND HENRIK B. OLESEN

We are grateful for the support of Norma and Frode Jacobsen (NFJ) Foundation to this and related project over the years. In particular, we appreciate the patience the Foundation has shown in the (numerous) periods where we have been involved in too many other projects. The aim of the NFJ Foundation is to support agricultural research in order to promote the competitiveness of the Danish pig industry. Part of the book is based on Henrik B. Olesen's submission for a competition promoted by the NFJ Foundation. Parts of the text have been used as teaching material for courses in The Economics of Cooperatives at the Royal Veterinary and Agricultural University (KVL) and elsewhere. We are grateful for many helpful comments from the participants. Several people have made helpful suggestions to earlier drafts of the manuscript. We would especially like to thank Frode Slipsager and Bent Claudi Lassen, both members of the Board of Trustees of Norma and Frode Jacobsen Foundation, Søren Büchmann Petersen, the Federation of Danish Cooperatives, Karsten Flemin, The Federation of Danish Pig Producers and Slaughterhouses, Hans Frimor of The University of Southern Denmark in Odense, as well as Jens-Martin Bramsen, Kostas Karantininis, and Misja Mikkers, KVL. We would also like to thank Pia Skogø for her help with the editing of the original Danish book, and Lisbeth Balle and Helle Gjeding Jørgensen for several rounds of final editing of this edition. Finally, Peter Bogetoft would like to thank his family, Victoria, Rasmus, Stina and Nete for their support. Henrik B. Olesen would like to thank Pia for her help and encouragement throughout this work.

Frederiksberg, October 1, 2006 Peter Bogetoft

Henrik B. Olesen

Guidance for readers Readership The book is aimed at three reader segments.

A decisionmaking tool

Cooperative economics

New ideas

1. Business people Business people and decision makers can use the analytical framework of the book to evaluate changes to a cooperative's payment scheme. Our analytical approach can be used in any branch of industry. The book uses examples from the Danish pig industry to illustrate the concepts discussed, but it has proved to be of interest to business people from many other sectors as well, including law and consultancy, utilities and health. The summary in Chapter 1 gives a rapid overview of the main conclusions of the book. 2. Students Students can use the book as an introduction to the economic theory of cooperatives. They can also use the book to see how modern economic theory can be used in practical problem solving. 3. Researchers We believe that the book can prompt researchers to make new use of and formulate new contributions to analytical business economics. We have, ourselves, gathered many ideas for research through our work on this book, and we would welcome further research on the special problems of cooperatives and cooperative payment schemes.

The arrangement of the text The book can be read without mathematics

Glossary

The book has been written for it to be understood by those who are not accustomed to reading mathematically based economic literature. The general text does not use mathematical expressions in its arguments. The way the text is laid out, makes it possible to skip the mathematical representations. The book has a short glossary explaining central terms. This should help readers with little prior knowledge of the terminology of modern micro economics or business economics. Of course, we also explain relevant terms in the text as they are introduced.

10

Example boxes

PETER BOGETOFT AND HENRIK B. OLESEN

We present examples in text boxes, to show how the theoretical concepts apply to actual cases. Most of these examples are taken from the Danish pig industry. Sometimes the example boxes contain simple calculations which illustrate the theoretical principles. Example: Perspectives from industry or a simple numerical illustration

Mathematical sections

Those who are used to reading mathematical expressions can benefit from the more detailed presentation in the mathematical sections. One of the advantages of using mathematical models is that it enforces discipline on our argumentation, and thus ensures that our arguments are consistent. In the text we use the symbol M to indicate where we give a more detailed analysis in the following mathematical sectionM. The mathematical section is always placed at the end of the relevant section and is presented with a shaded background. Mathematical representation: The mathematical model which gives details of the argumentation in the preceding section. We explain the mathematical notation used as it is introduced. At the end of this guidance for readers, we give a short overview of the most important notation.

The contents of the book Cooperatives

The main goals

The main conclusions of the book are summarized in Chapter 1. In Chapter 2, we give a general introduction to cooperatives and the scientific literature hereon. We also discuss the basic strengths and weaknesses of cooperatives from an economic perspective. Lastly, we give a brief description of the main characteristics of the Danish pig industry. In Chapter 3, we present the fundamental economic criteria which a payment scheme should satisfy. The chapter starts with a discussion of the goals of a cooperative. This discussion deals with the issues of efficiency and equality. This is followed by considering a number of requirements which limit the scope of the design of a payment scheme. Among other things these requirements are technical feasibility, a balanced budget, incentive compatibility and voluntary participation. The principle of voluntary participation not only sets restrictions on

GUIDANCE

Economic models of cooperatives

Analysis of payment schemes

Glossary Notation

11

payments to individual producers, but also on payments to different coalitions of producers who can threaten to collectively withdraw from the cooperation. We also consider the requirement for the payment scheme to be adaptable in a dynamic environment, and we close with a summary of the most important criteria structured as a goal hierarchy. In Chapter 4, we use the criteria from Chapter 3 to analyze in a series of more specific economic environments. We focus on cooperatives with a single product line and define the environments by making more specific assumptions on the production, processing and marketing conditions. We also discuss how, in actual cases, a cooperative can estimate the production costs and the revenue potential of the processing stage, e.g. the slaughterhouse. We illustrate the classic over-production problem in situations where the cooperative is operating in a “thin” market, and we discuss various ways of limiting over-production – a number of the usual proposals for limiting production results in a residual surplus which is typically either not dealt with in the literature or not dealt with satisfactorily. We review a number of different allocations generating a balanced budget, while eliminating over-production. Finally, we discuss the information needs of payment schemes and the possibility of reducing these needs. In Chapter 5, the criteria compiled in Chapter 3 are used to evaluate some specific payment schemes in the context of a multi-product cooperative. We analyze the principles of two payments schemes used in practice in the Danish pig industry, the National Payment System and the payment scheme for piglets. We also propose a payment scheme based on marginal pricing in which the surplus is allocated according to the ownership of special premium rights. Finally, we analyze three payment schemes which have a more theoretical basis. The chapter concludes with a summary of the strong and weak points of the different payment schemes. The book also contains a glossary and an index Mathematical representation: In general we use the following notation in the mathematical sections: A variable y with a superscript j refers to the value of the variable for member j, and a variable y without a superscript refers to a vector with the individual member's y values. We also use the superscript -j to indicate vectors with all members except j. We use the subscript i to refer to the product type i.

12

PETER BOGETOFT AND HENRIK B. OLESEN

The most important variables are: qij

q

is producer j’s production of product i, j=1,…n and i=1,…m, where n is the total number of members of the cooperative and m is the total number of product types (e.g. organic pigs and UK pigs). is producer j’s production. is the producers' total production of product I; i.e. qi qi1  qi2  ...qin . is a vector of the members' total production; i.e.

R q

is the cooperative's revenue

Sj xj cj N S Si

is producer j’s profit is producer j’s payment is producer j’s production costs is the set of primary producers; i.e. N {1,.., n} is a coalition or subset of primary producers; i.e. S Ž N is the producer group which produces product i (e.g. organic producers); i.e. S i ^j  N | qij ! 0`.

qj qi

q

 q1 ,...qm

1 Cooperatives

Payment scheme is the key

A number of considerations

Summary In broad terms, a cooperative (also co-operative or co-op) is a group of persons who join together or cooperate, to carry on an economic activity of mutual benefit. More specifically, cooperatives are firms that are owned and controlled by its users (as opposed to its investors). Cooperatives and cooperative payment schemes are found in all sectors of society. Moreover, many firms have more in common with cooperatives than with investor owned firms, regardless of their legal form. This is for example the case with: a group of consultants or lawyers sharing offices, secretarial assistants and clients, a group of citizens setting up a joint water-supply, or households in a region owning and operating a common electricity grid. We will usually take examples from agricultural marketing cooperatives, but the analysis can be used directly in other sectors, and can easily be modified to cover consumer cooperatives. The payment scheme plays a key role in a cooperative. It defines how costs and profits are shared among the members. The payment scheme therefore regulates the willingness of the members to participate, the effort they supply and the production they bring to the cooperative. This in turn determines the cooperative's opportunities in processing and marketing. It is not easy to design a suitable payment scheme. A payment scheme must take into account a number of considerations.1 It must reflect the existing conditions in production, processing and sales, and it must be flexible enough to accommodate changes in the business environment. It must be simple to understand and it must help in providing a steady income for individual members, without depriving them of the incentive to develop new ideas and to adjust to changes in the market. The payment scheme must be a compromise between different producer groups with different interests and different expectations, while allowing individual producers to change production, acquire capital and even to withdraw from the cooperative. However, the complexity of the problem is no excuse for conservatism. A cooperative ought regularly to evaluate not only the specific clauses of its existing payment scheme, but also the overall structure of the scheme. The cooperative cannot be sure that a scheme designed for one set of market and production conditions, is still optimal for current conditions.

14

Need for a theoretical approach No simple solution

Analytical framework

PETER BOGETOFT AND HENRIK B. OLESEN

The complexity of the problem means that the methods used to evaluate alternative payment schemes must have a sound theoretical basis. To ensure comprehensive and consistent evaluations there must be a clear frame of reference. Finally, the complexity of the problem means it is not reasonable to expect a simple solution. It is not possible to point to a single scheme which is best in absolute terms. Each scheme will have many consequences, and the extent and importance of these will depend on the specific conditions in production, processing, marketing, etc. The best that can be hoped for is to find a ranking of different schemes for a specific situation, based on different criteria. This book establishes an economic framework to analyse how different payment schemes best satisfy the interests of members. It gives a check-list and a holistic approach to systematic and comprehensive evaluations of alternative schemes.

1.1 The Danish pig industry as an example

Danish Crown's strategy

Allocating the gains from special production

This book takes as its point of reference and as a steady source of examples the Danish pig industry, one of the most successful in the world by many standards. Recent years have involved greater differentiation in pig production as a result of changing consumer demands. These developments have also changed the demands made on payment schemes, since the members of cooperatives have become more heterogeneous. An example of this is the differentiation strategy announced by Danish Crown (the biggest cooperative slaughterhouse in Denmark) in 1997. The strategy will reduce the overwhelming reliance on multi-pigs (90%) and introduce widespread special production of, for example, the EU heavyweight pigs (16%) and UK pigs (32%) in the course of a few years. The strategy is a response to changed market conditions. Buyers in the export and domestic markets are no longer merely interested in new cuts and new methods of processing the standard pig, the multipig. There is a development towards more individualised consumer demands, some wanting heavy pigs, some wanting organic pigs and some wanting better animal welfare, and it is expected that niche productions will continue to grow.2 In this connection, there has been considerable debate about the relative payments for different products. An extreme point of view, notably espoused by Kent Skaaning, the then Chairman of the Danish Association of Pig Producers, is that special products should be kept

SUMMARY

15

economically separate, enabling the special producers to receive all the gains while carrying all the risks associated with the production in question.3 Others, including the former Chairman of Danish Crown, Bent Claudi Lassen, have promoted the idea that all the members, not only the special producers, should share the added value from the special products.4

1.2 The theoretical challenge

The focus of the book

The theoretical basis

Economic method The producers’ behaviour

We seek to create a conceptual framework sufficiently broad enough to cover the main economic effects of a cooperative payment scheme. The conceptual framework must also be sufficiently coherent for its logical consistency and theoretical basis to be obvious. We have chosen to focus on the interaction between primary production, processing and market conditions. This is natural as the marketing cooperatives seek to coordinate and partially integrate production, processing and sales activities. We restrict ourselves to the study of economic models and the criteria for evaluating alternative payment schemes. This excludes historical, sociological, and political approaches, as well as approaches based on broad welfare and macro-economic considerations. However, this still leaves a number of matters for consideration. The theoretical approach is based on classic economic disciplines such as theories of production economics, as well as sales and marketing. However, modern developments in economic theory are also included. We have thus drawn upon modern industrial organisation and non-cooperative game theory to describe the interaction between primary production, processing and the market. We use agency theory to identify the fundamental problems of coordination and motivation in an integrated organisation consisting of producers and a cooperative. Finally, we use cooperative game theory and cost allocation theory in an attempt to create reasonable rules cost allocation between members and between different groups of members. The logic of the book itself is economic by nature. We seek “rational” payment schemes, and we therefore model the choice of scheme as a decision-making problem itself. Moreover, it is the individual and more or less autonomous responses of the cooperative’s members that determine the effects of the payment scheme. In this sense, cooperatives have many similarities with other economic systems, for example markets, where the result is determined by the interaction of a number of individuals. On the other

16

The context

Changed conditions

Impossibilities

PETER BOGETOFT AND HENRIK B. OLESEN

hand a cooperative is rather more complicated, because there is a limited number of members and specifically a limited number of groups of members. This increases the possibility of strategic behaviour. The evaluation of schemes is further complicated because the specific context; i.e. the production, processing and marketing conditions, has a decisive influence on the members' choice of action as well as on the consequences of such choice. Thus it is difficult to calculate the effects of a scheme without having a reasonably precise definition of the production and marketing context. We have therefore elected to study some key situations, corresponding for example to cooperatives with growing, constant or diminishing marginal returns and to cooperatives based on homogeneous or heterogeneous primary goods. This gives an insight into the set of choices confronting a cooperative in different contexts. From a theoretical point of view, the problems surrounding the choice of a payment scheme in today’s context are complicated enough. However, from a practical point of view, this is only part of the picture. Here, it is also necessary to think in a dynamic dimension, and to consider how a scheme can allow for a reasonable adaptation to future changes in production, processing and marketing conditions which may be more or less foreseeable. We have sought to introduce this aspect into the theoretical framework by discussing a number of dynamic properties. The economic literature contains several results which can help limit what is achievable via a payment scheme. Unfortunately many of these conclusions suggest that a payment scheme cannot simultaneously satisfy different simple and reasonable requirements. These conclusions are called impossibility theorems.

1.3 The practical challenge

Summarising criteria and possibilities

The practical challenge is to develop a systematic approach reflecting the complexity of the problem while also providing cooperatives with a reasonably workable method for assessing alternative payment schemes on a sound theoretical basis. In practice, we need to find a payment scheme in the midst of theoretical complexity. We have met this challenge by using multiplecriteria analysis. We have listed the most important requirements and have made a hierarchical division of this list into increasingly operational criteria. We analyse a number of specific payment schemes, showing how they can be evaluated according to the criteria in a given

SUMMARY

17

context, for example under imperfect competition (Chapter 4), or in situations with differentiated primary goods (Chapter 5).

1.4 The criteria Assuming that the producers are members of the cooperative for economic reasons, the overall goal of the cooperative should probably be to maximise the profit in the integrated organisation consisting of the members and the cooperative. Members' welfare

Coordination

Efficiency

Dynamic adjustment

Motivation

Individuals

Group

Information Member’s Risksharing Balanced budget

Market signals

incentives Management incentives

The core

Consistency

Monotonicity

Total monotonicity

Coalitionmonotoicity.

Investments

Investments on farms

Hold-up problems

Additivity

Equality

Member democracy

Figure 1.1 Goal hierarchy for payment schemes

Investments in processing

Horizonproblems Free rider problem Portfolio problem

18

The main considerations

PETER BOGETOFT AND HENRIK B. OLESEN

We identify three main dimensions of this, namely: ƒ Coordination - to ensure that the right members produce the right products at right time and place. ƒ Motivation - to give members the incentive to take the decisions which are most beneficial to the common aims of the cooperative. ƒ Dynamic adjustment - to ensure sensible adjustments in the future.

Efficiency

The need for information

Risks

Balanced budget

Market signals

Equality

We divide these considerations into a number of more concrete criteria which we arrange in the following goal hierarchy. We seek efficiency; i.e., to maximize the integrated profit. Alternatively, we seek at least Pareto-efficiency which is satisfied as long as no member can be better-off without this having a negative effect on other members. In order to ensure efficiency a number of subconditions must be satisfied. It is important to assess how much information is needed for a payment scheme to work. The need for information relates both to the cooperative and to its members. We discuss different procedures which a cooperative can use to obtain the necessary information in practice. We also point out different methods for limiting the need for information. For example, we analyse how tradable production rights can reduce the company's information needs, while imposing very high information requirements on members. In order to minimise the costs of risks (the risk premium), risk must be dealt with optimally. The payment scheme must minimise the risks and share them appropriately between the members. It is a fundamental and almost definitive requirement for a payment scheme that it creates a balanced budget in order for all profits to be allocated to the members. This is because, as owners, the members are entitled to that part of the revenues which is not used to satisfy the fixed obligations of other parties. Another aspect which we touch on briefly is, how a payment scheme can be used as an instrument to send signals about market behaviour to competitors. For example, a payment scheme generating over-production signals aggressive market behaviour to competitors. Good cooperation requires that the members feel they are treated equally. We suggest various operational criteria for equality. We describe direct equality which states that all members should receive the same payment and that this should be as much as possible. A reformulation of this leads to maximin equality which indicates that the best payment scheme is the one which treats the members with the lowest profit as well as possible. We also consider adjusted maximin

SUMMARY

Member democracy

Individual incentives

Management control

The core

19

equality which defines the best payment scheme as the one ensuring the greatest profit gain to the member who obtains the lowest profit gain through membership. Treating members equally reduces internal conflicts, and the time and energy wasted hereon, the influence costs. Cooperatives generally use the principle of one-man-one-vote. This means that changes to a payment scheme can only be adopted if it is advantageous to more than half the members. On this basis we describe the median equality which prescribes that the profit level, which half the members are above and half below, must be as high as possible. To actually implement a coordinated efficient production, processing and marketing effort within the decentralized framework of a cooperative we need incentives. Primarily, the payment should be individually rational for the members. This means that they should not be better off leaving the cooperative. Secondly, no member should be able to gain by deviating from the efficient plan. This requirement is called incentive compatibility. A general conclusion from the economic literature is that no payment scheme can fulfil the requirements for efficiency, a balanced budget and incentive compatibility in all situations. This illustrates the conflicts among the criteria and the need to make trade-offs in general. Another finding is that it is possible to design payment schemes which fulfil these requirements under certain production and market conditions. However, this in turn implies that it can be necessary to adjust the payment scheme when conditions change. In order to ensure the efficiency of the cooperative, the management must pursue the members' interests rather than its own. It is therefore necessary to develop methods for monitoring management or to ensure that management is rewarded in such a way that the aims of the members and those of the management coincide. In order to secure cooperation, it must be beneficial for all groups of members to cooperate. In other words, no group of members should be able to benefit by leaving the cooperation. This generalises the individual rationality constraint. A group of members must obtain a profit which at least corresponds to what the group could obtain outside the cooperative, called the stand-alone profit. Also, a group of producers should not be able to obtain a profit which exceeds that group's contribution to the profit of the cooperative, in other words the amount by which the profit of the cooperative would fall if the group left the cooperative. This is the group's incremental profit. If the payment to a group exceeds its incremental profit, this means that the group is subsidised by the other members of the cooperative. Between these limits (the stand-alone profits and incremental profits), we find

20

Consistency

Additivity

Monotonicity

Investments

PETER BOGETOFT AND HENRIK B. OLESEN

the so-called core. The core is the set of profit allocations enabling viable cooperation. There are allocations in the core as long as there are positive synergies from the cooperation. Consistency in a payment scheme can reduce internal conflicts. A payment scheme is consistent if payment is the same regardless of whether the profit is allocated to each producer group simultaneously, or whether distribution is made between ordinary producers and special producers first, and then among the special producers themselves. Consistency means that the order in which allocations are made, does not give rise to conflict. This in turn can facilitate profitable extensions and mergers of cooperatives. Conflicts over accounting principles can be reduced if the payment system is additive. This means that the profit allocation will be the same, regardless of whether the payment scheme is used to distribute all the resulting profit in one step, or whether the payment scheme allocate incomes and costs separately. It is also important to consider how the payment scheme will operate in a dynamic perspective. A good system will promote sensible production decisions, even under changed market conditions, etc. A good system also promotes appropriate investments both in primary production and in processing To discuss what can prompt members to take sensible individual and collective decisions for the future, we introduce different concepts of monotonicity. The weakest form of monotonicity is total monotonicity. The requirement here is that, all things being equal, an increase in the cooperative's total profits will not result in lower profit to any producer group. For example, this means that no producer group may lose from cost savings in the cooperative. We also define the stronger requirements of coalition monotonicity, which require that payment to a producer group will not fall if the stand-alone profit increases in all the coalitions which the group could belong to. If, for example, the organic products become more profitable, regardless of which coalitions the organic producers take part in, then the payments to organic producers may not fall. We define a number of criteria relating to investment incentives. We analyse how the motivation to invest is affected, if the basis for calculating payment depends on the extent of a producer's investment. We also discuss how the hold-up problem can reduce investments. The hold-up problem arises when one party has carried out specific investments and is vulnerable in subsequent negotiations, because the other party can threaten to terminate cooperation. We also deal with the

SUMMARY

21

horizon problem, where members have no incentive to invest in the cooperative if the return on the investment will not be realised till after they have ceased to be members. Finally we illustrate the free-rider problem, which arises when some producers can benefit from investments which they have not contributed to. Hold-up problems, horizon problems and free ride problems tend to undermine the incentives to invest.

1.5 Payment schemes

Proportional payment

The quantity control problem and possible solutions

We analyse a large number of payment schemes which each satisfy some but not all of these criteria. Here we give a brief summary of the most important properties of these payment schemes. Cooperatives have traditionally allocated revenues in proportion to the members' deliveries. This means that the deliveries are paid at a unit price equal to the cooperative's average revenue. The proportional payment scheme has a number of attractive properties. When the average revenue is constant, the scheme leads to optimal decisionmaking. In fact it has been shown that in certain situations the proportional payment scheme is the only scheme which leads to optimal decision-making. The payment system is also consistent, additive as well as coalition and total monotonic. We show that the proportional payment scheme is the only scheme in which members do not have an incentive to make side deals with each other before delivering their production to the cooperative. Finally, only the proportional payment scheme is independent of the farm structure ensuring the same payment to producers with the same production. Unfortunately, the proportional payment scheme often sends the wrong signals to members about revenues. In order to promote production levels which maximise the integrated profit, the payment price should reflect the cooperative's marginal revenue. In most cases the cooperative's average revenue will exceed the marginal revenue. Members will therefore over-produce. This is the quantity control problem. We illustrate the quantity control problem by comparing with the production decisions a disinterested wise chairman (central planner) with perfect information would make on behalf of the members. The wise chairman's decisions provide an upper limit benchmark of what can be achieved through a payment scheme.

22

Reduction in revenue

Transfer of surplus

Production rights

Marginal pricing

AumannShapley

The serial principle

PETER BOGETOFT AND HENRIK B. OLESEN

We analyse different possibilities for solving the quantity control problem within the proportional payment system. One possibility is for the management to make a significant reduction in the cooperative's revenues if production exceeds the optimal level, so that the average revenue falls sharply. If the fall is sufficiently large, it has a disciplinary effect on the members so they will not want to produce more than is optimal for the cooperative as a whole. As a consequence, it can be best for the cooperative to have a production capacity of such a size that over-production would lead to high losses, for example because of the need to pay overtime. The quantity control problem is especially noticeable for a special production sold on a “thin” market, where increased supply reduces the price. In order to solve the quantity control problem with special pigs, Danish cooperative slaughterhouses today control production quantities through contracts. However, a surplus arises from the special production which must be allocated. This surplus is typically allocated to all members of the cooperative slaughterhouse. This increases the payment made to the traditional producers, leading to an overproduction of standard pigs. When allocation is based on turnover, it is not possible to transfer surpluses to other branches of production without loss of efficiency. In New Generation Cooperatives, the quantity control problem is typically solved through tradable production rights. The free sale and purchase of trading rights ensures that production is carried out as cheaply as possible. The members have an immediate incentive to produce the optimal quantities if the marginal revenue is used as the basis for the price paid to members. Unfortunately, with marginal pricing a surplus is usually accumulated in the cooperative. The allocation of this surplus frequently distorts production decisions. However, the surplus from marginal pricing does not affect incentives if it is allocated according to a fixed weighting. This means that it is possible to achieve the wise chairman's solution. It is natural to use the average marginal revenue, called the Aumann-Shapley price, as the price for avoiding the problem of an unallocated surplus. However, we show that this method is equivalent to using the traditional proportional payment scheme. Thus the Aumann-Shapley price does not result in any improvement in the revenue signals to the members. We also briefly discuss the serial pricing principle. The serial principle is based on two fundamental ideas. First, producers with the same production should be paid the same. Secondly, payment to one

SUMMARY

Multiple products

Equal gross margins

Equal return on capital

Quota and premium products

23

producer must not depend on the production level of other producers with larger production. Thus, a producer must not be penalised because a larger producer over-produces. The payment schemes referred to so far are aimed at cooperatives with a single product line – or alternatively, they are aimed at the allocation of profit within a group of members producing the same type of product. In addition, we consider a series of six payment schemes for the allocation among producer groups within multi-product cooperatives. For approximately the last 100 years, all Danish cooperative slaughterhouses have used the same payment scheme, the National Pricing System.. One of the rules of the National Pricing System was that special pigs could only receive additional payment corresponding to the additional production costs. In other words, the payment was based on the principle that the gross margin should be the same for all types of product. This payment scheme has only a modest need for information, which is one of the great strengths of the scheme. Moreover the scheme generates good risk sharing. On the other hand, the system does not ensure that cooperation is always beneficial, since the payment is not always in the core. Finally, the principle of uniform gross margins contributes to a number of production inefficiencies. In contracts between producers of piglets and pig finishers it is common to use estimated prices. The idea is that the return on capital is the same in both production of piglets and pig finishing. The payment scheme has a relatively limited need for information. The scheme has the same weaknesses with regard to efficiency as the National Pricing System. The payment scheme for piglets does not always lead to a payment in the core. Another disadvantage with this scheme is that the risk is disproportionately borne by the producer group which has the greater capital investment, and is thus most vulnerable to variations of income. None of the criteria we analyse suggests that the payment scheme for piglets is preferable to the National Pricing System. We set out and analyse a payment scheme which combines marginal pricing with tradable rights for premium pigs. In this payment scheme which we call the premium pig scheme, all pigs are paid according to the cooperative's marginal revenue. This creates a surplus which is allocated as a supplement to the so-called premium pigs. These are that portion of the pigs delivered which have premium pig rights. The individual producer is free to choose his production level, but he receives only the basic price for the pigs for which he does not have premium pig rights. Premium pig rights can be traded between producers in accordance with rules laid down, and this counteracts

24

ACA (Alternate Cost Avoidance)

Nucleolus

Shapley

PETER BOGETOFT AND HENRIK B. OLESEN

internal conflicts of interest between the members. This payment scheme is, to some extent, based on the ideas of the Californian milk quota system. This payment scheme does not ensure that the payment is always in the core, and it requires more information than the National Pricing System. Risk sharing is also weaker than in the National Pricing System. On the other hand, the payment scheme ensures efficiency and it solves the horizon problem, in contrast to the other payment schemes. In other words, the payment scheme bestows good incentives for investment. In discussions in the pig industry, some argue that special producers should be paid according to the revenue which they generate for the cooperative, in other words according to their incremental revenue. If all groups of producers were paid according to their incremental revenue, there would be a deficit in the cooperative. Therefore, a supplementary rule is needed. According to the ACA method, the deficit is apportioned according to each participant's contribution to the gains of the cooperative. The ACA method requires a lot of information, so it is difficult to apply in practice. The ACA method does not always lead to a solution in the core, since coalitions of producer groups (for example organic producers together with producers of UK pigs) can have an incentive to leave the cooperative. However, it is never advantageous for a single producer group to leave the cooperation unilaterally. This payment system generates reasonable efficiency. The only payment scheme we analyse which always leads to a solution in the core is the nucleolus. This payment scheme is based on adjusted maximin equality which requires that the coalition that gains the least from the cooperation should gain as much as possible. In other words, the payment scheme leads to a payment in the centre of the core. The disadvantages of the nucleolus are that the system requires large amounts of information, and generates a great deal of inefficiency. The Shapley value is a theoretically based payment scheme. In this scheme the payment to a producer group is determined according to the group's expected incremental revenues. The system requires a large amount of information, so practical implantation is very difficult. Shapley value is not always in the core, so coalitions of producer groups can have an incentive to leave the cooperative. However, it will never be advantageous for an individual producer group to stand alone outside the cooperative. The payment scheme leads to reasonable efficiency, but gives a poor distribution of risks.

SUMMARY

25

1.6 Multiple-criteria evaluation As explained, in this book we evaluate different payment schemes on the basis of a number of criteria. An example of some of these evaluations is given in Table 1.1 below. System

National Pricing

Piglets

Criteria

Premium Pigs

ACA

Nucle-

Shap-

olus

ley

Efficiency

**

**

***

**

*

**

Core

*

*

**

**

***

**

Info. Need

***

***

**

*

*

*

Total Mono.

**

**

**

*

**

***

Coalition Mono.

**

**

**

*

*

***

Investment

**

**

**

**

**

**

Risk

***

**

*

**

**

*

Table 1.1 Multiple criteria evaluation of six payment schemes

The premium pig system or the National Pricing System

In the table, six payment schemes are evaluated against seven criteria. The stars indicate how well the schemes perform. The more stars, the better the criterion is satisfied. In practice, the most important criteria in any given cooperative are presumably the need for information, efficiency and the core. Therefore, these criteria should be given special weight when choosing a payment scheme. Our analysis of payment schemes for cooperatives with more than one product type leaves three payment systems which do not have insurmountable information needs, and these are the National Pricing System, the payment scheme for piglets and the premium pig scheme, cf. Table 1.1. However, we can disregard the payment scheme for piglets as it is bettered, if only slightly, in all criteria by the National Pricing System. This leaves two relevant alternatives: the National Pricing System and the premium pig scheme. The specific circumstances of a cooperative will determine which of the two payment schemes should be preferred.

1.7 Conclusion We establish an analytical framework which decision makers in cooperatives can use for evaluating how well alternative payment schemes satisfy the aims of the members.

26

Overall welfare

Coordination

Motivation Dynamic adjustment

Payment schemes Compromise

PETER BOGETOFT AND HENRIK B. OLESEN

The overriding goal of a cooperative is to secure the highest possible economic welfare for its members. We have divided this goal into a number of sub-goals. Using these, a number of operational criteria which a payment scheme should satisfy are formulated. One sub-goal is that the payment scheme should coordinate the activities of the members so that the right goods are produced at the right time and place. The system ought also to reduce risks for individual members and have a minimum information need. A second sub-goal for a payment scheme is that it should provide the necessary motivation in order for members to have a personal interest in carrying out the activities which optimally benefit the cooperative. This means, among other things, that all producer groups must gain from participating in the cooperative. A third sub-goal for a payment scheme is that it should be able to operate in a dynamic perspective. The payment scheme should induce appropriate investments, by the primary producers as well as by the cooperative. The payment scheme should also allow reasonable adjustments when production or market conditions change. We analyse a number of payment schemes which each satisfy certain criteria. We consider schemes for both single product and multiproduct cooperatives. No scheme dominates the others in all criteria and in all situations. In fact, it is in general impossible to satisfy all the requirements simultaneously. Therefore it is necessary to make trade-offs between them, when designing a payment scheme. The goal must be to be aware of and explicit about the pros and cons of different schemes and about the trade-offs involved in choosing a specific scheme.

Notes 1

See e.g. Bogetoft, “Afregning for økologisk mælk - en model til efterfølgelse?”, 1997, for an analysis of some of the consideration which can lie behind an actual payment scheme. 2 See e.g. Jyllandsposten, 19th August 1997, Andelsbladet, no. 18, 1997. 3 See e.g. Andelsbladet, no. 18, 1997, Andelsbladet, no. 19, 1997, Jyllandsposten, 2nd December 1998. 4 See e.g. Jyllandsposten, 19th August 1997, Andelsbladet, no. 18, 1997, Jyllandsposten 1st December 1998.

2

Cooperatives This chapter gives a general introduction to cooperatives. We identify and discuss some of the key features distinguishing cooperatives from investor owned firms. The aim is to provide a balanced background to the more focused analysis of alternative payment schemes in the following chapters.

2.1 What is a cooperative

Three perspectives

Pragmatic definition

Law firms, electricity companies, etc.

Consumer and labour coops

Cooperatives come in many forms both nationally and internationally. It is not easy to give a universal definition of cooperatives. However, traditional cooperatives have been constructed around some more or less similar principles. Below we identify the central cooperative principles from three perspectives: a practical perspective, an official perspective, and a theoretical perspective. A practical perspective A pragmatic definition of a cooperative is: a firm that is owned and controlled by its users (instead of being owned and controlled by investors). This simple definition captures the central aspects of cooperatives. From a pragmatic perspective, the interesting thing is how an organization works – not the legal form it takes. Many different types of firms have more in common with cooperatives than with investor owned firms, regardless of their legal form. This is for example the case with: a group of consultants or lawyers sharing offices, secretarial assistance and clients, a group of citizens setting up a joint water-supply, or households in a region owning and operating a common electricity grid. We shall usually take examples from the agricultural sectors. However, the underlying problems, and several of the principles of cooperatives, are the same in many other organizations. For example, our analysis is relevant to worker-owned firms even though they may be organized as limited companies. Cooperatives can be owned by different types of user groups, for example, the consumers, the suppliers, or the workers. In consumer

28

Marketing cooperatives

Cooperative principles

PETER BOGETOFT AND HENRIK B. OLESEN

cooperatives a group of agents cooperate to acquire goods, production factors or other inputs. Another type of cooperative are labour cooperatives In this book, we concentrate on situations where a number of suppliers seek to promote the processing and marketing of their products in co-operation. In such a case the suppliers are called the members and the firm is called a producer or marketing cooperative. The specific case could be a group of pig producers joining forces to build and operate a slaughterhouse. An official perspective The ICA (International Cooperative Alliance) is a world-wide umbrella organization for cooperatives. The ICA revises the principles of cooperatives over time. However, from an economic point of view the most important principles are still 1. Membership: voluntary and open to all who have an obvious interest in the activities of the cooperative. 2. Decision-making rights: democratic member control, on the principle of one-man-one-vote. 3. Capital: the members' equity capital (the common assets) gives no return, or at least only a minimal return. The members are jointly liable for the debts of the cooperative, often with limited liability. 4. Earnings: allocated to the members according to their – physical or monetary – turnover with the cooperative.

Bylaws

A clarifying comment is relevant about the capital returns. A cooperative's equity capital can be divided into two types. One type is the non-allocated equity capital (common assets). The other type is equity capital which is allocated to so-called personal accounts inside the cooperative. Most cooperatives have personal accounts to a greater or lesser extent. Some cooperatives pay interest on the personal accounts, but interest is never paid on the non-allocated common assets. The rate of interest paid on personal accounts varies. In some cooperatives there is no interest paid, while in others there are provisions that the interest shall fulfil. One possibility is to require it to correspond to a welldefined bank rate.1 Apart from the four general principles above, most cooperatives have a number of bylaws with a decisive influence on the activities of the business and with more or less direct linkage to the above principles. Two common provisions are

COOPERATIVES

29

5. The right to supply: members are entitled to supply all of their production to the cooperative. 6. The obligation to supply: members are obliged to supply all of their production to the cooperative. In addition to these more formal provisions, most cooperatives are based on a generally accepted principle of 7. Equality: members shall be treated equally. Equality reduce transaction costs

Social capital

Allocation of residual earnings

The exact meaning of the equality principle varies over time as well as from cooperative to cooperative. We shall discuss several possible formalizations in Chapter 3. The equality principle plays a significant role in many cooperatives – both in day to day operations and in relationship with strategic decisions. The principle is important because it guides and facilitates negotiation about supply conditions etc. Fewer resources are needed and transaction costs are lower if individual members do not expect special terms. Later in the book we return to the importance of limiting the so-called influence costs, i.e. the costs of having individual producers or producer groups that seek to influence decisions in their own favour. A generally accepted idea of equality may limit these costs. Another way to appreciate the principle of equity is to look at it as part of the capital of the cooperative. While human capital is vested in the skills of the individuals, social capital rests in the relationship among the individual members. It represents a genuine although intangible economic value to have generally accepted values and a common code of conduct. A theoretical perspective In general, the cooperative principles are formulated as relatively specific and practical rules. Part of the challenge we face here and in the rest of the book is to link these rules with more fundamental economic considerations, for example the ability to coordinate and motive appropriate behaviour. From a micro-economic point of view the allocation of decision rights and residual earnings are probably the most important characteristics of a cooperative. In a marketing cooperative the right to make decisions and the right to the residual earnings belong to the suppliers. In an investor owned firm these rights belong to the providers of capital. 'Residual earnings' is that part of the earnings which remain after all the “external” obligations have been met.

30

Allocation of decision rights

PETER BOGETOFT AND HENRIK B. OLESEN

In a cooperative the individual members retain a relatively high degree of autonomy in the sense that important decisions, e.g. on production levels, are decentralized among the individual members. From an industrial organization point of view it can be said that marketing cooperatives are based on vertical integration and horizontal coordination. There is vertical integration because the members expand their activities so as to include processing and marketing. There is horizontal coordination because the members make collective decisions to coordinate the use of their primary products.2 By acting together horizontally, a group of producers can obtain good terms for its members when negotiating with the processing and marketing stages of the process. The horizontal coordination is very important. If there is sufficient competition in processing and marketing, many of the economic arguments for vertical integration disappear. In particular, the threat of a powerful processing stage exploiting the small individual producers may be overcome via horizontal coordination. The horizontal coordination of agricultural marketing cooperatives is allowed in many countries – even though it, in principle, undermines competition and hence could be considered illegal according to anti-trust laws. Part of the reason for this is probably that the purpose of the coordination has been to ensure a sufficient economic surplus for small and otherwise vulnerable producers. Although competition for primary products in general is attractive for the producers and may reduce the need for horizontal coordination and vertical integration, competition does not solve all problems. Recent advances in industrial economics suggest for example that too harsh competition for the primary products may be disadvantageous for the primary producers in cases of asymmetric information and quality differentials3.

2.2 Traditional cooperatives Changing principles

The cooperative principles are not static, and have always been variable in response to new challenges. However, most mainstream cooperatives have used a number of principles consistently through many decades. We refer to these cooperatives as traditional cooperatives. Traditional cooperatives use the official principles mentioned above, i.e. open membership, democratic voting, common equity capital, and payment proportional to turnover, delivery right, delivery obligation, and equality.

COOPERATIVES

Rationales for proportional payment rule

Equality and structure

Side trading

31

In this section, we focus on the proportional payment rule in cooperatives with just one product, e.g. pigs. In this setting allocating the income in proportion to the turnover is the same as using a single price per unit (linear pricing) to compensate the members for their deliveries. Here, as a foretaste of the use of the general theory of cost and profit allocation, we give two possible rationales for the traditional payment scheme where the earnings are allocated in proportion to the members' physical turnover with the cooperative. The idea is that the proportional payment scheme is the only scheme that has certain very reasonable properties. One reasonable requirement is that producers who produce the same quantities should be paid the sameM. (The symbol M is used to indicate that this part of the text is dealt with in greater details in the following mathematical section). Another reasonable requirement is that payment to one producer should not depend on whether another farm is divided into two smaller farms with the same total productionM. An alternative interpretation of the latter requirement is that it should not be advantageous for any member either to sub-divide his production into smaller units, or to gather his production into larger units. That is, it should not pay for a producer with one farm to formally split them in two or vice versa. The payment should not depend on the farm structure. A simple result from the axiomatic theory of cost and profit allocation shows that an allocation rule fulfils these two requirements if, and only if, it is the proportional ruleM. This provides a rationale for the traditional method of allocating earnings in a cooperative. A third – but obviously related – requirement is that there should be no advantage to members from striking deals between each other before they deliver their production to the cooperative. A fourth natural requirement is that the cooperative should not make payment to members who do not deliver any products. Now, it can be shown that only the proportional allocation rule combine the equality (same-production-same-payment) principle with the no-side-deals and the no-production-no-payment requirementsM. Mathematical representation Each of n producers produces q j output units, j=1,..,n,. The total production is Q q1  q 2  ...  q n , and the net earnings of the cooperative is R(Q) . We assume that R (Q) is increasing. We must find an allocation x1 ,..., x n of the earnings such that 1 2 n x  x  ...  x RQ .

32

PETER BOGETOFT AND HENRIK B. OLESEN

The first requirement, that two members who produce the same quantity shall receive the same income, can now be formulated as follows Axiom 2.1 If q j

q k then x j

x k for all j,k

The second requirement, that payment shall be independent of the farm structure, can be formulated as follows Axiom 2.2 Let x1,..., x n be the allocation that occurs in the current k 1 k1 k2 k 1 n situation, and let x1new ,.., xnew , xnew , xnew , xnew ,.., xnew be the allocation that occurs in a situation where farm k is split in two, k1 and k2, with productions q k1 and q k 2 so that q k1  q k 2 q k . Then x nyj x j for all jzk. These axioms are fulfilled if and only if the proportional allocation rule is used. This is formally expressed as Proposition 2.1 An allocation rule fulfils Axioms 2.1 and 2.2 if and only if qj R(Q) Q

xj

i.e. if and only if the profit is allocated in proportion to the production quantities, as in a traditional cooperative. (Banker, 1981). Hereby, Proposition 2.1 gives a possible rationale for the proportional distribution rule. Alternatively, the proportional distribution rule can be rationalized by using the argument that side trading must not be beneficial. That is, producer j and producer k should not be able to gain by doing a deal with each other, before delivering to the cooperative. This can be expressed as follows Axiom 2.3 If x1 ,..., x n is the distribution corresponding to productions n q 1 ,..., q n , and x1new ,..., xnew is the distribution corresponding to 1 j 1 j production q ,..q , q  ',q j 1,.., q k 1 , q k  ', q k 1 ,., q n , then j k xnew  xnew

x j  xk

Another entirely reasonable requirement seems to be that members who have made no deliveries should not receive any payment. This can be formalized as follows Axiom 2.4 If q j

0 then x j

0

COOPERATIVES

33

We can now formalize the second rationale for the proportional allocation rule Proposition 2.2 An allocation rule fulfils Axioms 2.1, 2.3 and 2.4 if and only if xj

qj R(Q) Q

i.e. if and only if the profit is allocated in proportion to the production quantities, as in a traditional cooperative (Bogetoft and Olesen, 1999). Equality between product lines

Above, we have assumed that any surplus is allocated according to turnover. However, this presupposes that the members have comparable types of products and therefore, strictly speaking, it gives no specific indications about the allocation across different product types, including quality levels. The general approach in such situations seems to be that 'members should be treated equally'. One implementation of this idea is that 'price differences may only correspond to objective cost differences4. There are many other possibilities, however. Such allocation issues and several possible solutions occupy a central position in this book and they are subject to detailed discussion in Chapter 6.

2.3 New Generation Cooperatives (NGCs) During the 1990s a number of new cooperatives appeared in the USA. They were sufficiently different from traditional cooperatives to be labelled New Generation Cooperatives (NGCs)5. NGCs have primarily been introduced in order to avoid some of the problems of traditional cooperatives relating to niche and specialized production. Among other things this concerns the problems of controlling quantities when there is a free supply right, and the problems of obtaining sufficient capital investment when equity capital does not give returns. The elements which make up the New Generation Cooperatives are not in themselves new. What is new is the combination of elements and the relatively large number of cooperatives which share these characteristics. NGCs are – in particular - distinguished from traditional cooperatives by having: x Closed membership x Tradable production rights

34

Closed membership

Tradable production rights

From traditional cooperative to NGC

PETER BOGETOFT AND HENRIK B. OLESEN

When a cooperative can exclude producers from becoming members, the cooperative can use any knowledge it may have about potential new members, say about their talents or business strategies. This may be advantageous for the incumbent members as they can better protect their initial investment. The primary effect of the closed membership, however, goes hand in hand with the ability to limit total production. To ensure efficiency in processing and sales, a cooperative may want to limit total production6. Moreover, to ensure that the individual farms can be run at an efficient level – with limitations in total production – it may be important to control the number of producers. It typically requires quite a large capital contribution to become a member of a NGC. New production rights can be bought when the cooperative is starting up, or when there is an expansion of its capacity. Production rights give a right to supply as well as an obligation to supply. Members can only supply in accordance with their production rights, and the cooperative can buy production from a third party at the member's expense if a member cannot fulfil his production obligations. Production rights are tradable, and the price will reflect the expected value to future producers. Good decisions will make future membership more attractive leading to an increase in the value of production rights. Likewise, bad decisions will lead to falling prices. This allows incumbent members to profit from the gains they create for future members, and it forces the existing members to cover the losses they may impose on future members. In this way, the interests of present and of future members are aligned via the market for production rights (in the same way as stock prices align the interests of present and future stock holders). This improves the incentives for investments and for long term decision making in a NGC. Most NGCs were created like NGCs, but more and more traditional cooperatives consider the possibilities of introducing some of the NGC elements. The introduction of such elements can be driven by more heterogeneous members and by the need to make large new investments in a cooperative. The restructuring of a traditional cooperative by introducing NGC elements is challenging. One challenge is to allocate the common assets amongst the producers. In a start-up NGC, the members buy production rights, but in an established cooperative the members already own the production rights, even though they are held in common. In the transformation process, the production rights must therefore be allocated. Production rights could, for example, be allocated on the basis of previous production quantities, or they could be allocated equally

COOPERATIVES

35

between members. It is obvious that conflicts may arise in this allocation of production rights. From the point of view of economic efficiency, however, the initial allocation is less important. The allocation results in a number of one-off gains to the existing members, but once the rights have been allocated the market enables the rights to be priced and sold, so that they become efficiently allocated in relation to the members' marginal values etc.

2.4 General problems of cooperative ownership

Multiple criteria evaluation

Criticism of checklists

From an economic point of view, cooperative ownership has a number of more or less attractive characteristics. We set out below the general economic problems emphasized in the more recent literature on the economics of cooperatives. In Section 2.6 we provide a brief overview of different branches of the literature on cooperatives. We also assess the extent of these problems in a traditional cooperative, in a NGC and in cases where processing and marketing is done by an investor owned firm. We review the general problems for two reasons. First, the review gives a good understanding of the special nature of cooperative ownership. Secondly, the listing, with its evaluation of the different forms of ownership, illustrates a method of multiple criteria evaluation which we use throughout the book. As any payment scheme, every form of ownership has a number of consequences which can be more or less important, depending on the circumstances. It can be helpful to bear in mind this multiplicity of consequences, both for practical and theoretical purposes. When specific payment schemes are discussed in the literature, and in the following chapters, the focus is often on solving a single problem, or at most just a few problems. However, there is a risk of creating other problems outside the frame of the analysis. To avoid this, it is useful to have a checklist to remind one about other central economic issues which may also be affected. The examples in this section give such an initial checklist of the most significant economic problems. Our initial list of possible problems is based on what has been found in the literature. The problems thus have a solid theoretical basis, and they can be modelled relatively easily. However, the initial list does not necessarily give a comprehensive description of all problems - or all relevant criteria for evaluating changes in a cooperative. In Chapter 5, a more comprehensive list is given, together with a hierarchical method for mapping the various considerations.

36

Underinvestment due to a weak negotiating position

PETER BOGETOFT AND HENRIK B. OLESEN

The Hold-up problem The hold-up problem7 arises when the value of a producer's production or investment is much greater when trading with one particular purchaser than with alternative purchasers. Once the production or investment has been carried out, the purchaser can exploit his special position by demanding a large share of the gains as the price for continuing to trade. This means that the producer may end up bearing all the costs of production or investment without receiving a sufficient share of the gains. The fear of this leads to under-production or under-investment. That is, the producer does not produce or invest enough to begin with. It is worthwhile emphasizing that it is the very fear a subsequent hold up that leads to the reduced production and investment. This means that hold-up problems may exist even though we do not observe a processor exploiting his market position. Cooperatives solve the hold-up problem through the principles of production rights and profit sharing. These principles give producers a guarantee that they can sell their production. Moreover, the principles ensure that the producer retains all his gains if he reduces his costs. The member of a cooperative does not have to make a deal with a purchaser (for example, a privately owned meat processor or a dairy), who can have a strong bargaining position because of transport costs and because the products are perishable. Thus cooperative ownership often promotes reasonable production and investment decisions by individual members. Avoiding under-investment etc. as a result of the hold-up threat is one of the classic economic rationales for the traditional cooperative. However, hold-ups cannot be avoided in NGCs if the market for production rights is small or if it is not working well. For example, the seller of production rights can hold-up a purchaser who may have created attractive possibilities for expansion. Likewise, hold-up problems can potentially occur in traditional cooperatives with different producer groups. To accept the marketing of organic milk in a dairy cooperative the producers of conventional milk could for example holdup producers of organic milk by demanding an unreasonable share of the extra earnings from the organic milk production. Example Graversen (1999) analyses the organization of slaughter pig production by means of the so-called multi-site concept, in which production is broken down into three steps: piglet production, fattening from 7 to 30 kg, and fattening up to the slaughter weight. In order to reduce the risk of infection, it is important that all piglets in a piggery building are delivered from the same herd. If a piglet producer

COOPERATIVES

37

terminates a supply arrangement, this will lead to an increased risk of infection for the producer of slaughter pigs, because he will have to introduce new infections into his piggery. This gives the piglet producer a stronger negotiating position which can potentially be used to obtain better sales terms by holdingup the slaughter pig producer. In term, one may fear under investments in the fattening stage.

Negative spillover effects from increased production

Underinvestment because some members 'hitch a ride'

The quantity control problem The quantity control problem8 refers to the fact that the total production quantity is not necessarily optimal. Problems of over-production typically occur in cooperatives selling in a 'thin' market, where increased production leads to lower prices. Also, over-production may occur when there is decreasing returns to scale in processing9, such that extra units are processed at higher costs. The proportional allocation rule and the free right to supply, means that a producer will not himself bear all the costs of increased production. If a producer increases his supplies to the cooperative, this will reduce average earnings via a price fall in the market for final goods or a cost increase in processing. However, the producer in question only bears part of this fall in average earnings. The reduced average earning also affects the other members. The result of “forgetting” the negative spill-over effect is over-production. Everyone could be better-off if production were reduced. NGCs solve this problem by operating with limited production rights and contract production. However, there are other possible ways to give the individual producer incentives to make better production decisions, for example marginal price payments, which we return to in Chapter 4. Free-rider problem The free-rider problem refers in general to the ability of some agents to freely use a 'common good' created by others. Ultimately this means that there is too low production of the 'common good' because those who produce it pay all the costs but do not reap all the benefits (in the same way as with the hold-up problem). In the literature on the economics of cooperatives10 the free-rider problem usually refers to the fact that by investing in processing and marketing, existing members create future earnings potential. Because of the policy of open membership, new members can reap benefits from these investments without paying for them. The problem is reduced in NGCs because the production rights can rise or fall in value, depending on the values created. This means that new members pay for the values which existing members have created as we discussed above. In this way

38

PETER BOGETOFT AND HENRIK B. OLESEN

the existing members can benefit from what they create and they thus have the right incentives to make improvements. The free-rider problem not only occurs in relation to new members. For example, less committed members can benefit from a reputation for quality which especially skilled farmers may create for the cooperative. Similarly, non-members may benefit from investments made by the cooperative, e.g. a large promotion campaign for organic products. Example In the pig industry, the free-rider problem can occur when pioneers for organic products invest in building up the market for organic products. Once the market for organic products has been established, new members can join the organic producers, and enjoy the fruits of the investments made by the pioneers.

Underinvestment due to shortterm decisionmaking

The horizon problem In the literature on the economics of cooperatives11 the horizon problem refers to the fact that investments in processing and marketing often have effects which extend beyond the current members' time as members. The problem exists, at least theoretically, even in connection with short term investments because existing members are never certain that they will be active members in the ensuing period. Since the capital in a cooperative gets no direct return or only a very limited return, existing members do not benefit fully from current investments. They will therefore underinvest or use a large amount of debt in order to transfer the costs to others. The horizon problem is often blamed for being the major cause of insufficient investments in cooperatives. The problem can be reduced by personal accounts because they introduce a clearer allocation of the members' equity capital. This is less of a problem in NGCs where the value of production rights reflects the net present value of all future expectations. Because of the horizon problem one would expect that younger members are more willing to invest in a cooperative than older members. However, discussions in cooperatives often give a different picture. Older members sometimes appear more willing to invest in cooperatives than younger members12. This could mean that members have other considerations than their narrow personal economic interests. Another possible explanation is that positive prospects for cooperatives will be reflected in higher property prices. In turn, this may allow even older members to benefit from future increases in the earnings of cooperatives. Although personal accounts in theory should reduce the horizon problem and hereby facilitate sufficient capital accumulation, the

COOPERATIVES

39

practice of cooperatives is less clear cut. In the Danish pig industry, for example, Tican (Andelsslagteriet Tican a cooperative slaughterhouse) has relatively more equity capital than Danish Crown even though Tican does not use personal accounts13 as Danish Crown does.

Does the management pursue members’ goals?

Hard to motivate the management of a coop?

Active board

Control and motivation problems Control and motivation problems arise in decentralized organizations in general when it is not possible to perfectly monitor individual agents. The lack of monitoring makes it difficult to ensure that all agents behave appropriately in all circumstances – and possibly at the expense of their own direct interests. In the literature on cooperatives14, the control and motivation problem usually refers to the problem of ensuring that the professional management of the cooperative does in fact adhere to the goals set by the members. It is widely held that incentives for the management are stronger in investor owned firms than in cooperatives. In traditional investor owned companies, e.g. limited companies, the stock market can be a useful tool for motivating the management. Firstly, a fall in the value of the shares can alert the owners to the fact that the management is not effective. Secondly, it is generally believed that the risk of a hostile take-over motivates the management15. The idea is that speculators have an incentive to buy up a firm in order to replace the management, if an analysis of the firm indicates that it is not managed sub-optimally. Thirdly, in recent years it has become widespread practice to reward the management in part with stock options. In this way the management has a common interest with the stockholders. These motivational tools do not exist in cooperatives and it may therefore appear to be more difficult to motivate the management of cooperatives. Also, the goals of a cooperative are more diffuse because, as distinct from an investor owned firm, a cooperative does not have the simple goal of profit maximization. This means that the results achieved by the management are more difficult to measure in a cooperative. In Chapter 3 we will look at the issue of setting the goals for a cooperative in greater detail. In spite of these problems it would probably be wrong to exaggerate the special problems of motivation and control in cooperatives. Some control is possible by simply comparing the producers’ payment in different companies – much like stock prices are compared across limited companies. Besides this, the members of a cooperative have a very strong incentive to take an active interest in the management of the cooperative because their individual economic success is highly dependant on the economic success of the cooperative. The board is very

40

PETER BOGETOFT AND HENRIK B. OLESEN

actively involved in cooperatives. Last but not least, it is possible to motivate managers by imitating the use of stock options and similar financial instruments that have become so popular in investor owned firms. In a cooperative, one can for example make the salary to the cooperative’s managers dependent on the payments made to members. It is usually assumed that control is easier in NGCs, both because they are relatively small, and because it is possible to judge their performance according to the value of the tradable production rights. As regard the motivation and control of individual producers, it can be expected that this is easier in cooperatives and in NGCs than in a traditional investor owned firm. Firstly, the suppliers to cooperatives have not only supplier interests but also processor interests, since they co-own the processing. Secondly, local social pressure can be applied if undesirable behaviour is observed by other members of the same cooperative. Naturally, both effects are most pronounced when the cooperative is small.

Poor risk diversification?

Positive or negative correlation?

The portfolio problem The portfolio problem16 refers to the difficulty that an individual producer has diversifying his investments when his primary capital is tied up in his farm and when furthermore he invests in the processing stage. If there is a positive correlation between returns from primary production and returns from the processing activities then, from a risk perspective, it is inappropriate for the producer to tie up capital in processing activities. However, this is precisely what happens in traditional cooperatives and to an even higher degree in NGCs. In a multi-product cooperative it is easier to diversify as different producer groups can share the risk. Using non-proportional functions for the distribution of surpluses can also reduce the problem of risk. Of course, it is an empirical question whether the correlation between primary production and processing is positive or negative. However, there is a need for caution when this question is assessed. The profits of a cooperative and its members are partly artificial since they both depend on what the members are paid. By varying the payment it is possible to create an artificial negative correlation. Thus, for example, it is not enough to establish that a cooperative meat processor has high profits if the farmers only have low profits. It is more relevant to look at the relationship between profits of an investor owned processor and the profits of farmers. In many cases the correlation is positive due to spillover effects; if the processor earns more money, he will pay more for pigs and vice versa. Likewise, if farmers can produce more they can sell at a lower price to the slaughterhouses, who will, in turn, earn more. In

COOPERATIVES

41

general it is therefore considered to be bad from a risk perspective to integrate into the next level in the production chain. Nevertheless there can still be actual situations which lead to the contrary result. For example it can be advantageous from a portfolio point of view to integrate into an alternative market in order to spread sales through several markets. It has been shown that it is often optimal for a processor with market power to even out the prices for raw materials17. If the raw materials prices are determined on another unrelated market there will be a negative correlation between the profits of the processor and the profits of the producers of the raw materials. For example, this means that a cooperative slaughterhouse can achieve good risk spreading by investing in processing for a particular market segment if the pig price is fixed on the world market for carcasses. On the other hand, the investment gives a bad risk spreading if the pig prices are primarily dependant on the production costs. The example below shows how investment in processing can both increase and decrease risks. Example We consider a cooperative slaughterhouse which has a possibility of investing in processing. The demand for processed pig meat is PPRO

2000 - Q

where Q is the number of pigs processed and PPRO is the resulting prices of processed meat. If we disregard the costs of processing (or assume that PPRO is net of processing costs) the profit from processing is S PRO  PPRO  PPIG ˜ Q 

where PPIG is the price the slaughterhouse has to pay for pigs. Hence, profit equals the price gain from processing multiplied by the quantity. The table below shows the optimal production quantity of processed pigs when the price of pigs is 1000 and 500 respectively. The optimal quantities are found by maximizing the profit above with respect to Q and taking into account how the price on processed meat is affected by the quantity. The table also shows the associated prices for processed meat and the total profits from processing.

42

PETER BOGETOFT AND HENRIK B. OLESEN

Situation

Pig price

A B

1000 500

Price for processed pigs 1500 1250

Optimum no. of pigs

Profit from processing

500

250,000

750

562,500

Table 2.1 Earnings from processing Is the pig price determined … … on the world market …or by the production costs?

The costs of the decisionmaking process

Csts of trying to exert influence

In the table, the profit from processing is highest when the pig price is lowest. There are two possible interpretations of this result, depending on what causes the changes to pig prices. We have intentionally not given the producers' profits in the two situations as there are two possible interpretations. The first interpretation is that the high pig prices are due to conditions in other markets, for example a high price on the world market. In this situation high pig prices are equivalent to high earnings for the producers. In effect, there is a negative correlation between the profits of the producers and the profits of the processors. When the producers have high earnings because of good world market prices, the returns from processing are low, and vice versa. This also means that investment in processing reduces the risks. The other interpretation is that the high pig prices are caused by high costs at the producers. In this situation the profits of the producers are typically low when the pig price is high18. This means that investment in processing gives a poor spread of risk because the producers will take a double hit in years with high costs. Their earnings from their farm will fall and they will earn less from their investment in processing. In this situation, there is a positive correlation between the earnings of the producers and the processing activities respectively. The influence problem Up until now, we have focused on the fact that payment schemes and the organization of decision-making can lead to sub-optimal decisions. However, there are costs associated with the decision-making process itself. In general, every planning and decision-making process has a number of consequences. Decision-making can take time, opportunities can be missed or otherwise be lost, confidential information may be revealed, and so on19. Some of the costs of decision making and planning are of especial interest to cooperatives, namely the so-called influence costs. In cooperatives, the influence problem20 concerns the members' influence on decisions and the costs which result from attempts by

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43

different groups to exert influence over these decisions. Influence costs are usually assessed as being greater in cooperatives than in investor owned firms. This is due to the differing interests of the membership and the absence of means to reconcile these differing interests, for example through profit sharing or personal accounts. These internal conflicts, and thus the influence problem, can be reduced by choosing sensible payment principles. To the extent that a NGC has a smaller and more homogeneous membership, the influence problem is expected to be less in a NGC than in a traditional cooperative. Example The cooperative principles of the right to supply, the duty to supply and the equal treatment of members help to reduce the influence costs. In German slaughterhouses it is normal to have large purchasing departments which are responsible for negotiating the terms of supply with the pig producers. In the Danish cooperative slaughterhouses most of the influence costs associated with negotiating terms of supply with individual members is avoided, because no one expects to obtain special terms21. The above discussion of the various problems and the ways they can be dealt with by different corporate forms can be summarized as in Table 2.2 below. In the table *** indicates that the corporate form has solved the problem in question rather well, ** indicates that the problem has only been partially solved, and * suggests that the problem is largely unsolved. Corporate forms Criteria Hold-up Quantity control Free-rider Horizon problem Control of management Control of members Portfolio Influence

Traditional Cooperative

New Generation Cooperative

Investor Owned

*** * * * **

** *** ** ** **

* *** *** *** ***

**

**

*

** **

* *

*** **

Table 2.2 Evaluating different corporate forms on economic criteria22

44

PETER BOGETOFT AND HENRIK B. OLESEN

For example, we can see that the hold-up problem can be regarded as being practically solved in traditional cooperatives, that it can occur in NGCs, though to a limited extent, and that it can arise as a large problem between an investor owned processor and a producer.

2.5 Coordination and motivation Decentralised knowledge and decision making create problems

General economic problems

Unequal distribution of costs and benefits

All the problems dealt with in the previous section are fundamentally associated with the complications which arise when a group of individuals with partially conflicting interests attempt to pursue their common interests in a setting with decentralized knowledge and decision-making. We have given an introductory description of these complications with the above listing. We have focused partly on the factors which can hinder an ideal solution in which everyone is as well of as possible. We have also discussed how it is possible to approach such an ideal by adjusting the corporate form. The fundamental concepts as well as the problems are formalized in Chapter 3. It is worth noting that achieving a common goal in a system with decentralized knowledge, decentralized decision-making and partly conflicting interests is an entirely normal economic problem not at all peculiar to cooperatives. In fact, it is one of the fundamental problems in any economic system, apart, of course, from trivial systems with only one individual in a kind of 'Robinson Crusoe' world. The overriding problem is to ensure coordination and motivation. Coordination should ensure that the optimal quantities of the right products are produced at the right time and in the right place. Motivation should ensure that the overall coordination is carried out by partially autonomous individuals whose actions cannot be supervised or rewarded down to the smallest detail. There is no ideal solution to the problem. In other words, any system must make a compromise between coordination and motivation. Therefore economic theory is less concerned with finding the ideal solution in absolute terms, and more concerned with finding the least bad system with regard to the actual problems of coordination and motivation. The question is not whether a traditional cooperative, a NGC or an investor owned processing business is the ideal system. The question is rather, taking their failings into account, which system is best? It is also worth noting that at least the first six of the problems referred to above (hold-up, quantity control, free-rider, horizon and control and motivation problems) are all the result of a simple underlying problem. This problem consists in ensuring optimal

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45

behaviour in a partially decentralized organization, when certain decision-makers (members or employees) are not themselves responsible for all the costs or all the benefits resulting from their decisions. If a decision-maker bears all the costs but does not receive all the benefits of an activity, he will not carry it out to a sufficient extent. This is the situation which applies with hold-up, free-rider, horizon and generally also the control problem, which all lead to poor levels of investment, production or effort. If, on the other hand, a decisions-maker does not pay all the costs but has all the advantages of some activity, he will carry out the activity too extensively or too frequently. This is a cause of the quantity control problem where too much is produced because the individual producer 'forgets' the fall in price which he causes for the other producers. Such cases, where someone bears all the costs without obtaining all the advantages or the converse, are in fact the cause of many problems in many different economic systemsM.

46

PETER BOGETOFT AND HENRIK B. OLESEN

Mathematical representation A common mathematical formulation of the underlying problem in cases of hold-up, quantity control, free-riding, horizon problems as well as the problems of control and motivation, can be given as follows e E C (e) B (e)

is the effort of a member, is the organization’s total costs of the effort e, is the organization’s total benefits from the effort e.

In addition, c(e) and b(e) represent the relevant member's personal costs and benefits associated from effort e . We will typically have that B ' ! 0, B '' d 0, C ' ! 0, C '' ! 0, b ' ! 0, b '' d 0, c' ! 0 and c' ' ! 0 . The optimal activity at the level of the organization is now given by max eE B (e)  C (e)

while the optimal activity at the level of the individual is given by max eE b(e)  c(e)

The associated first order conditions are that the organisation's marginal benefits should correspond to the organization’s marginal costs B ' ( e)

C ' (e)

and that correspondingly the individual's marginal benefits should correspond to his marginal costs b ' ( e)

c ' (e)

It is clear that either very special conditions or a very cleverly designed payment system is required to ensure a common solution to these equations. In other words, it cannot be expected that the optimal individual action (corresponding to a solution to the last equation) will simultaneously be an optimal action at the level of the organisation (corresponding to a solution to the first equation). For example, if B ' (e) ! b' (e) but C ' (e) c' (e) , then the individual will choose too low a value for e . This is the typical situation in connection with hold-up, free-rider, horizon and control problems where individual producers carry all the costs, but do not receive all the benefits. On the other hand the individual will choose too high a value for e, if B ' (e)  b' (e) but C ' (e) c' (e) . This is typically the situation connected with the quantity control problem where the private benefit of increased production does not account for the social loss from decreased prices. These two situations are illustrated in Figure 2.1.

COOPERATIVES

47

Marginal costs and benefits

Marginal costs C'

c'

Marginal benefits, organisation B' Marginal benefits, individual b' Action e Underproduction

Marginal costs and benefits

Marginal costs C'

c'

Marginal benefits, individual b' Marginal benefits, organisation B' Action e Overproduction

Figure 2.1 Individual actions in an organisation

2.6 The literature on cooperatives The cooperative organizational form has been studied from many angles using many different approaches, both economic and non-economic. The purpose of this section is to give an introduction to the way economists have thought about cooperatives. We give a brief overview of the economic literature on cooperatives. Our overview is based in part on Staatz (1989) and Cook, Chaddad and Illiopolis (2004).

48

Three categories

Market behaviour of cooperatives Monopoly cooperatives

Competitive yardstick

PETER BOGETOFT AND HENRIK B. OLESEN

Staatz (1989) provides a systematic and comprehensive review of the literature on the economics of cooperatives. Staatz divides the literature into three main categories23: ‘cooperative as a firm’, ‘cooperative as a coalition’, and ‘cooperative as a nexus of contracts’. Cook, Chaddad and Iliopoulos (2004) extends the literature review and cover the period 1990-2000. In the following we describe the three main approaches to the economics of cooperatives. Cooperative as a firm One approach is to look at cooperatives as market players. The main question is how cooperatives behave differently from investor ownedfirms. This branch of literature is also a part of the Industrial Organization literature on competition, antitrust, etc. The early literature on the market behaviour of cooperatives only considered situations where cooperatives were alone on the market, i.e. monopsonies or monopolies; cf. the literature reviews made by LeVay (1983) and Sexton (1984). The central result in this literature was that a monopolistic marketing cooperative lead to the socially first best outcome (much like perfect competition) because the management cannot control the quantities, c.f. Helmberger and Hoos (1962). Viewed from the firm perspective, this outcome is unattractive and a result of the quantity control problem, cf. Section 2.2. However, viewed from a public policy perspective, the quantity control problem is convenient because it means that cooperatives cannot exploit their market power. Therefore, the quantity control problem has been used to justify favourable policies towards cooperatives in antitrust and taxation areas (see for example Helmberger and Hoos (1962) or Tennbakk (1996)). Most of the more recent articles on the market behaviour of cooperatives build on oligopoly models. The central argument in this line of research is based on the ‘competitive yardstick school of thought’ which was first proposed by Nourse (1922), see Torgerson et. al. (1998). The argument is that since cooperatives pay out their profit to the members, other competitors will have to offer their suppliers equally good terms – otherwise their suppliers will join the cooperative instead. Hence, a cooperative with open membership will have a disciplining effect on the other firms in the market. The central idea of a competitive yardstick has been expanded upon in a large number of articles. Sexton (1990) develops a model of spatial competition in agricultural marketing industries, and analyzes how the presence of cooperatives alters the market equilibrium. Sextons shows that the competitive yardstick effect depends on the membership policy

COOPERATIVES

Aggressive market behaviour

Lower welfare with price discriminating coops

Focus on member heterogeneity

Cooperative game theory

49

and the pricing policy. Cooperatives with open membership are more pro-competitive than cooperatives with restricted membership. Albaek and Schultz (1998) analyze a dynamic Cournot model of the competition between an investor owned firm and a cooperative. The basic idea is that the quantity control problem in cooperatives serves as a commitment to an aggressive market strategy, which in a Cournot model will force the competitor to reduce his production level. The model offers an explanation for why the cooperative organizational form has been able to gain large market shares in many agricultural markets at the expense of investor owned firms. Tennbakk (1996) uses a Cournot model to analyze duopolistic competition between firms with different ownership structures: investor owned firms, cooperatives, and publicly owned firms. She concludes that cooperatives lead to higher total welfare than investor owned firms – but that nationalization (i.e. publicly owned firms) may be an even better solution from a welfare perspective. Bergman (1997) analyzes the market behaviour of marketing cooperatives when they are able to price discriminate, e.g. sell at high price on the domestic market and at a low price on the export market. He shows that under monopoly, a cooperative sets the same price on the high-price market as an investor owned firm, but the cooperative will produce more and sell more on the low-price market due to the quantity control problem. This creates a deadweight loss because the marginal production costs exceed the price on the low-price market. Hence, when discrimination is important, a cooperative monopoly may lead to lower total welfare than an investor owned monopoly. Cooperative as a Coalition This branch of literature views cooperatives as a coalition of subgroups with different objectives. The focus is on the heterogeneity of the members. The main question is: how does member heterogeneity influences the cooperative? Other important questions are: how should the benefits be distributed among the members to ensure a stable cooperative where all members and all subgroups benefit from participating? How does the internal bargaining between the members affect the decision in the cooperative? How should the by-laws be designed etc. The line of literature uses game theory (both noncooperative and cooperative game theory), contract theory and voting theory. Staatz (1983) and Sexton (1986) used cooperative game theory to analyze the coalition structures in cooperatives. A key result from this work is that charging the same price from all members may not generate

50

Two-part pricing can implement first best production

Member heterogeneity distort sales

Relations between members

PETER BOGETOFT AND HENRIK B. OLESEN

a stable equilibrium. Some members are more likely to exit the cooperative because they have better market alternatives than other members, therefore it may be necessary to price discriminate among the members. Fulton, Hyde and Vercammen (1996) analyze the use of non-linear pricing in a marketing cooperative with heterogeneous members. They show that non-linear pricing, i.e. deviation from the traditional proportional payment scheme, can improve efficiency because it reduces problems with asymmetric information. Bourgon and Chambers (1999) derive pricing rules for a marketing cooperative with heterogeneous members who differ in their cost efficiency (private information) and their bargaining power. They show that two-part pricing mechanisms can implement the first-best production levels in cooperatives with heterogeneous members (highcost producers and low-cost producers). The first-best solution will, however, not be implementable if the bargaining power is not proportional to the production quantities of the member groups. Albaek and Schultz (1997) develop a model of investment decisions in cooperatives. They conclude that the traditional system, where costs are allocated in proportion to size and where voting rights are allocated according to the one-man-one-vote rule, usually will not distort investment decisions in any significant way. The reason is that, generally, the interests of the median voter are very similar to the interest of the average voter (measured according to size). Bogetoft and Olesen (2004) analyze how conflict of interest influence the marketing decisions in a cooperative with both standard and specialty producers. Their central result is that the standard producers, who hold the majority vote, will limit the sale of specialty products because this will reduce the internal bargaining power of the specialty producers. Cooperative as a nexus of contracts This literature views business relationships between cooperative stakeholders as contractual relationships. It includes work based on agency models, transaction cost economics and property rights theory. Hendrikse and Veerman (2001a,b) use property rights theory to analyze the governance structure that best captures the benefits of member investments. The members may be reluctant to invest due to hold-up problems. The optimal organizational form depends on the market structure, the incentive structure and the asset specificity. This basic model concerning hold-up problems in cooperatives has been expanded in Hendrikse and Bijman (2002).

COOPERATIVES

Competition after grading give problems

Quantity control problem Group incentives

Transaction costs

51

Bogetoft and Olesen (2003a) use a standard principal-agent model to analyze the investment incentives with imperfect grading and private information about the investment costs. The central result in their article is that competition among buyers may hinder optimal incentives. Competition forces the buyers to pay the ex post expected value of the product, whereas optimal investment incentives require that the prices reflect the ex ante expected values. Bogetoft and Olesen (2003a) show that horizontal integration, where the sellers form a cooperative, is one solution to the problem, another solution being long contracts. This book This book covers all three branches of the literature on the economics of cooperatives. We view the ‘cooperative as a firm’ when we analyze objectives concerning the market behaviour of the cooperative. In Chapter 4, we show how a proper design of payment schemes can enable a marketing cooperative to solve the quantity control problem. We view the ‘cooperative as a coalition’ when we analyze group incentives and focus on the member heterogeneity. In Chapter 3, we focus on the constraints that must be satisfied to have a stable cooperative, where all member groups benefit from participation. We view the ‘cooperative as a nexus of contracts’ when we analyse how the payment scheme affects transaction costs and hold-up problems. In Chapter 3, we use a principal agent model to analyze the interaction between the cooperative and its members. In Chapters 4 and 5 we analyze how payment schemes affect the information requirements and the transaction costs.

2.7 Case: The Danish pig industry In this Section, we describe the institutional and competitive conditions of the Danish pig industry as of year 2004. This industry is interesting in itself since it is very successful internationally24, and since it is almost entirely dominated by cooperatives. The case description can also help to give the general discussions an applied illustration. Moreover, it provides a framework within which we shall illustrate numerous mores specific payment schemes in this book. To emphasize this we shall also make some of the numerical examples in Danish Crowns (DKr), although we do not suggest that all the numerical illustrations are calibrated on actual data. One US $ is approximately 6.5 DKr.

52

Primarily for export

Very little competition about pigs

Price set each week

PETER BOGETOFT AND HENRIK B. OLESEN

Pig production is the most important sector of Danish agriculture. The country's approximately 11,000 pig producers supply about 25 million slaughter pigs each year which represents a production value, at the farm gate, of nearly 15 billion DKr. The major part (85 per cent) of Danish pig production is exported as standard cuts for further processing in the importing countries. This means that the quality of Danish slaughter pigs to a large extent reflects the demands of foreign consumers. This is carried over in the payments schemes in which standardisation, in the form of a uniform slaughter weight, plays a decisive part. The slaughter pigs are almost entirely delivered to the country's two cooperative slaughterhouses, Danish Crown25 and Tican. Danish Crown slaughters 20 million pigs per year, Tican slaughters 1,5 million pigs, private slaughterhouses slaughter 1 million pigs and 2 million pigs are exported live (primarily to Germany). There is very little competition for the Danish pig producers. Firstly, because Danish Crown is so dominant. Secondly, because Tican is a closed membership cooperative. This means that, for most producers, the only relevant alternative to delivering to Danish Crown is to export the pigs to Germany. The limited competition gives the slaughterhouses room for manoeuvre because it is difficult for the members to sell their pigs elsewhere. In addition the members of both Tican and Danish Crown have an obligation to supply their pigs to their cooperative, although the members of Danish Crown can sell 15 percent of their production elsewhere. The cooperative slaughterhouses co-operate under an umbrella organisation called Danske Slagterier (The Federation of Danish Pig Producers and Slaughterhouses) which handles the interests of the pig industry. National pricing (Landsnoteringen) We describe the national pricing system for two reasons. First, we are going to analyze the national pricing system as one of the payment schemes in Chapter 6. Second, the system has had a large impact on the Danish pig industry for more than 100 years until the competition authorities prohibited the system in 1999. Each week The Federation of Danish Pig Producers and Slaughterhouses determined the payment price for slaughter pigs26. This price was used by all slaughterhouses and all slaughter pigs were paid for on the same basis, regardless of which cooperative slaughterhouse they were delivered to.

COOPERATIVES

Main principles for national pricing

After payment

Two quality parameters

53

The national pricing system was based on three main principles: 1. All pig producers should get the same price (for the same quality) regardless of which cooperative slaughterhouse they were a member of. 2. The price paid should reflect the sales value of the pigs in the market. 3. The payment scheme should only include quality parameters which the pig producer could influence. At the end of the year the cooperative slaughterhouses paid out to the pig producers that portion of the surplus which was not used for consolidation. This so-called after-payment was shared between the members in proportion to the weight of pig meat supplied. From 19931998 the after-payment was about 4 to 8 per cent of the total payments. Because of the common weekly settlement price, this supplementary payment was the most important economic criterion in the pig producers' choice of cooperative slaughterhouse. The common weekly settlement price made the system highly transparent for the pig producers. There were two quality parameters in the national payment scheme: slaughter weight and lean meat percentage. The national pricing system used bonuses to give the producers incentives to improve the quality of slaughter pigs in these two dimensions.

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PETER BOGETOFT AND HENRIK B. OLESEN

Weight calculation DKr/kg 0

-,10

-,10

-,10

-,10

-,20 -,10

-,10

-,10

-,10

-40 -,10

-,10 -,10

-,60 -,10 -,10 -80 -,10 Underweight deduction

Overweight deduction

Reference weight

-,10 -1,00

62

67

79

89

110 kg

Figure 2.2 Supplements and deductions in the national pricing scheme (Danske Slagterier, 1999a) Supplements

The national pricing system allowed the slaughterhouses to pay a special supplement to producers of special pigs. However, individual slaughterhouses could not freely determine such supplements since the national pricing committee had to approve any supplements.

COOPERATIVES

55

Furthermore any such supplement was only permissible to the extent that it corresponded to the additional costs of the production in question. (Danske Slagterier, 1999), i.e. the extra compensation to producers of special pigs should simply cover their extra production costs.

Strategic importance

Most important special pigs

Special pigs There has been a growing emphasis on the production of special pigs and the special pigs play a central role in the slaughterhouses’ strategies. Special pigs are produced in order to meet particular consumer requirements regarding production methods and meat quality. The production of special pigs is primarily aimed at certain segments of the domestic market, but they are also to some extent aimed at export markets. It is often just a few cuts of the special pigs which bear the entire price premium27. Therefore, the revenue from special pigs is subject to relatively large uncertainty since the special cuts, for example the middle cut of UK-pigs, only generates a premium price when sold in the specific markets, in this case the UK. Thus, the sales opportunities for special pigs are rather limited. We give a short overview below of most of the special pigs that are produced in the Danish pig industry28. UK-pig The production of this special pig is designed to meet the requirements of the British animal welfare laws. This means that, among other things, the sows must be unfettered. EU heavyweight pigs This special pig is primarily aimed at the German and Central European market for pork. The pig has a higher slaughter weight, which leads to a higher level of fat marbling. National Specialty Label The label was introduced by the Ministry of Food. Producers must satisfy a number of special conditions in order to obtain the National Specialty Label. Among other things there are special requirements for animal welfare (the area available to the animal, the provision of straw bedding, free range sows etc.). Also the meat may only be re-processed once in the retail sector. The quality label may stand alone or it can be combined with other brands. Gourmet Gris, Porker, Mester Kvalitet, Frilandsgris, Vitalius, Vores Egen Gris and Antonius are all examples

56

PETER BOGETOFT AND HENRIK B. OLESEN

of pigs sold as branded goods which are included in the National Specialty Label Antonius pigs Since 1976 this special pig has been produced for those segments of the Danish market which demand special taste characteristics. Subsequently, requirements relating to production has been introduced. Now, the Antonius concept includes requirements about the selection of breeding animals, feeding, animal welfare (straw bedding etc), slaughter weight and lean meat percentage. Outdoor pigs This special pig makes particular demands on production systems, which must be approved and controlled by Dyrenes Beskyttelse (The Danish society for the protection of animals). For example, the sows must be kept out of doors and the slaughter pigs should have outdoor access. Outdoor pigs produced for the retail chain Irma are sold as Irma's outdoor pigs. Organic pigs This special production follows the general directions for production under the state controlled organic foods marking scheme. Among other things this means that the pigs must have outdoor access and that at least 75 per cent of their feed shall be organic. Meadow pigs (Enggris) This special pig is produced for the seven large butchers in the Copenhagen area which operate under the name of De Grønne Slagtere (The 'Green' Butchers). Meadow pigs must have outdoor access and have a higher slaughter weight. Only female pigs are sold as meadow pigs, and they must not have had medical treatment.

2.8 Conclusions

General problem

In this chapter, we have given an introductory description of the nature of cooperatives. We have compared cooperatives with other corporate forms, especially the so-called New Generation Cooperatives (NGCs), as well as investor owned firms. We have identified a number of issues from economic theory which are particularly relevant to cooperatives. These are the general problems of a firm with autonomous members who have partially conflicting

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57

interests and who seek to attain a common goal. We have particularly focused on the hold-up problem, the quantity control problem, the freerider problem, the horizon problem, the control and motivation problem, the portfolio problem and the influence problem. The hold-up, quantity control free-rider and horizon problems as well as the problems of control and motivation all arise from a common problem. This problem consists in ensuring optimal behaviour in a decentralised organisation when the decision-makers do not themselves bear all the costs or receive all the benefits from their decisions. The roots of the hold-up, free-rider, horizon and control problems are that the decision-maker does not himself receive all the benefits of his activities. On the other hand, the problem of the quantity control problem is that the decision-maker does not bear all the costs of his actions.

Notes 1

Cf. e.g. Danske Andelsselskaber (1998). See e.g. Sexton (1995). 3 Cf. e.g. Bogetoft(1999) and Bogetoft and Olesen (2003a). 4 This is for example the formulation used in 1996 by the Federation of Danish Cooperatives (Danske Andelsselskaber). 5 See for example Büchmann Petersen (1998), Cook and Tong (1997), Harris e.a. (1996) and Nilsson (1997). 6 Cf. for example Harris (1996). 7 See for example Tirole (1988), Hansmann (1996), Hart (1995) or Hendrikse G. and C. Veerman (2001a). 8 See Helmberger and Hoos (1962), Fulton (1995) or Schultz and Albæk (1998). 9 Correspondingly, with a large market for final goods and the advantages of large-scale production (increasing returns to scale) in processing, there is a possibility of under-production 10 See for example Fulton (1995), Sexton (1995) or Hansmann (1996). 11 See for example Porter and Scully (1987), Fulton (1995), Sexton (1995), Cook (1995) or Hansmann (1996). 12 Büchmann Petersen (2000). 13 Danske Andelsselskaber 1999a. 14 See for example Hart (1995), Hansmann (1996) and Fama (1980). 15 See Hart (1995) for an overview. 16 See Cook (1995), Hansmann (1996) and Fulton (1995). 17 This corresponds to 'pricing to market' in industrial organisations. Here, empirical research shows that export businesses often even out the effects of changes in the exchange rate by adjusting their sales prices, see Knetter (1987). 18 For example, this will be the case if the producers' marginal costs are given by MC A Q 667  2 3 Q in situation A and MCB Q 2 3 Q in situation B. This will give the producers a profit of 83.250 DKr in 2

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situation A and 187.500 DKr in situation B. If instead the marginal costs are MC A Q 2Q in situation A and MCB  Q 2Q 3 in situation B, the producers will earn 250.000 DKr and 187.500 DKr respectively. In the latter case, the high pig prices more than outweigh the increase in costs, so that the producers will earn more with high pig prices. 19 See for example Bogetoft and Pruzan (1991, 1997) for a discussion of the advantages and disadvantages of decision-making and planning processes in general 20 See for example Hansmann (1996) or Milgrom and Roberts (1990). 21 Flemin (2000). 22 This representation is inspired by, among others, Bogetoft and Pruzan (1991, 97), Cook and Partridge (1995), and Simonsen (1998). 23 There is a fourth category “Cooperative in the planning sector” which is not particularly relevant for this work. 24 See For example Hobbs (2001). 25 In 1999 this company was merged with Vestjyske Slagterier and in 2001 the company merged with Steff-Houlberg. 26 The national pricing system was in place for more than 100 years. The description of the national pricing system (Landsnoteringen) is based on 'Principper for fastsættelse af afregningsprisen for slagtesvin', Danske Slagterier (1999a). 27 Claudi Lassen (1997). 28 The description is based on information from Danske Slagterier (1999b).

3 Relevance of the discussion

Theoretical basis

Economic objectives and conditions In this chapter, we discuss what the overall objectives of a cooperative may be, and the conditions under which the objectives must be pursued. Alternative payment schemes must be designed and evaluated on the basis of these objectives and conditions. In Chapter 2, we described both traditional cooperatives and New Generation Cooperatives. The descriptions were relatively operational. The corporate forms are defined in part by the principal allocation of decision-making rights and residual rights1 and in part by the operational details of the payment schemes, entrance and exit rules, delivery rights etc. However, in order to evaluate whether these principles and more specific rules and schemes are reasonable it is necessary to take a more general starting point. One must ask what the overall goals and objectives are and whether the principles applied contribute effectively to achieving these goals in the actual situation. It is this more general perspective which we seek to establish in this chapter. We also need a more general starting point to evaluate the suitability of more specific rules. For example the rule in the national pricing system2 that differences in payment can only reflect the actual cost differences between products. In this connection it is noted that even though the principles of cooperatives are relatively operational (or perhaps because they are so), they do not in fact lay down the payment rules for all circumstances. This applies in particular to situations with differentiated products. When evaluating specific payment schemes it is therefore necessary to bear in mind what the overriding objectives and the general circumstances of the cooperative really are. This chapter is based on the fundamental economic model of optimal behaviour, sometimes referred to as the rational ideal. We view decision making as a systematic search for the best means to pursue ones ends. Hence, to make rational decisions, one must have well-defined goals and possibilities, and part of the challenge in this chapter is to define these. We use both non-cooperative and cooperative game theory to give a more in-depth treatment of the special characteristic of cooperatives – namely the cooperation between partly autonomous members who attempt to pursue common goals despite partially conflicting interests.

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Game theory

PETER BOGETOFT AND HENRIK B. OLESEN

Game theory is the fundamental approach used by economists to model situations where the behaviour of one person or group has an important impact on others and vice versa. Such interactions necessitate so-called strategic thinking, i.e. a person or group must consider how its behaviour affects others and how their response in turn affects itself. Non cooperative game theory concerns how different persons or firms can identify and pursue common goals in spite of conflicting individual interest. It focuses on how individual decision-makers can be given incentives to take decisions which serve the interests of everyone. In extension of this, cooperative game theory focuses on group behaviour and the formation of coalitions. Cooperative game theory is concerned with how stable different systems are toward group deviations. Cooperative game theory also defines a number of other criteria for the proper allocation of the gains from cooperation3. Thus, both noncooperative and cooperative game theories are obviously relevant for cooperatives4.

3.1 Efficiency

Pareto-efficiency

Nearly all economic systems contain several individuals. It can therefore be difficult to decide what is good and what is bad for the system. What is good for one person may not be good for another. In economic theory, however, there is wide-spread agreement on at least one approach to this problem, namely the so-called Paretoefficiency principle. We seek solutions that are Pareto-efficient in the sense that they cannot be changed so that some firms will be better off without others thereby becoming worse off. The Pareto-efficiency principle: A payment scheme is Pareto-efficient if it is not possible to make some member better off without making others worse off M.

Profit maximisation

To make this concept operational we assume that producers are primarily members of a cooperative for economic reasons. Of course, we realize that this can be an over-simplification. In practice all individuals and firms pursue a multiplicity of goals which cannot easily be summarized into something as simple as an assumption of profit maximization. On the other hand, profit maximization is a useful and widely used assumption that in a simple way explains the general characteristics of behaviour. For the individual producer, the profit is the difference between the payment he receives from the cooperative and his production costsM.

ECONOMIC OBJECTIVES AND CONDITIONS

The producer's profit depends on the equilibrium

Profit allocation Choosing the payment scheme

Exclusion of payment schemes

61

The profit which the individual member receives depends on the payment scheme. The payment scheme affects the different members' choice of production level, their production costs, as well as the revenues in the cooperative, and thus what will be paid out to the members. In practice it can be difficult to determine the profit for a given producer. The optimal production for a given member depends on the production of all the other members. In order to find a member's profit it is therefore necessary, in principle, to make an equilibrium analysis. All the members' production must be determined in relation to the others' production so that none of the partially autonomous members want to change their production. Later in this chapter we limit the number of possible equilibriums by using a number of conditions. Also, we illustrate the formation of equilibrium under specific market and production conditions in the next chapter. For the present it suffices to think of payment schemes in terms of the profit allocations that they generate. The list or vector consisting of the different members' profits is called the profit allocation. A profit allocation shows how well the different members are situated under a given payment scheme. Once these terms are established, the choice of a payment scheme is reduced to a choice between the profit allocations which correspond to the respective payment schemesM. This is illustrated in Figure 3.1. Each point in the shaded area corresponds to a payment scheme. The payment scheme is judged according to the resulting profit for Member 1, shown on the x-axis, and the resulting profit for Member 2 shown on the y-axis. In this and the following figures the explanations are given not only in words, but also by using mathematical symbols. The mathematical symbols are explained in the mathematical sections. The Pareto-efficient payment schemes correspond to the top righthand edge of the possibility set, where no producer can obtain a higher profit without the other producer obtaining a lower profit. The Pareto-efficiency criterion allows us to disregard the payment schemes which are not Pareto-efficient. However, the criterion does not identify a single scheme as the only relevant one5. There will typically be many Pareto-efficient schemes. It is therefore not only possible but also necessary to include other criteria in order to make the choice of a payment scheme. We introduce a number of such criteria below.

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Profit to producer 2

S 2 a Pareto-efficient profit allocation

Possible profit allocations 3

A

S  a

Profit to producer 1

Figure 3.1 Pareto-efficient payment schemes Mathematical representation: Consider a cooperative with n members, identified as j=1,...,n. A is the possible payment schemes a  A is a specific payment scheme U j a is the utility6 of member j under payment scheme a We have the following formal definition of Pareto-efficiency: Definition 3.1 The payment scheme a  A is Pareto-efficient, if and only if there is no alternative system a ' A , so that U j (a') t U j (a) for all j=1,…,k,…,n and U k (a') ! U k (a) for at least one member k. The profit to the individual member is given by: S j (a )

x j (a )  c j (a) ,

where: S j (a ) is the profit to producer j x j (a ) is the payment from the cooperative to producer j c j (a ) is the production costs of producer j

If we represent utility by profits, the choice of payment scheme will be a question of choosing profit allocation S (a ) (S 1 (a),..., S n (a)) from the number of the profit allocations which corresponds to the number of possible payment schemes S ( A) {(S 1 (a ),..., S n (a )) | a  A} . Note that, as referred to in the guidelines for readers, we have used the following notations: a variable y with a superscript (exponent) j refers to the variable's value to member j, a variable y

ECONOMIC OBJECTIVES AND CONDITIONS

63

without a superscript typically refers to a vector of all the individual members’ y values. In the following, we also use the superscript -i for vectors with all individuals except i, and we use a subscript k, when referring to product type k.

3.2 Equality and the integrated profit Cooperation requires equality

All should have the same

It is widely held that a fundamental requirement for a cooperative to work effectively is that the participants feel they are treated equally7. It will therefore be natural to include an equality requirement in the choice of a payment scheme. Unfortunately, there is no single definition of equality. We illustrate some of the main concepts of equality here. The most obvious way of defining equality is presumably to require that all receive the same, which of course should be as much as possible. According to the Pareto-efficiency principle it is desirable to give more to one member if this can be done without affecting the others. However, if we focus on equality this possibility is not interesting, because it will always be better to allocate the profit to all members. As stated, what matters most is that all get the same, and as much as possible. This idea can be stated as follows: Direct equality: The best system ensures that all get the same – and as much as possible M

Consideration for the weakest

Direct equality can also be given another definition which may appear somewhat different, but which can in fact easily be shown to give the same result. The alternative formulation of equality ensures that the person who is worst off receives the best possible terms. This idea can be stated as follows: Maximin equality: The best system ensures the highest possible profit to the member who obtains the smallest profit M.

Concern for the median member

The principle is that a scheme is no better than it is perceived to be by the person who obtains the least attractive result from it. We return to this concept in connection with the so-called Nucleolus payment scheme in Chapter 6. A third possibility, which is interesting in view of the one-man-onevote principle in cooperatives, is to seek a scheme which gives the median members the highest possible profit. This is the profit level which half the members are above and half are below8.

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PETER BOGETOFT AND HENRIK B. OLESEN

Median equality: The best system ensures the highest possible median profitM. Equal benefits

Some may object that these proposals try to solve general equality problems rather than the equality problems inside the cooperative, which should be concerned with the gains from membership. From this point of view consideration should be given to what an individual member can obtain outside the cooperative. The better the outside options, the more an individual member should be allocated inside the cooperative. On this basis equality is a question of ensuring that the individual who benefits the least from membership should benefit as much as possible, i.e. Adjusted maximin equality: The best system ensures the greatest possible profit gain to the member whose profit gain is the leastM.

Integrated profit as a goal

All these different concepts of equality make it difficult to identify what the overriding goal of the cooperative should be. However, we can get a little help from the structure of the problem and the focus on the economic returns9. Since, in principle, profit can be re-allocated between the members of the cooperative, it is natural for the overriding goal of the cooperative to be the maximization of the aggregate profit. If namely the aggregated profit could be increased, we could – via a reallocation – create a Pareto superior outcome. The literature usually refers to the aggregated profit as the integrated profit. It covers the profits of the individual producers plus any profit to the cooperative. Since the cooperative's profit will eventually be transferred to the members, the profit of the cooperative as such can be considered as nil10. Integrated profit maximization: The best scheme ensures the biggest total amount of profitM.

Definition of integrated profit

The literature on the economics of cooperatives supports the idea that maximizing the integrated profit is a sensible principle for evaluating a payment scheme. Over the years, many somewhat similar goals have been proposed11. However, there is general agreement that the relevant goal, from an economic point of view, should indeed be the maximization of the total profit of the integrated system. The integrated system consists of the members and the cooperative, and the aim is therefore to maximize:

ECONOMIC OBJECTIVES AND CONDITIONS

integrated profit =

+ -

65

revenues from sales of final goods processing and marketing costs primary production costs

This corresponds precisely to the sum of the profits of the members of the cooperative. The four different equality criteria are illustrated in Figure 3.2 below. They correspond to what, in the general literature, is called social benefit functions, since they give different ways of evaluating and aggregating the utilities of the different individuals. Mathematical representation: Formally, the different criteria for equality can be formulated as a choice of system a, which leads to the following Direct:

max max H

Maximin:

max min S j (a )

Median:

max S median ( a )

Adjusted maximin:

max min S j (a )  S

Integrated profit:

max ¦ S j (a)

a

H :H ˜eS ( a )

j

a

a

j

a



j



n

a

j 1

where j=1,…n are the members of the cooperative, e 1,...,1 is a vector with 1 in each of the n coordinates, S median (a) is the median of the profits which the members receive when the payment scheme a is used, and S j is the best alternative profit for member j.

Simple efficiency

It is relevant to make three comments about the use of integrated profit as an overriding goal. Firstly, the significance of the integrated profit is so fundamental that frequently the solutions which maximize the integrated profit are simply called 'efficient'. In order to distinguish this special form of efficiency from the general Pareto-efficiency, this will be called the simple efficiency principle. The simple efficiency principle: A payment scheme is (first best) efficient if it maximises the total integrated profit.

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PETER BOGETOFT AND HENRIK B. OLESEN

Profit to producer 2

Maximin and direct equality

S 2 a

H ˜e

1

S a 

1

Profit to producer 1

Profit to producer 2 Adjusted maximin

S 2 a

S2

S

Profit to S  a producer 1



Profit to producer 2

S 2 a

Integrated profit

1 1

S  a

Profit to producer 1

Figure 3.2 The overall goals in the choice of payment schemes

ECONOMIC OBJECTIVES AND CONDITIONS

Efficiency and coordination

Profit allocation is especially important in cooperatives

67

Efficiency concerns the fundamental problems of coordination. Coordination problems arise in any economy which has several persons. In practice, for example, coordination must ensure that the right pig producers produce the right pigs at the right time and at the lowest possible cost, that the cooperative processes the pigs into the right products with the lowest possible input, and that the resulting final goods are sold in the right market at the highest possible price. To the extent that there is uncertainty related to the production, processing and marketing, the coordination also concerns minimization of the negative effects of this uncertainty. Thus, the coordination must also ensure an optimal risk sharing in which the risk neutral parties should bear the risk as far as possible, and where the risk is otherwise shared and minimized. Secondly, it should be noted that we follow the general economic concept of optimality when we choose maximization of the integrated profit as the goal. In the economic literature on industrial organization, the general goal is to create the largest aggregate profit to be shared between the parties. This literature puts less emphasis on how the profit should be allocated. On the other hand, the allocation of the profit is tremendously important in a cooperative. Therefore, it is problematic to use the maximization of the integrated profit as the overriding goal if achieving this goal leads to an unsatisfactory profit allocation between members. This is why it is necessary to consider the equality principles above. In a cooperative the equality principles are important and attempts must be made to satisfy their requirements, even if this may cost some of the integrated profit. Thirdly, maximizing the integrated profit does not necessarily give a clear-cut solution12. Even when a re-allocation of profits is possible, there is still a need for principles of equality or other criteria in order to choose one specific payment scheme from among all the possible payment schemes. Even if there is agreement about using the maximization of the integrated profit as the overriding goal, it is still not clear that the cooperative's operational rules contribute to the achievement of this goal. In fact, it can easily be demonstrated that this is often not the case. Therefore, a main theme in this book is how different adjustments to the traditional payment scheme can increase the integrated profit. Above, we have introduced the most basic elements in deciding between alternative payment schemes. However, we are still missing two important elements.

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How is a payment scheme to be chosen?

How to determine feasible profit allocations?

PETER BOGETOFT AND HENRIK B. OLESEN

First, it is not clear how the members should decide which principles should be used in allocating the total profit. In practice, the decision is the result of political manoeuvring, with room for discussion of the principles of equality, contribution to the common good, etc. In this connection the equality principles referred to above and a number of the subsequent principles can be argued. In our view, the principles13 are interesting as a part of the properties which a payment scheme should have. Part of the decision will certainly also be based on more direct economic bargaining where different individuals and groups try to extract as much as possible of the gains from cooperation. There is a large literature on bargaining, both non-cooperative14 and cooperative15 and from a conceptual and modelling point of view it is straightforward to use the models to investigate the allocations of the gains from cooperation. The linkage to economic bargaining theory is one of the advantages of placing the problem of the choice of payment scheme within the framework of decision theory. Still, we do not describe the different economic bargaining models here, because cooperative bargaining solutions are – to some extent at least – based on principles which are already covered in other approaches below. The other important thing missing from the discussion so far is how to determine the number of possible payment schemes, and the associated profit allocations. That is, we have not described how the bargaining set, the set of possible allocations, is determined in the first place. The determination of the set of viable allocations depends on several factors. One factor is the technical applicability. It must be technically feasible to generate the total profits that are allocated, i.e. to ensure budget-balancing. Another factor is the behavioural responses. It is not enough to work out an advanced or fair scheme since there is no guarantee that the members will behave in the way such a scheme presumes. This is because of the fundamental motivational problem which exists in every economic organization with several partly autonomous individuals. In other words, we have yet to define how the motivational feasibility of a scheme can be determined. This brings us to the members' fundamental freedom to determine their production levels and their freedom to resign from the cooperative. The motivational aspects, the individual and group incentives, limit the number of viable payment schemes. We end the chapter with a discussion of a third group of criteria. They concern the dynamic properties of payment schemes and their

ECONOMIC OBJECTIVES AND CONDITIONS

69

robustness in the face of changes in the conditions of production and the market.

3.3 Technical applicability

Are the plans technically feasible?

To design or evaluate a payment scheme it is necessary to make an exact description of the production, processing and sales activities which will be the result of the systemM. A number of conditions must be taken into consideration. Part of these conditions concern the framework within which the scheme must function, including the conditions of primary production, the technical possibilities for processing and the market conditions. There is naturally no point in preparing a plan for production, processing and sales, which gives the highest conceivable integrated profit if the plan cannot be carried out technically. This situation can arise, for example, because the primary producers cannot produce the planned quantities of the planned quality, because the quantities received cannot be processed. Therefore, the first requirement is that the plan should respect the exogenous conditions for production, processing and sales. We refer to this as technical applicability: Technical applicability: The plan must be feasible, given the existing conditions for production, processing and salesM. Mathematical representation: We are still concerned with a cooperative with n members, but we now explicitly introduce a description of an individual producer's production conditions. Let us assume that producer j produces q j , j=1,..,n, so that altogether there is a production Q

q 1  q 2  ...  q n .

It is easiest to think of a situation in which all members produce the same type of fully homogeneous products, for example pigs. However, the framework can also cover cases where there is differentiated production. In this case it is necessary to consider production q j of member j as a vector which indicates how many units producer j has produced of the different product types. That is to say that q j q1j ,...q mj , where i=1,…m indicates the different product types.

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PETER BOGETOFT AND HENRIK B. OLESEN

The total production of a single product type by the n producers is referred to as qi , i.e. qi qi1  qi2  ....  qin . The list, or vector, q indicates the total production of each of the individual product types of n producers, i.e. q ( q1 ,..., q m ) . For example, it is possible to have a cooperative slaughterhouse with three producers and two products. Producer 1 produces 1000 UK pigs and 500 organic pigs, i.e. q 1 (1000 UK pigs, 500 organic pigs), Producer 2 produces just 800 UK pigs, i.e. q 2 (800 UK Pigs, 0 organic pigs), while Producer 3 is purely an organic producer q 3 (0 UK pigs, 900 organic pigs). In this case the total supply to the slaughterhouse is q = (1800 UK pigs, 1400 organic pigs). In this chapter we use an aggregated description of the individual producer's production possibilities. We look at their cost functions which indicate the costs of producing the quantities delivered: c j (q j ) = producer j's costs for the production of q j

Formally, technically impossible production corresponds to infinitely high costs. In the next chapter we discuss how the cost function can be determined. For now it simply summarizes the production conditions for the j'th producer. We assume that member j's profit from the best alternative to membership of the cooperative is S j . We describe in aggregated form the company's processing and marketing activities with the resulting revenue before payment to members. We define the revenue R as: R( q 1 ,..., q n ,V ) =

=

revenue of the cooperative sales revenues (gross revenue) processing and marketing costs of the cooperative

The revenue depends on the quantities delivered and on the company's processing and marketing plan. The latter we refer to as V , and 6 is the set of such plans, i.e.: V  6 = the cooperative's processing and marketing plans

In cooperatives the revenue corresponds to the total sales revenue received by the producers. If a given processing and marketing plan cannot be carried out due to the technical limitations of processing or suchlike, then, by definition, the value of R is minus infinity. This description of technological and market conditions can be expressed formally as:

ECONOMIC OBJECTIVES AND CONDITIONS

71

Proposition 3.1 It is technically possible to implement the production, processing and marketing plan ( q1 , q 2 .., q n ,V ) when none of the primary costs c j (q j ), j 1,..n, are infinitely large and when the revenue R( q1 ,.., q n ,V ) is not infinitely small.

3.4 Balanced budget All profits go to the members

A second requirement for a payment scheme is that the total payments to members shall exactly correspond to the revenue of the cooperative. This requirement is almost technical and it is in any case definitive because of the members’ rights to the residual earnings due to their ownership of the cooperative. In the literature on the economics of cooperatives it is often called the break-even constraint or the no-profit constraint. Balanced budget: The revenue, neither more nor less, must be allocated to the members M.

Problematic requirement

Long term requirement

It may seem quite innocent to require a balanced budget. It is obvious that more cannot be allocated than has been received, and on the other hand can it be such a problem to allocate all the revenues? However, when the requirement for a balanced budget is combined with our next requirements, it becomes the source of quite a number of problems for cooperatives. It makes it complicated indeed to design sensible payment schemes. In the next chapter we give a number of examples of this. The balanced budget requirement is also the reason why a number of previously suggested goals for cooperatives, for example the maximization of supplementary payments, the maximization of the price including supplementary payments, profit maximization as in a private firm and so on, are meaningless. These goals are incompatible with the requirement for a balanced budget and with the next requirement dealt with which is incentive compatibility16. Needless to say budget-balancing in practice is a long term rather than a short term requirement. Limited and contemporary deficits can be covered via the credit market, and surpluses can be eliminated by increased spending and investments in the cooperative. Again, however, such adjustments may come at a cost since the production signals to the members are blurred by such measures. Thus, budget balance comes at a motivational cost.

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Mathematical representation: Let x j ( q1 , q 2 ,.., q n ,V ) represents payment from the cooperative to member j as a function of the applied plan for production, processing and marketing, i.e.: x j ( q 1 , q 2 ,.., q n ,V ) = total payment (including supplementary

payment) to producer j The requirement for a balanced budget (BB) can now be formalised as: n

¦x

j

( q 1 , q 2 ,.., q n ,V )

R( q 1 , q 2 ,.., q n ,V )

q 1 , q 2 ,.., q n , s

(BB)

j 1

In other words, for every plan for production, processing and marketing, the total payments to members shall correspond to the cooperative's revenue

3.5 Individual incentives

Independent decision-makers

Apart from the technical requirements from production and the market, a plan for production, processing and marketing must also satisfy a number of behavioural requirements. These stem from the fact that cooperatives usually allow their members to retain a high degree of autonomy. Our analytical framework takes account of this provision17. A cooperative does not function as one central decision-maker. The primary producers are independent decision-makers, who determine for themselves their production levels and their possible resignation from the cooperative. A payment scheme can therefore only be expected to generate the production levels which it is in the interests of members to produce. In the economic literature this is called incentive compatibility (IC for short). Incentive compatibility: No member should be better off by changing the parts of the plan (for production, processing and marketing) he controlsM.

Registrations

Apart from incentive compatibility, the plan ought to take into account possible threats of resignation by members, which can be the extreme result of incentive incompatibility. It can also be said that the plan ought to support the principle of voluntary participation. The standard expression for this condition is individual rationality (IR).

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73

Individual rationality: No member should be better off by resigning from the cooperativeM. As referred to above, fulfilling the requirement for a balanced budget together with other reasonable requirements is problematic. In fact we arrive at the following general result: Proposition 3.2 No allocation mechanism exists which is both (first best) efficient and incentive compatible and which ensures full allocation of revenues for all revenue functions (R) and production cost functions (C) (Green and Laffont, 1979). The basic requirements cannot always be fulfilled

In other words it is not possible to find a method for allocating the revenue which meets the basic requirements for efficiency, incentive compatibility and a balanced budget in all situations. However, this does not prevent the finding of appropriate rules for special classes of such allocation problems, for example problems with a linear revenue function. The proposition shows the strength of the requirements which have been introduced. The proposition also shows that one cannot hope to find a scheme which is independent of its context. This means that cooperatives must change their payment schemes when there are sufficiently large changes in the conditions of production and the market. Mathematical representation: We can formalise the requirement for incentive compatibility of a plan (q1 ,..q j ,..., q n , σ ) as follows: x j (q1 ,..q j ,..., q n , σ ) − c j ( q j ) ≥ x j (q1 ,.., q ' j ,.., q n , σ ) − c j (q ' j ), ∀j , q ' j ⋅

(IC)

These inequalities mean that it must not be beneficial for any producer j to change production from the planned production q j to an any alternative production level q' j , if none of the other producers change their productions. It is worth noting that it is possible to formulate other requirements for individual incentive compatibility. The literature refers to the above requirement as implementing the plan as a Nash equilibrium, where no producer will want to diverge from the plan if none of the others do so. It is also possible to make a stricterrequirement, for example the implementation of the plan as a

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PETER BOGETOFT AND HENRIK B. OLESEN

dominant strategy equilibrium, where none of the producers wish to diverge from the plan, regardless of what the other producers choose to do. This latter is naturally more difficult to achieve but is also much more attractive. Dominant strategy implementation makes the situation much more stable. Furthermore, it means that the individual producer does not need to use time and energy collecting information on and speculating about what the others will do, when he chooses his own production plan. In Chapter 4 we suggest a couple of alternatives to the traditional payment principle which have this attractive characteristic. We can formalize the individual rationality constraint as follows: x j (q1 , q 2 ,.., q n , V)  c j (q j ) t S j j

(IR)

In other words, the profit which member j obtains through membership (over a certain period of time determined by the contractually binding period plus any quarantine period), must at least be equal to the highest profit he could achieve outside the cooperative. This requirement is mild, in the sense that we have not taken account of the threat of collective action by a group of producers. We will return to this question later in this chapter in connection with the threat of collective resignations. We also note that IR and IC, in contrast to BB, need only apply in equilibrium (apart perhaps from modifications in member j's own production). It is, of course, possible to restrict BB so that it only applies in equilibrium and this would in fact sometimes ease the problem. We show this in Chapter 4. However, for the time being we assume that BB must apply to all possible strategies for production, processing and marketing. This reflects the fact that the members are the residual claimants and are by definition the only possible recipients of any surplus. Example It can be useful to look at these conditions by considering cooperation between two producers. Imagine that two pig producers agree to sell special pigs to a buyer. Both producers can produce either 5,000 or 10,000 pigs per year. Producer 1 has average costs of 600 DKr per pig at all levels of production. Producer 2 has average costs of 400 DKr per pig when producing 5,000 pigs and 500 DKr per pig when producing 10,000 pigs. Because of the special circumstances relating to transport, sales, contracts with

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75

slaughterhouses etc., the buyer will pay 1,000 DKr per pig for up to 10,000 pigs, 520 DKr per pig for the next 5,000 pigs, and 480 DKr per pig in excess of the production of 15,000 pigs. The situation can be summarized as in Table 3.1 below, where the three figures in a given cell indicate the total sales revenue, costs for Producer 1 and costs for Producer 2. All sums are in million DKr. Producer 2 Producer 1 Production 5,000 Production 10,000

Production 5,000

Production 10,000

(10, 3, 2) (12.6, 6, 2)

(12.6, 3, 5) (15, 6, 5)

Table 3.1 Sales revenue and costs The integrated profit in each of the four cases will therefore be: Producer 2 Producer 1 Production 5,000 Production 10,000

Production 5,000

Production 10,000

5 4.6

4.6 4

Table 3.2 Integrated profit On the basis of the simple efficiency principle the best solution is that each of them should produce 5,000 pigs. A payment scheme for the two producers' common sales company should specify the payment to the two members for each combination of production. A payment scheme is therefore described by 8 figures, four of which indicate Producer 1’s payment in each of the four cells above, and four of which indicate Producer 2's payment. Using the notation from the mathematical section, we have that x1(5,5) for example, represents the payment to Producer 1 when both producers produce 5,000 pigs. The 8 payments appear as in the following table: Producer 2 Producer 1 Production 5,000 Production 10,000

Production 5,000

Production 10,000

x1(5,5), x2(5,5) x (10,5), x2(10,5)

x1(5, 10), x2(5,10) x1(10,10), x2(10,10)

1

Table 3.3 Payment scheme The payment scheme specifies, for example, that Producer 1 shall have x1(5, 10) and Producer 2 shall have x2(5,10) when Producer 1 supplies 5,000 pigs and Producer 2 supplies 10,000 pigs. The balanced budget conditions now give:

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PETER BOGETOFT AND HENRIK B. OLESEN

x1(5,5)

+

x2(5,5)

=

x1(5,10)

+

x2(5,10)

= 12.6

x1(10,5)

+

x2(10,5)

=

12.6

x1(10,10)

+

x2(10,10)

=

15

10

If we try to implement the efficient production levels, and if we assume that the producers do not have any real alternative to pig production or the joint sales activity, we have the following individual rationality constraints (IR): x1(5,5) –3 t 0 x2(5,5) –2 t 0 and the following incentive compatibility constraints (IC): x1(5,5) –3 t x1(10,5) –6 x2(5,5) –2 t x2(5,10) –5 We can now investigate whether the traditional payment scheme in cooperatives, namely allocation of joint processing profits in proportion with turnover, will work. In this example the payments to the two producers in each of the four instances will be: Producer 2 Producer 1 Production 5,000 Production 10,000

Production 5,000

Production 10,000

10 ˜ 510 , 10 ˜ 510

12.6 ˜ 515 , 12.6 ˜1015

= (5, 5)

= (8.4, 4.2)

12.6 ˜1015 , 12.6 ˜ 515 15 ˜10 20 , 1510 20 = (8.4, 4.2)

= (7.5, 7.5)

Table 3.4 Payments with proportional allocation If these figures are inserted in IR conditions the result is: 5-3 t 0 5-2 t 0 where both are satisfied. However, if the payments are inserted in IC conditions the result is: 5-3 t 8.4-6

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77

5-2 t 8.4-5 and as neither of these are satisfied, in this case the proportional payment scheme does not support an efficient result. Both producers deviate from the best solution, and each produces 10,000 pigs instead of 5,000 pigs. This is also easily seen by comparing the producers' profits in each of the four instances. Producer 2

Production 5,000

Production 10,000

(5-3, 5-2) = (2, 3) (8.4-6, 4.2-2) = (2.4, 2.2)

(4.2-3, 8.4-5) = (1.2, 3.4) (7.5-6, 7.5-5) = (1.5, 2.5)

Producer 1 Production 5,000 Production 10,000

Table 3.5 Profits obtained with proportional allocation The only Nash equilibrium under the proportional payment scheme is that both produce 10,000 pigs. Thus the result is that together they lose 1 million DKr compared with the efficient result, or 20% of the maximum integrated profit. As a more technical note we may observe that producing 10,000 pigs each is not just a Nash equilibrium under the proportional scheme. It is also a dominant strategy equilibrium, where the response of the individual farmer is independent of the response of the other. This is an instance of what is know as a Prisoners’ Dilemma in game theory.

3.6 Group Incentives Individual conditions not enough

It is of course not only individual activities that can threaten a cooperative. Individual incentive compatibility and individual rationality are necessary but not sufficient conditions for ensuring the functioning of a payment scheme. It is also necessary to take into consideration that groups of members may want to act together. In this section we look at group incentives. The collective threat from groups of members can take many forms. The most obvious is to think of a group of members collectively leaving the cooperative, for example to start an alternative cooperative. This corresponds to a generalization of the individual rationality. Another possibility is that a group of members collectively lobbies for changes in the payment scheme within the cooperative. A group of members could

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also coordinate a departure from the planned production levels etc. This corresponds to a generalization of incentive compatibility. Our treatment of group incentives is relevant to many different groupings, for example groupings on a geographical basis, grouping by size, grouping according to delivery times, or according to the resulting profit level. To ease the understanding and exposition, however, we will usually give examples where the producer groups produce different types of products, for example different types of pigs such as multi-pigs, UK pigs, organic pigs, EU heavyweight pigs etc.

3.6.1 Stand-alone profit Possible profit outside the cooperative

Stand-alone revenue and stand-alone profit

Determining the stand-alone profit

When designing a payment scheme it is important to consider what different groups could earn outside the cooperative. The total profit which a group or coalition of producers could obtain alone, is called the group's stand-alone profit. The stand-alone profit represents the total revenue of the producers in the group in question minus their total production costs. For the full coalition consisting of all the cooperative's members, the stand-alone profit consists of the company's revenue minus the producers' production costsM. If the producers' costs do not depend on which group they belong to, (because, for example, they always produce the same), we need only be concerned with their revenue inside and outside of the cooperative. A group's revenue outside the cooperative is called its stand-alone revenue. Since both interpretations are possible, we will to some extent switch between talking about revenue (where it is understood that the producers' primary production costs are fixed across different coalitions) and profit (where it is understood that in addition to profit, the members have their primary costs refunded)M. Now it is an obvious question, how are these stand-alone profits and stand-alone revenue determined in practice? In order to determine the stand-alone profit for the individual coalitions, it is necessary to have a large amount of information. The stand-alone profit of a coalition depends, among other things, on market conditions. Hence, it is necessary to consider questions such as: x

x

What are the alternative sales channels for a group of producers? Can the group deliver to another cooperative, export unprocessed products, or do they have other possibilities? What will be the market reaction of the members who remain in the cooperative if a group leaves? Will there be a price war or suchlike?

ECONOMIC OBJECTIVES AND CONDITIONS

x

Difficult to determine the stand-alone profit in practice

79

Can the members of the coalition collect their capital in the cooperative (personal accounts) when leaving?

These factors mean that in practice it is very complicated to determine the stand-alone profits of all coalitions. Later we analyze payment schemes that require less information. Moreover, it should be emphasized that in practice it is often relatively easy to identify “critical” coalitions in the cooperative. The producers with a reasonable probability of earning more outside the cooperative have an interest in analyzing alternative profit possibilities – and to make themselves known. Thus the debate within the cooperative will probably reveal for which coalitions it will be especially relevant to know the stand-alone profit18. Mathematical representation: Let N {1,.., n} be the number of primary producers. A producer group can now be identified by the members it contains, i.e. as a subset of N: S Ž N is a coalition of primary producers

When we speak of a producer group we mean a coalition of primary producers who produce the same product. We use the subscript i=1,…, m for both producer group and product type. For example i=1 can refer either to organic producers or to organic products. Recall that qij is the amount of product i produced by producer j. Also, the production by producer j is in general given by a vector q j (q1j ,.., qmj ) . A producer group is now formally defined as: Si

^j  N | q

j i

! 0`

For example the organic producer group is defined as: Sorg

^j  N | q

j org

`

!0

The total production of a given product is: qi

¦q jS i

n

j i

¦q

j i

j 1

i.e. a summation of the production levels for the product i, for example organic pigs. We use the term stand-alone profit for the profit which the group

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PETER BOGETOFT AND HENRIK B. OLESEN

could obtain outside the cooperation: 3 ( S ) = the stand-alone profit for coalition S

Formally, the stand-alone profit function is a mapping of 2 N o ƒ , where 2 N is the set of subsets of N, i.e. the possible coalitions between the N members, and ƒ is the set of real numbers. The stand-alone profit function satisfies 3 Ø 0 where Ø is the empty set, i.e. a coalition with no members can not extract any profit. We will talk about such stand-alone profit functions as allocation games, and we will sometimes denote the set of such function by * . Technically, we are using a part of cooperative game theory, where the situation is described by a so-called characteristic function 3 . that assigns a pay-off to each coalition. The pay-off is what the coalition effectively is able to ensure for its members. Exactly how this pay-off is shared among the members is not directly defined. The idea is simply that the pay-offs can be transferred. Games with this property are in general called transferable utility games, TU games. Returning to the more specific setting of this book, we have for the full coalition consisting of all members that: n

3( N )

R (q 1 ,.., q n , V )  ¦ c j ( q j ) j 1

1

n

where q ,.., q represent the individual production levels. The correspondence to the individual profit levels is: 3 ({ j}) S

j

When we say that a producer group is allocated the profit S i , it means that the profit is paid out plus the primary costs ci , which means that the payment is: xi

S i  ci

If we assume that the producers in producer group i only produce product type i, then the production costs ci for the producer group i are given by: ci

¦c

j

(q j )

jS i

To ease the notation we normally suppress the specific production levels when we deal with group incentives. This reflects the theoretical difference in the starting points for non-cooperative and cooperative game theory respectively. Non-cooperative game theory describes with some precision which strategies (actual production and

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81

other activities) relate to the relevant utilities (profits etc.). Cooperative game theory merely describes the achievable utilities of different groupings, and not how these can be achieved by specific actions.

3.6.2 The core Cooperation must pay

In order for independent parties to enter into cooperation, the cooperation must be worthwhile. In other words, each of the parties must earn more by participating in the cooperation than by staying outside it. Only when this condition is fulfilled is there no incentive to break off cooperation. We call this the stand-alone profit or stand-alone revenue principle. The stand-alone profit (revenue) principle: No producer group should receive less profit (revenue) than the profit (revenue) which the group could obtain outside the cooperative. The stand-alone profit principle thus lays a number of restrictions on how the profit can be allocated in a cooperation in which all groups must have an incentive to participate. The number of remaining allocations of the profit is called 'the core' in game theory. The core: The profit (or revenue) allocations which satisfy the standalone profit (revenue) principle are said to be in the coreM.

Individual rationality and the core

The stand-alone profit principle, as applied to individuals, corresponds to the individual rationality described in Section 3.5. What is new is that the condition now applies to groups of individuals. No coalition should be able to be better off by being outside the cooperative. It is natural to consider the individual's requirements as being more fundamental and indispensable than the collective requirements. With individual rationality a producer has merely to agree with himself whether he has an advantage from the cooperation, and if he thinks he has not, then he can resign. With group rationality, i.e. the requirement of the core, the members must coordinate any resignations and possibly their behaviour after leaving the cooperative. From a practical point of view, it is often sufficient to keep an eye on especially obvious coalitions. This is why, in our examples, we operate with coalitions corresponding to different product types. These constitute focal points for obvious coalitions because there are often

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great similarities within such groups. Furthermore they constitute natural units in an analysis of group incentives because they are typically of a size which gives them a certain influence in discussions about alternative payment schemes.

Two types of production

How to read the figure

Example Consider a cooperative slaughterhouse with two types of production, multi-pigs and UK pigs. The production level of a given type of pig does not depend on which coalition the producer group belongs to, cf. above. We assume that cooperating is beneficial, so that the integrated profit of the cooperative is higher than the profit which the producer groups could obtain if they were split into two independent slaughterhouses. One possible allocation of the profit would be that the producers of the UK pigs receive their stand-alone profit while the rest of the profits are allocated to the producers of the multi-pigs. Another possibility is the opposite approach, where the producers of the multi-pigs receive their stand-alone profit, while the producers of the UK pigs get the rest. Both possibilities, as well as all the solutions which lie between them, are within the core. This example is shown graphically in Figure 3.3. The profit which is allocated to the producers of the multi-pigs can be read from left to right, while the profit which is allocated to the producers of the UK pigs can be read from right to left. The length of the line reflects the total integrated profit of the cooperative. In the figure the allocations which lie in the core are in the interval where both the producers of multi-pigs and the producers of UK pigs receive at least their standalone profit.

Stand-alone profit UK pigs

Stand-alone profit Multi-pigs Multipigs

UK pigs The core

Figure 3.3 Allocation between multi-pigs and UK pigs Contribution

The concept of the core can also be defined differently. In the same way that the stand-alone profit sets a minimum payment to each group of producers, the so-called incremental profit can be used to fix a maximum for the profit which can be allocated to a producer group.

ECONOMIC OBJECTIVES AND CONDITIONS

83

The incremental profit is the amount by which the total profit would fall if the group left the cooperative. In other words, the incremental profit is the coalition’s contribution to the cooperation. Incremental revenue is defined in the same way. The incremental profit principle: No producer group may be allocated greater profit (revenue) than the group's incremental profit (revenue)M.

No crosssubsidies

Reading the figure

The allocations which satisfy the incremental profit principle are the same as those which satisfy the stand-alone profit principle, i.e. they are the core allocations. This is not complicated to see. The requirement that a coalition C should get at least its stand-alone profit is equivalent to the condition that the coalition formed by the remaining producers, i.e. N\C, should get at the most its incremental profit. The condition that no participant (whether individual or group) may receive a greater profit than the participant’s incremental profit is the same as requiring that there shall be no subsidizing of any of the participants. As long as one participant receives a payment greater than his incremental profit, this means that what remains for allocation between the other producers is less than the stand-alone profit for the coalition consisting of the other producers. Example We expand the example given above so as to include production of EU heavyweight pigs. The situation is as shown in Figure 3.4. The problem is three-dimensional. The possible profit allocations are shown below. The corners correspond to the individual producer groups getting all the profit from the cooperative. So point A illustrates a situation in which all the profit goes to the producers of EU heavyweight pigs. In practice this means that the other producers only receive payment for their production costs while the rest is paid to the producers of EU heavyweight pigs. The stand-alone profits and the incremental profit of the different producer groups are as shown by the dotted lines. We know, from the concept of the core, that each producer group must receive at least its stand-alone profit and at most its incremental profit. The small arrows in the diagram indicate on which side the payment should be compared to the stand-alone profit and the profit contribution restrictions.

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To identify where the core lies, we also need to take account of coalitions consisting of two of the groups, for example EU heavyweight pigs and UK pigs. Each of these shall have at least their stand-alone profit and at most their contribution. However, as we are only dealing with three groups the conditions for groups consisting of two production lines are the same as the conditions for the groups with just one product line19. Put differently, if we stick to one principle, say the stand-alone principle, it may look as if the standalone conditions for coalitions of two product lines are not present. This is not correct, however. They are present via the marginal contribution condition of the one product line coalitions. It is apparent from the figure that there are several possible allocations (corresponding to the grey area), where the requirements relating to stand-alone profit and contribution are satisfied for all production types. These allocations constitute the core.

EU heavyweight pigs

A

Stand-alone profit UK pigs Contribution UK pigs

Contribution EU heavyweight pigs Stand-alone profit heavyweight pigs

Multi-pigs

The core

Contribution Multi-pigs

Stand-alone profit Multi-pigs

UK pigs

Figure 3.4 Core allocations with three product groups

ECONOMIC OBJECTIVES AND CONDITIONS

Many different allocations in the core

85

As the examples show, there are often many different allocations in the core. And in fact, it appears that under reasonable assumptions, one can be sure that the core is not empty. A non-empty core means that there are possible allocations where all coalitions receive their standalone profit, or equivalently, where no coalition receives more than its incremental profit (and none are therefore subsidized). Proposition 3.3 If the stand-alone profit function is convex, the core is not empty M (Shapley, 1971).

The core changes over time

A simple allocation may not belong in the core

In this context convex means that there must be synergies, so that the cooperation between two coalitions increases the total profits of the coalitions. Thus, two groups together should be able to obtain more than they could get individually20. As long as there are positive synergies from the collaboration, it will be possible to find an allocation in the core. The requirement that the allocation shall be within the core appears obvious when one considers setting up a cooperative between different producers or types of production. Independent parties only enter into cooperation if they can gain from it. However, the requirement that there is no incentive to leave the cooperation becomes more important in a dynamic perspective when the profit potential from the individual types of production changes. Changes in relative market potentials or in the costs of different types of production can make it necessary to change the payments to keep them within the core. Part of the challenge is to define the payment schemes or the payment principles such that they do not need to be changed. If this is possible, the cooperative can avoid costly re-negotiations. We shall return to this below when we discuss some robustness requirements. Example The situation can be illustrated with an example showing the initial situation for a cooperative slaughterhouse with two lines of production, multi pigs and UK pigs. Assume that each of the lines of production can obtain a profit of 100 by remaining independent, but that the profit with cooperation is 220. There is thus a gain of 20 from the cooperation. We assume that the parties share the profit equally between them, so that there is 110 to each of the production lines. There is now a change which means that the production of UK pigs becomes more profitable. Assume that the stand-alone profit from this line of production is now 150 and the profit of the

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PETER BOGETOFT AND HENRIK B. OLESEN

cooperation likewise increases by 50 to 270. If the parties use the same distribution key as before (half each) each of the parties gets 135. However, this solution is no longer in the core and the producers of UK pigs have an incentive to end the cooperation.

Mathematical representation: The core can be defined formally as follows: Definition 3.2 In an allocation game 3 the core is defined as: core(3 )

­ ½ j ®S  I (3 ) | S  N , ¦ S t 3 ( S )¾ j  S ¯ ¿

where S j is the profit allocated to the j 'th producer, and I (3 ) is the number of possible allocations, where the amount distributed is equal to the total profit of the cooperation, i.e. the distribution meets the profit budget condition: n

¦S

j

3( N )

j 1

Note that this condition is equivalent to the usual condition for a balanced budget n

¦x

j

R ( q1 ,.., q n , V) .

j 1

If we consider a random coalition of producers, S, the definition of the core requires that the coalition should at least be given the coalition's stand-alone profit. This applies for all possible coalitions. The core can also be formally defined on the basis of the principle of the incremental profits: Definition 3.3 In an allocation game * the core is also defined as: core(3 )

­ ½ j ®S  I (3 ) | S  N , ¦ S d 3 ( N )  3 ( N \S ) ¾ jS ¯ ¿

where 3 (N ) is the profit of the whole cooperation, i.e. the integrated profit, and 3 ( N \ S ) is the profit for the other parties in the cooperation if coalition S resigns from the cooperation. Thus, this definition of the core states that no coalition may be given a profit which exceeds its contribution.

ECONOMIC OBJECTIVES AND CONDITIONS

87

Formally the requirement for convexity, which ensures a non-empty core, can be expressed so that for all coalitions S and S’: 3 ( S ‰ S ')  3 ( S ˆ S ') t 3 ( S )  3 ( S ')  S , S ' Ž N

For coalitions that do not overlap, this gives the very intuitive notion of synergies from cooperation when the (stand-alone) profit function 3 (.) is super-additive: 3 ( S ‰ S ') t 3 ( S )  3 ( S ')  S , S ' Ž N

3.7 Robustness and dynamics Which core allocation should be chosen?

Often, the core contains many possible allocations. It is therefore necessary to make a further selection. One way to do so is to look for schemes with attractive dynamic properties. We look at two forms of dynamic properties. The first concerns the payment scheme's ability to give groups the incentive to make relevant changes, investments, etc. The other concerns the capacity of the scheme to continue to function well, when there are changes to production and market conditions. These dynamic properties are of course useful in their own right and not just to make a selection from the core. On the other hand, allocations outside the core are not sustainable with rational players and coalitions. The core requirement is therefore more fundamental than the dynamic properties.

Adjustment of the payment

An important criterion in choosing a payment scheme is whether the individual members or groups are given an incentive to make proper adjustments. It is especially important that producer groups have an incentive to make decisions that benefit the entire cooperative. This is discussed below through three types of monotonicity. If the profits of the total cooperative increase (for example through cost savings in processing) then, other things being equal, none of the producer groups should be worse off. A payment scheme with this property satisfies total monotonicityM. When a scheme is totally monotonic none of the producer groups has any incentive to oppose profit increases in the cooperative, including investments which benefit all in the cooperative. Total monotonicity also gives a payment scheme some robustness. It ensures a positive relation between the development of the total profit

3.7.1 Monotonicity

Total monotonicity

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PETER BOGETOFT AND HENRIK B. OLESEN

and the price signals to the producers. In such a system, no producer group receives lower prices when the total profit of the cooperative increases21. Example In the example with the cooperative slaughterhouse producing multipigs and UK pigs, total monotonicity requires that none of the producer groups is worse off if the integrated profit of the cooperative increases, while the stand-alone profits for multi-pigs and UK pigs remain unchanged. Coalition monotonicity

Total monotonicity only deals with the particular situation where the profit of the whole cooperative changes while the stand-alone profits of all sub-coalitions are unchanged. Often, however, the changes in the profit potential have a more widespread effect. Therefore it is relevant to consider a more general form of monotonicity. The so-called coalition monotonicityM considers what happens if the stand-alone profit increases in all the coalitions containing a given producer, while everything else remains unchanged. In such a case the producer should not get less than he did previously. If a payment scheme is not coalition monotonic it means that a producer (group) lacks incentives to improve the profitability of his product. He may refuse to implement reasonable costs savings on his farm, or otherwise oppose higher profits/revenues in his coalitions. Coalition monotonicity also contributes to robustness since a producer cannot receive lower price signals if his product becomes more profitable. Example If the producers of organic pigs arrange 'open house' events all round the country, and they in this way improve the sales of organic pig meat, coalition monotonicity requires that the payment to the organic producers shall not fall. This is because sales of organic pigs will be improved, regardless of what coalitions the organic producers take part in. The requirement for coalition monotonicity may seem modest, but combined with the requirement that allocations shall be within the core, it is in fact quite a strict limitation of the possible allocations. Especially when there are a reasonable large number of producers involved, the possibility of achieving both coalition monotonicity and a core solution is limited.

ECONOMIC OBJECTIVES AND CONDITIONS

89

The two requirements may collide since by coalition monotonicity a producer must be rewarded even if he has only contributed to improvements for sub-coalitions without contributing to improvements for the whole cooperative. An improvement in the stand-alone profit of a coalition which only consists of a part of the producers of the cooperative means that it becomes more likely that this coalition will leave the cooperative. Therefore a problem with coalition monotonicity is that it is not possible to penalize producer groups promoting the dissolution of the cooperative in this way. Proposition 3.4: If there are five or more participants, no allocation rule can ensure both a core solution (when the core is non-empty) and coalition monotonicity (Young, 1985). Cohesion or good incentives

Strong monotonicity

This result means that it is difficult, and often impossible, to construct an allocation rule which gives incentives to cooperate without simultaneously giving individual producers an incentive to oppose an increase in profits on their own products (so-called 'perverse incentives'). Seen in relation to the Danish pig industry, this outcome can help to explain the conservative attitudes toward product differentiation, which the cooperative slaughterhouses have often been accused of22. The fact is that differentiation of the primary production can make it impossible to find a payment scheme which supports collaboration without simultaneously giving perverse incentives. In many cases the changes in profit potentials have other effects than those assumed under coalition monotonicity. If the stand-alone profit either increases or falls in all the groups which a producer is part of, there are often simultaneous changes to the stand-alone profit of the groups which the producer in question is not a part of. This means that the conditions used in the definition of coalition monotonicity are not fulfilled. Thus, for example, coalition monotonicity gives no indications as to how the payment to an organic producer should be adjusted if there is an increased demand for organic products. In this case the stand-alone profit will presumably be increased in all the coalitions containing the organic producers, but the changes in demand also mean that other product lines are less profitable. This means that there will be a breach of the condition that the stand-alone profit in all coalitions without organic producers should be unchanged. Sometimes the literature on cost and profit allocation uses a more general form of monotonicity. It seems reasonable that payment to a producer group should rise when the group's incremental profit rises.

90

The advantages….

…. and disadvantages of strong monotonicity

Worse conditions for UK pigs can benefit multi-pigs

PETER BOGETOFT AND HENRIK B. OLESEN

This requirement is called strong monotonicity M. Strong monotonicity is associated with relative change in the profit of different producer groups, as distinct from the two concepts of monotonicity previously referred to, which concern absolute changes to profits. It is an advantage of strong monotonicity that it ensures a reward to a group which contributes to an increase in the profit of the cooperative as a whole. Strong monotonicity thus brings some robustness to the revenue signals. Strong monotonicity also contains serious problems. Firstly, strong monotonicity requires that payment to a producer shall not fall as long as his incremental profit does not fall, even if the stand-alone profit falls in all the coalitions of which the producer is a member. The incremental profit of a producer will in fact rise if the stand-alone profits of the coalitions of which he is a member fall less than the stand-alone profits of coalitions without the producer in questionM. This means that the producer can receive price signals indicating higher profit, even if the profit is in fact falling23. Secondly, strong monotonicity can prevent profitable risk-sharing. The reason, as referred to, is that a producer's incremental profits may increase even if the total cooperative profit falls. This happens if the stand-alone profit of his colleagues falls and the aggregate profit is constant – or falls less. The example given below illustrates this problem. Thirdly, just as with coalition monotonicity, strong monotonicity can lead to rewarding producers who have only contributed to improvements of sub-coalitions. This means that there may be an obligation to reward producers who have promoted the dissolution of the cooperative without benefiting the integrated profit. The problems referred to above mean that in the rest of this book we primarily concentrate on the first two concepts of monotonicity, viz. total monotonicity and coalition monotonicity. Example We will again use the example of a cooperative slaughterhouse with two product types, UK pigs and multi-pigs. Again we assume that in the initial situation each can obtain a profit of 100 if acting independently but that the profit of the two together is 220. The profit is shared equally between the two product lines with 110 to each. Next, we assume that the revenue potential changes so that the producers of UK pigs would only obtain a profit of 80, if they acted independently, while the producers of multi-pigs can still obtain 100. When the producers cooperate they can obtain a profit of 210. In this

ECONOMIC OBJECTIVES AND CONDITIONS

91

example the fall in demand for UK pigs will affect the cooperative less than it affects the independent production of UK pigs. This seems entirely reasonable, because within the cooperative there are better opportunities for exploiting alternative sales channels. If the profit is now shared equally each product line will get 105. In this situation the strong monotonicity is not complied with because the payment for multi-pigs falls from 110 to 105 in spite of the fact that the incremental profit from multi-pigs goes up from 220 - 100 = 120 to 210 - 80 = 130. Strong monotonicity requires that the payment to the producers of multi-pigs should be at least 110, corresponding to the payment which they received previously. This means that these producers should not help carry the losses from the fall in demand for UK pigs. Mathematical representation: ˆ ˜ represent two (stand-alone) profit In the following 3 ˜ and 3 functions. The two functions can for example, correspond to different marketing strategies in the cooperative. An allocation rule now determines how the total profit 3 (N) (or ˆ ˆ ) ) represents 3 (N) ) is divided between the members. S j (3 ) (or S j (3 the profit received by group j. Formally the three types of monotonicity can be defined as: Definition 3.4 An allocation scheme is total monotonic if, for any ˆ ˜ we have that if 3 (N) t 3 ˆ (N) and profit functions 3 ˜ and 3 j j ˆ ˆ 3 (S) 3 (S) for all S  N implies that S (3 ) t S (3 ) for all members j. Definition 3.5 An allocation scheme is coalition monotonic if, for any ˆ ˜ , and any member j, we have that if profit functions 3 ˜ and 3 ˆ (S) for all coalitions S, which include j, and 3 (T) 3 ˆ (T) 3 (S) t 3 j j ˆ for all coalitions T, which do not include j, then S (3 ) t S (3 ) . Definition 3.6 An allocation scheme is strongly monotonic if, for any ˆ ˜ , and any member j, we have that if profit functions 3 ˜ and 3 ˆ (S )  3 ˆ ( S \ j ) for all coalitions S, which include j, 3(S )  3(S \ j) t 3 j j ˆ then S (3 ) t S (3 ) .

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Rewriting the conditions for strong monotonicity reveals the problems in relation to risk sharing: ˆ S  3 ˆ S \ j 3 S  3 S \ j t 3 ˆ ( S ) t 3( S \ j )  3 ˆ S \ j œ 3 S  3

This reformulation shows that j's incremental profit increases (the first inequality) if, in all the coalitions which include j, the standalone profit would fall more if j were excluded from the coalition (the last inequality). Hence, in a situation where the total profit decreases – but decreases most in the coalitions without member j – the profit allocated to member j should still be increased. This implies that he will not carry part of the fall in total profit. Note that the coalition monotonicity is a special case of strong monotonicity where 3 ( S \j ) 3ˆ ( S \j ) and that the total monotonicity is a special case of coalition monotonicity where 3 (S) 3ˆ (S) for all coalitions which are subsets of N. In other words, strong monotonicity implies coalition monotonicity which implies total monotonicity24.

3.7.2 Consistency Reducing influence costs

When selecting an allocation rule it is important to try to limit arguments and conflicts within a cooperative, cf. Section 2.4 on influence costs. One way to accomplish this is to look for a rule that is not only acceptable or fair when looked at from a total perspective but also when looked at in any sub-group. In effect, no group wants to renegotiate. Such a property is known as consistency or stability in the allocation literature. A practical way to think of it is as follows: In a large cooperative with heterogeneous membership it is advantageous to have an allocation rule which makes it possible to break down the allocation into steps. In this way the profit can first be allocated between business divisions (for example between pigs and cattle) and thereafter be allocated between producer groups within the division (for example between multi-pigs, UK pigs and EU heavyweight pigs). As long as this allocation rule gives the same final distribution of profits using this break-down as with allocating the profit between members in one step, the rule is said to be consistent. Thus, the individual producer shall receive the same profit regardless of whether the profits are distributed to all producer groups at once in a flat structure or whether there is a hierarchical distribution, as shown in Figure 3.5.

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Cooperative

Beef cattle

Dairy cattle

Multi-pigs

UK pigs

Cooperative

Cattle division

Beef cattle

Pig division

Dairy cattle

Multi pigs

UK pigs

Figure 3.5 Flat and hierarchical allocation rules The order does not matter

Intuitive division

Agreement about mergers

Consistency is an attractive property in a payment scheme in a cooperative. A consistent payment scheme prevents arguments about the order of priority in the allocation scheme, i.e. whether a flat or a hierarchical allocation system should be used. Consistency probably also makes it easier to get acceptance of the division principles. It is more intuitively appealing to have one “cooperative” principle that applies at different levels of the organization – rather than to base some divisions of profit on one principle and other divisions of profits on other principles. Consistency also limits the changes in the allocation inside a group, for example the pig producers, when the cooperative expands to include another group, say the slaughter of cattle. This is an important property that may lead to fewer internal arguments in connection with an expansion of business activities. Mathematical representation: To formulate the consistency requirement, we need to define the stand-alone profit function restricted to a coalition T of N. We denote this 3 T . The profit that a coalition S in T can ensure itself is 3T (S )

­ ½ max S 'Ž N \T ®3 ( S ‰ S ')  ¦ S j (3 ) ¾ jS ' ¯ ¿

where S j (3 ) represents the profit received by member j, when the total profit is allocated directly to all members (flat allocation rule).

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We see that the restricted stand-alone profit function defines a new allocation problem among the members in T. The definition hereof is a little complicated as it depends on the allocation of the total profit in the whole set N, i.e. it depends on the direct allocation S j (3 ) . In particular, the total profit to be allocated is what T is allocated in the total, direct allocation, i.e. 3 T (T )

¦S

j

(3 ) .

jT

Now, let S j (3 T ) represents the profit received by member j, when the same allocation rule is used to distribute 3 T between the members of T. Consistency can be formalised as: Definition 3.7 An allocation rule is consistent, if S j (3 ) S j (3 T ) for all coalitions T  N and for all j  T .

3.7.3 Additivity Accounting principles

Accounting principles are another potential source of conflict within a cooperative, and therefore also a potential cause of influence costs. For accounting purposes it is often useful to distinguish between different types of costs and revenues, e.g. revenues from sales in different market segments, costs from processing, costs from marketing, etc. The total profit is then sum of these revenue categories minus the sum of the cost categories. From an accounting point of view it would be convenient if the allocation of revenues and costs could be done for each category and then added up. This would make it possible to present accounts for the whole firm, in which payment to each individual group is split up in various entries for revenues and costs. In order to do this, the resulting payment to each producer group ought to be the same regardless of how many and which categories revenues and costs are split up into. This will be the case if the allocation rule is additiveM. The situation is illustrated below in Figure 3.6. An additive allocation rule gives the same payment to each group, regardless of whether the allocation is made in accordance with the principles of the upper figure, with the distribution of the resulting revenue, or whether it is made in accordance with the lower figure, with payments made according to the results of each revenue and cost category.

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Revenue = sales revenue - processing costs

Group 1

Group 2

Sales revenue

Group 1

Group 3

Processing costs

Group 2

Group 3

Figure 3.6 Revenue allocated in one step or via account categories Mathematical representation: Assume that the stand-alone profit for coalition S can be written as: 3 S V S  F S

for all coalitions S Ž N

where V(S) is the sales revenue for coalition S and F(S) is the processing and production costs for coalition S. Also, let I j 3 , I j V and I j F represent respectively the share of the profit 3 , the share of the sales revenues V and the share of the costs F, which member j is allocated, if the allocation rule25 I is used to do the allocations of the total profit, the total sale revenues and the total costs, respectively. Note that we have previously used S j  3 to denote the allocation of profit to producer j, but we now denote this I j 3 , i.e. we use a new symbol I j . for the allocation principle. We do this because we now allocate not only profit but also individual costs and revenue elements. Additivity can be formalized as: Definition 3.8 An allocation rule I is additive if for any decomposition 3 S V S  F S for all coalitions S Ž N , we have that I j  3 I j V -I j  F for all j. By using this property iteratively, we also get that revenue and costs can be split further, say as

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V S V1 S  V2 S

S

F S

S

F1 S  F2 S

and that the direct allocation of total profits and the indirect allocation hereof via an allocation of the different revenue and cost categories should again give the same final allocation of profit.

3.8 Holistic evaluations Holistic approach Designing a scheme

Modifying a scheme

Summary

So far, we have identified a series of desirable criteria, properties and conditions that we would like cooperative payment plans to have. In a specific application some of these may be more important than others, but in general it is relevant to consider a multiplicity of properties in the evaluation and design of payment schemes. The holistic (systematic) approach of multi-criteria evaluations is a useful step towards choosing a payment scheme. First, inefficient schemes; i.e. schemes that can be improved in some dimensions without worsening others, can be disregarded. Secondly, a systematic comparison of the remaining schemes against the different criteria can ease the explicit or implicit weighting of the different criteria and hereby pave the way for the right choice of scheme. Lastly, in an actual situation, it is often possible to include additional information about the relative importance of different criteria. If this information is included, then the number of relevant efficient choices can be further reduced, helping to identify the final choice. Also, in the adjustment of a given scheme, there is often a focus on one or a few of the drawbacks of the existing scheme. It pays, however, to keep a broader perspective, since it reduces the risk of creating new unforeseen problems when trying to fix the known drawbacks of the existing system. In this section, we shall therefore summarize the criteria identified above in Chapters 2 and 3. In Chapters 4 and 5, we shall analyse more specific payment plans using these criteria. An alternative although overlapping hierarchy of criteria that can guide the design of contracts between producers and processors more generally is discussed in Bogetoft and Olesen (2004).

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3.8.1 Goal hierarchy The overall goal

Hierarchy

Use of hierarchy

Three main criteria

The overriding goal of a payment scheme is to maximise the economic welfare of the members. However, this goal is neither particularly tangible nor operational. Therefore, we divide the overriding goal into a number of subordinate goals which are more operational. These subordinate goals can then be further subdivided, and so on. The hierarchy is organized in order that each level of the hierarchy gives an adequate, comprehensive yet more operational coverage of the goals of the level above. The advantage of establishing such a hierarchy is that it gives a systematic overview of the many considerations which a payment scheme should take into account. The hierarchical method ensures that no important consideration is forgotten. In practice, it operates as a checklist. Discussions and analyses of cooperatives often focus on solving single problems or merely a few problems by using certain payment schemes. But there is, as mentioned above, the risk that in solving one problem, a new problem is created in another area. The advantage of a goal hierarchy is that it gives an overview of the interactions between different sub-goals. It is a system for evaluating the consequences of a payment scheme for a large number of criteria. The first level of division into sub-goals consists of three main criteria: ƒ Coordination - to ensure that the rights members produce the right products at the right time and place. ƒ Motivation - to give members the incentive to take the decisions which are most beneficial to the common aims. ƒ Dynamic adjustment - to ensure sensible adjustments in the future. We have subdivided these three main criteria into a number of more concrete criteria, as shown in Figure 5.3. All of the criteria have been discussed above, so a brief summary will suffice here.

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Members' welfare

Coordination

Efficiency

Dynamic adjustment

Motivation

Individuals

Group

Information Member’s Risksharing Balanced budget

incentives Management incentives

Market signals

The core

Consistency

Monotonicity

Total monotonicity

Coalitionmonotoicity.

Investments

Investments on farms

Hold-up problems

Additivity

Investments in processing

Horizonproblems Free rider problem Portfolio problem

Equality

Member democracy

Figure 3.7 Goal hierarchy for payment schemes

3.8.2 Coordination The right products - as cheaply as possible

A payment scheme must coordinate the actions of members and management, so the common goal is achieved as effectively as possible. This means that the payment scheme must be efficient and the integrated profit as big as possible. In practice, efficiency requires that the producers and the management of a cooperative choose production, processing and marketing plans in order for the right products to be produced at the right time and in the right place, as cheaply as possible. For this to be possible the right information must be available. The form of payment scheme chosen, determines the information requirements for the cooperative and its members. Similarly, the total production should be allocated in order to share risk optimally, ensuring that risks are borne by those who can bear them at the lowest cost. It is also important that the payment scheme should help to reduce risks. There are naturally also a number of technical requirements that a scheme must fulfil to be operable. As we have already hinted at, and will expand on in Chapter 4, one special technical requirement, which

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99

is significant for the other criteria, is the requirement for a balanced budget. It is also important for the functioning of a cooperative that members are treated fairly. Therefore a payment scheme should allocate incomes and expenditures so as to achieve equality between members. The payment scheme must be adopted by a democratic membership. Most cooperatives have the principle of one-man-onevote so that any changes to the payment scheme must be advantageous to at least half the members. Below we give a more detailed description of some of the central criteria for coordination, including efficiency, information needs, risk sharing, equality and member democracy.

The greatest possible profit

A strong requirement

The needs of the cooperative and of the members

Efficiency Efficiency concerns generating the greatest possible profit for sharing between the members. The desire to improve efficiency is therefore an important reason for adjusting a payment scheme and, perhaps, giving up on the classical proportional principle. The desire for efficiency is a very strong requirement from which it is often necessary to depart in order to satisfy other criteria. For example, the desire for equality can mean that a decision is made not to implement the most efficient production plan. The 'social choice' theory contains a number of examples of how some reasonable characteristics of a payment scheme, necessarily cause loss of efficiency26. It is therefore necessary to balance the conflicting claims of efficiency against the other criteria. Models can illustrate the trade-offs between efficiency and other criteria. In Chapters 4 and 5, we shall present several such models. Information When designing or evaluating a payment scheme, it is important to bear in mind how much information the scheme requires to function. It can be appropriate to compromise on efficiency if this reduces the information requirement, creating an administratively simpler system. The information needs can affect both the cooperative and its members. A payment scheme which is administratively attractive for the cooperative can impose a huge burden of information and analysis on its members. An example of this is the use of tradable production rights, as used in New Generation Cooperatives for example, cf. Chapter 2.

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Risks should be borne as cheaply as possible

The sources of uncertainty

Ways to tackle risk

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Risk sharing Agricultural production is exposed to both production and market uncertainty. It is therefore impossible to eliminate income risks. A payment scheme should be designed in order for the risk to be carried as cheaply as possible (or for it to be exploited as well as possible). Risk sharing and insurance arrangements are relevant if the producers are risk averse, i.e., if they consider variations of income to be disadvantageous27. Risk sharing is important in connection with special production. Producers of special products are often tied by special investments, thus it is difficult for them to change their production should demand for the special product fall. In addition, special products are sold on relatively limited markets, so there are fewer possibilities for selling products through other channels if the demand from the target market sector should fall28. Income variation is caused by a number of factors. One cause of income variation is the institutional risk from changes in the politically determined framework. These can be changes in exchange rate policy, trade policy (trade conflicts between the EU and the USA), environmental policy (more stringent requirements for the storage of manure) and so on. Another cause of income variation is the biological risk associated with agriculture. This can either be the particular circumstances on an individual farm or more general conditions affecting all producers (e.g. swine fever). A third main cause of uncertainty is the market risk. Large variations in pig prices in recent years indicate that the sales risk is the most significant cause of uncertainty in the pig industry. Even though it may be impossible to avoid risk entirely, there are various methods for dealing with it. Various causes of income variation may affect producer groups differently. The income variation on an individual farm can be reduced by the farmer diversifying his production so the income is dependent on more types of product. The problem of this approach is that diversification leads to the loss of some of the advantages of specialisation. It is therefore desirable to find a method which enables both the gains from specialisation to be achieved on the individual farm, as well as spreading the income risk across several products. The cooperative form of organisation allows this. The individual producer can maintain his specialised production while spreading risk, if the payment depends on the cooperative's revenues from several products. This risk sharing means that a single producer group does not bear all the losses arising from a fall in sales of one particular product type.

ECONOMIC OBJECTIVES AND CONDITIONS

Risk sharing efficiency

Principal agent literature

Competitive reaction

Over-production can be an advantage

101

Risk sharing can also cause inefficiency. The problem is that a producer group may not have a sufficiently strong incentive to adjust production levels when there is a permanent fall in demand, if other producer groups partially cover their loss of income29. In Chapter 5, we shall further illustrate how the payment plan can affect the information need, as well as the possibility of sharing risk without blurring incentives. There is a large so-called principal agency literature on coordination and motivation in situations with imperfect and asymmetric information. This literature is particularly important in the design of individual contracts, and is the basic approach of Bogetoft and Olesen (2004) mentioned above. In the context of cooperatives, we consider it to be only one of several issues; even if information is perfect, incentive problems remain simply because of the restrictions imposed on the possible payment schemes by the cooperative principles. Market signals A payment scheme not only influences the members of the cooperative, it also indirectly affects others in the market. Therefore, changes to a payment scheme can affect the behaviour of other market players. For example, changes which result in more production can be perceived as an aggressive market signal by the cooperative's competitors. There is an example of this in Schultz and Albæk (1998), which explains the large market share of cooperatives on the basis of the proportional payment rule giving a strategic advantage. Their model analyses competition between a cooperative and a private firm. When a member of a cooperative, using the proportional payment rule, increases his production, the price of the processed products falls. This externality affects both the suppliers of the cooperative as well as the suppliers of the private firm. The private firm pays its producers in relation to the marginal revenues. Therefore, suppliers to the private firm choose the first best production levels and do not create externalities. The intuition of the model is that the externalities that occur under the proportional payment rule, the quantity control problem from Chapter 2, force the private firm out of the market. In this market set-up, it is therefore optimal for the cooperative to retain its payment according to the average price, even if this leads to overproduction. Likewise, a payment scheme with large penalties for low quality could be perceived as a signal to customers that product quality has improved.

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Equality and efficiency

Member democracy and efficiency

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Equality and member democracy It is frequently considered to be a basic principle that the members of a cooperative should feel that they are being treated fairly. In Section 3.2 we have put forward a number of different principles of equality which can be used in judging a payment scheme. Equality is an important principle which it is often sought to satisfy at the expense of efficiency. In Section 2.4 we argued that equality between members reduces the costs on the purchasing side for Danish cooperative slaughterhouses, since equality reduces the influence costs. Most cooperatives are based on the principle of one-man-one vote, which means that changes to payment schemes are only adopted if they are advantageous to the majority of members. On this basis in Section 3.2, we put forward the concept of median equality which seeks to maximise the profit level of the median member, with half the members above this level and half the members below. The idea behind this is that the median member has the decisive vote in a cooperative. As with the equality criterion, majority decisions may mean that a cooperative does not adopt the payment scheme leading to the highest possible integrated profit. The one-man-one-vote principle may also reduce the inefficiency which often arises with the proportional payment scheme. In fact with decisions taken on the basis of one-man-one-vote, it can be expected that at least part of the surplus will not be allocated according to the volume of production, cf. also the discussion in Section 4.8.

3.8.3 Motivation A cooperative consists of many independent decision makers. It is therefore important that the payment scheme gives members and the cooperative's management incentives to behave so the common goal is achieved. In this respect, there is a particular requirement that no one should have an incentive to leave a cooperative which is profitable overall. This is illustrated by the concept of the core. Conflicts of interest between different producer groups in a cooperative can lead to internal disputes causing influence costs, as described in Section 2.4. It is therefore desirable that a payment scheme should be consistent and additive, to reduce disputes about the principles of accounting and the allocation of payments.

ECONOMIC OBJECTIVES AND CONDITIONS

IC

Efficiency versus incentives tradeoff

Management must pursue the aims of the members

Rewarding management

Interaction with the payment scheme

Cooperation must pay

103

Members’ incentives Members of cooperatives act as partially autonomous decision makers. This means that the members' decisions about production are prompted by personal economic incentives. We have formalised this in the requirement for incentive compatibility (IC). It is frequently necessary to sacrifice some production efficiency in order to obtain incentive compatibility. The two basic characteristics of efficiency and incentive compatibility can be incompatible. This is one of the main points of agency theory30.

Management incentives It is not only the members who must be motivated to act in the common interest. This also applies to the professional management of cooperatives. Management can have personal interests which differ from the interests of the members. It is therefore important for the members to supervise the management, as well as otherwise ensure that there is goal congruence between management and members. In terms of management, the large cooperatives probably do not differ greatly from investor-owned firms, so the extensive literature on management motivation applies31. Of course, the widespread use of share options, etc. in investor-owned firms cannot apply to cooperatives, which are not subject to the same valuation in the capital markets. However, it is possible to substitute this by rewarding the management of cooperatives according to the price of a given quantity of primary products or the price of tradable production rights, for example. There is some interaction between management incentives and payment schemes. The payment scheme determines which problems the management are motivated to solve. It also influences what information is available for assessing the management. There is also the possibility of interaction in the opposite direction, with the payment scheme arranged on the basis of what can motivate the management. We believe this interaction is of limited relevance for the design of payment schemes. We therefore take no further account of the motivation of management as a criterion for the choice of a payment scheme.

Participation: IR and the core A cooperative will be weak and in danger of breaking down unless all participants benefit from the cooperation. Above, we have put forward

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the criterion of individual rationality which states that no producer should be worse off from participating in the cooperative. We also defined the stricter core concept that no group of producers should be better off by leaving the cooperation.

Accounting principles

Consistency and additivity It is important that a democratic cooperative should not engage too many resources in the decision process itself32. Internal conflicts will be reduced if the payment scheme complies with the criteria of additivity and consistency. An additive payment scheme increases transparency, because the income and expenditure can be allocated to individual groups, category by category. Consistency is an advantage, because it dispenses with internal disputes about how many stages there should be in the allocation procedure.

3.8.4 Dynamic adjustment Long-term investment

Monotonicity

Investments in farms

Most industries require long-term investment and must live with changes in the market condition in the short and medium term. In pig production, for example, investment in buildings and installations has a lifetime of up to 20 years. Market conditions will typically change considerably during the pay-off time of such investments. It is therefore not enough to design a payment scheme, which has a number of attractive characteristics with regard to efficiency, information requirements and so on, on the basis of current market conditions. It is important to consider how the payment scheme will work in a dynamic world where the conditions continually change. The payment scheme must be designed to be robust toward changes to income conditions. The criteria concerning dynamic adaptability of the payment scheme are monotonicity and investment incentives. We defined a number of monotonicity concepts in Section 3.7 above. Payment schemes which satisfy monotonicity conditions have a certain robustness toward changes to income conditions, because the payment is reasonably adapted to the new market conditions33. In Section 3.7, we argued that the conditions for total monotonicity should be satisfied, so no member should have an incentive to resist cost savings in the cooperative. Nor should producer groups have an incentive to reduce revenues on their own products. This is ensured by coalition monotonicity. It is important to consider, how a payment scheme affects incentives to undertake investments in order to ensure future earnings potential. It would be most unfortunate, if a payment scheme were to undermine the incentive for producers to invest in private cost saving measures. This

ECONOMIC OBJECTIVES AND CONDITIONS

Investments in cooperative

General improvements in effectiveness

Sales promotion

105

would be the effect of a payment scheme which gave all producers the same gross margin for each product. Producers who make specific investments on their farms can sometimes put themselves in a vulnerable position. This is the hold-up problem which can result in under-investment, cf. Section 2.4. In Section 2.4, we discussed a number of general problems with the cooperative ownership structure, which can result in under-investment in the processing stage. We described the horizon problem and the free rider problem, both of which can result in the members paying for an investment without receiving all the benefits of the investment. We also discussed the portfolio problem, which arises when there is a positive correlation between the earnings from primary production and the earnings in the processing stage. The payment scheme is important to how general investments in primary production or market development should be financed. Under one payment scheme it can thus be the cooperative which ought to finance general investments, for example in the development of new pig-pen systems. Another payment scheme may mean that the individual producer groups have better incentives to make general investments than the cooperative as a whole. The payment scheme should not discourage investment in marketing activities. This requirement is met by payment schemes satisfying the conditions for coalition monotonicity. In such a scheme, an investment in market development which benefits the income of all the coalitions which the producer group concerned can belong to, leads to a slightly higher payment to the producer group.

3.9 Conclusions Goals and conditions

In this chapter we have presented a general economic framework for evaluating alternative payment schemes. We have modelled the choice of a payment scheme as a classic decision problem with multiple decision-makers. In this connection we have discussed some of the overall goals which a cooperative could have. Besides this, we have introduced some technical and behavioural conditions which must be respected in the design of a system. In considering the choice of a payment scheme as a decision problem, we have kept to a fundamental idea in economic science, namely to understand behaviour and institutions as an expression of rational choice, where individuals or groups seek the best means for achieving their goals.

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Objectives and conditions

PETER BOGETOFT AND HENRIK B. OLESEN

We have drawn from both classical business economics, as well as from a number of newer theories of business economics, including especially those concerned with the economics of organizations. We have thus defined optimal systems to be those that maximize the integrated profit of producers as well as processors. At the same time, we have pointed out that optimal systems should not only satisfy technological requirements. It is also necessary to include some behavioural conditions, as emphasized by the newer economics of organizations. It is thus important that the various producers and producer groups have individual as well as collective interests, both in participating in collaborations and in making decisions which contribute to maximizing the integrated profit. It is also important that these incentives are dynamic, so that changes in technology or in market conditions are exploited by the cooperative system. It is worthwhile emphasizing that, at least in our approach, the payment scheme does not in itself affect the preferences of the economic agents nor do they have direct preferences for the alternative schemes. What matters is the behaviour which a scheme induces, and thereby how much profit it generates and how this is allocated. To understand and analyze a payment scheme, it must therefore be considered in the light of the production, processing and marketing plans which the scheme leads to. In this way we have arrived at a number of objectives and conditions for the choice of a payment scheme. We have covered: Efficiency, possibly Pareto-efficiency: The scheme should generate the largest possible integrated profit to be shared between the members, or at least lead to a situation in which no one can be better off without others becoming worse off. Equality: A payment scheme should treat all members equally and fairly: Fairness could for example be measured by so-called simple equality, maximin, adjusted maximin or median profit equality. Technological conditions and market conditions: The payment scheme and its associated behaviour must respect the framework set by the technological conditions and market conditions. We have referred to these framework conditions as technical applicability. Balanced budget: The whole of the cooperative's surplus or deficit shall be allocated to the members. Individual incentives: No member should be able to gain from deviating from the basic plans for production, processing and marketing. This has been formalized using the notions of individual rationality and incentive compatibility.

ECONOMIC OBJECTIVES AND CONDITIONS

Hierarchy

Compromise is necessary

More specific schemes and models

107

Monotonicity: Members, or groups of members, must have incentives to improve their own as well as the cooperative's revenue. Consistency and Additivity: Members or groups of members should not have cause to disagree about the priority of distribution or about accounting principles. Collective incentives: No group of members should be able to gain by deviating from the planned production, processing and marketing activities. In particular, every group must get at least its stand-alone profit. This limitation leads to the core solution. In the final Section 4.8, we summarized the concerns in a goal hierarchy in which we organized the different objectives and conditions covered here, as well as the insights from Chapter 2 according to the three main goals of a payment scheme, namely to support coordination, motivation and dynamic adjustments: Coordination: Ensure that the right members produce the right products at the right time and place. Motivation: Give members the incentive to take the decisions which are most beneficial to the common aims. Dynamic adjustment: Ensure sensible adjustments in the future. Unfortunately, it is not possible to satisfy all these goals and restrictions completely in one system. This means that any payment scheme must be a compromise between the different interests and requirements. It also means that it is important to have more precise ideas about what is achievable and how different payment schemes can make tradeoffs between the different goals. To obtain such knowledge it is necessary to study a number of more specific schemes in the context of more specific models of the cost and market conditions. We do so in the next chapters.

Notes 1

The right to residual income is the right to that part of the revenue that remains when all the fixed obligations have been met. 2 Even if the national pricing scheme has in principle been brought to an end, as noted, the idea of costbased payment is still relevant, amongst other things because it is used internally by a number of cooperatives 3 Technically, cooperative game theory is distinguished from non-cooperative game theory by allowing binding agreements. The precise mechanisms used to enforce these agreements are not specified in cooperative game theory. 4 It is noted that these theories do in fact constitute a significant part of modern micro economics. The expansion of the optimisation criteria of traditional economics by these theories is considered by some to be a paradigm shift. Amongst other things this development is due to the acknowledgement that any

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organisation or cooperative enterprise contains both elements of common goals and conflicting interests and partially autonomous agents. This applies independently of whether the cooperation consists of, for example, a cartel, an alliance, a trading relation, or simply a business with more than one employee or owner. 5 In certain circumstances it can be argued that inefficient solutions cannot be ignored but we shall not pursue such a sophisticated line of argument here. See for example Bogetoft & Pruzan (1991) for a thorough discussion of the relevance of the efficiency concept. 6 We follow the tradition in the use of ordinal functions: the value of the function is not important in itself. The only thing that matters is that the preferred system is given a higher value. 7 This is the basic point of view in Søgaard & Just (1995) 8 Schultz & Albæk (1997) use this principle. The idea is that the median member has the decisive vote in a co-operative with one-man-one-vote. 9 As distinct from more general non-transferable benefits. 10 Cf. the discussion below of the conditions for a balanced budget. 11 For example maximization of supplementary payments, maximization of the price including supplementary payment, profit maximization as in a private firm, collective profit maximization of the cooperative and of the members (i.e. integrated profit), cf. for example Helmberger (1964), LeVay (1983) and Bateman, Edwards and LeVay (1979). 12 The possibility of allocating income between members means that the number of payment schemes described by the resulting profit allocations is large and (at least piecewise) linear at the edge. 13 In the literature these principles are often called axioms. 14 See for example Binmore and others (1986), Rubinstein (1982), Sutton (1986), or for a textbook presentation Friedman (1986). 15 See for example Kalai & Smorodisky (1975), Nash (1950), Roth (1979), or for a textbook presentation Friedman (1986). 16 However, it can be possible to obtain a balanced budget, incentive compatibility and, for example, a payment price inclusive of supplementary payment at the same time, if the revenue and cost functions fulfil special requirements. This will typically require either that the revenue function or the cost function are not continuous, cf. Section 4.7. The conditions can be met if the co-operative has growing average revenue. 17 There are many good reasons for maintaining autonomy. The most important economic argument for private ownership in agriculture is presumably that farmers possess considerable amounts of private information and also that it is very difficult to supervise them. This is why the arrangement whereby producers having property rights in, and therefore residual income rights from, agricultural holdings is the best means of achieving optimal behaviour. 18 There is a discussion of this in the debate on payments to organic milk producers in co-operative dairies, see Andelsbladet (1997b). 19 For example, the conditions for the stand-alone profit in a coalition of producers of multi-pigs and UK pigs correspond precisely to the conditions for the contribution for EU heavyweight pigs. M, E and T are the three different production types. We assume that the profit of the co-operative is entirely allocated so there is no waste, cf. the terms of Pareto-efficiency. This means that S  M , E 3  0 ( 7  S  T . If this is included in the requirement for stand-alone profit for the coalition (M,E) the result is: S  M , E 3  Ȃ  Ǽ ȉ  S T t 3  Ȃ  Ǽ œ S T d 3  Ȃ  Ǽ ȉ  3  Ȃ  Ǽ , which is precisely the requirement for contribution from T. Correspondingly, the conditions for the contribution from the coalition (M,E) is reformulated to the condition for stand-alone profit for T: S  M , E 3  Ȃ  Ǽ ȉ  S T d 3  Ȃ  Ǽ , T  3  T œ S T t 3  7 . 20

If the two groups have an amount in common, the profit from the collaboration plus the stand-alone profit for the amount held in common shall exceed the sum of the stand-alone profits for the two groups.

ECONOMIC OBJECTIVES AND CONDITIONS

21

109

However, there can be situations where a producer group ought in fact to receive a lower revenue signal even if the revenue of the co-operation has risen. This is because the incremental revenue of the cooperative can very well fall at the same time as the revenue of the co-operative increase, if, for example, there is a shift towards less price sensitive demand. We will return to this in Section 6.7. 22 See for example Andelsbladet (1997a), Büchmann Petersen (1998), Jyllands-Posten (1998a) or Kent Skaaning (1996) 23 This is indeed the case with the example below. 24 This connection means that we can exclude the possibility of the payment scheme satisfying coalition monotonicity if we know that it does not satisfy total monotonicity. This means that non-total monotonicity leads to non-coalition monotonicity, which leads to non-strong monotonicity. We use this argument in the analysis of the ACA method in Chapter 6. 25 Here we use the general term 'allocation rule' rather than 'payment scheme' because we use the same rules to allocate both revenues and costs. To avoid confusion of terms we have restricted the use of the term 'payment scheme' to describe situations where revenue or profits are distributed. 26 These results are frequently known as impossibility theorems. 27 See Section 3.1. 28 See Chapter 2. 29 Cf. Bogetoft (1996) 30 See e.g. Bogetoft (1994). 31 See e.g. Milgrom and Roberts (1990). 32 See Hansmann (1996) for an analysis of the costs of collective decision making, as well as Sections 2.4 and 3.8 in this book on influence costs. 33 See Section 3.7.1.

4 Models of cooperatives

Single or multi product cooperatives

Examples of trade-offs

Single product payment schemes In this chapter, we introduce more specific assumptions about the production, processing and market conditions of the cooperative. These more specific assumptions in turn allow us to derive more precise properties of alternative payment schemes. We present a classic model of a cooperative, and emphasise its similarity with a Cournot competition model. We demonstrate the over-production problem that arises in ‘thin markets’ and we discuss a number of suggestions for reducing this problem. We also discuss the fundamental problems of allocating profits and equity among the members and consider how this affects incentives. Our main focus is on simple settings where the members produce the same type of good, the single product homogenous goods case. The heterogeneous goods, multi-product, case is considered in more detail in Chapter 5. Many cooperatives can be modelled as single product cooperatives. In reality, there may be variations in quality and characteristics of the products produced by different members, but this may be handled by simple quality add-ons to the basic payment plan, cf. for example the price adjustment depending on deviations from target slaughter weight as illustrated in Chapter 2. Also, many multiproduct cooperatives effectively operate as a series of parallel single product cooperatives, as it has been decided to allocate earning directly to the different product lines. In Chapter 3 we suggested a number of desirable properties for a payment scheme, and we derived a series of technical and behavioural constraints which these schemes should take into account. We shall investigate several of these criteria in this chapter. By studying alternative schemes and alternative production and market settings, we gain insight into the necessary trade-offs between the different criteria.

4.1 Technologies and markets We start by describing the basic elements of a classical model of a cooperative. We also discuss, in summary form, how these elements can be determined in practice.

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To make it less abstract, we will usually refer to a case where the cooperative being studied, is a cooperative slaughterhouse. In a pig slaughterhouse quantities can be measured in units or in kilos, possibly normalized into standard pigs or kilo equivalents to take quality differences into account. For the sake of simplicity, we refer here to pigs measured in numbers and, for the time being, we assume that all the pigs are identical. The slaughterhouse kills and processes the pigs received, and sells them in different cuts or processed products, cf. Figure 4.1. Member 1 Member 2 Co-operative

Processed products

Member N

Figure 4.1 Production chain Primary production

Total costs

The production conditions in the member firms, the individual farms for example, can be described in a number of ways. For our purpose it is sufficient to consider the total production costs at different production levels. A member’s cost function =

the member's production costs at different production levelsM.

Based on the cost function it is possible to determine the marginal costs; i.e., the increase in production costs as the level of production increases by one unit Marginal costs

The marginal production costs of a member =

the member's additional costs for the production of one extra unitM.

We also use the concept of average costs. Average costs

A member's average production costsM. =

the member's total production costs divided by the total number of units produced

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In the case of a cooperative slaughterhouse, the marginal costs are the costs of producing the last pig, while the average costs are the total production costs divided by the total number of pigs. In theoretical models it is generally assumed not only that the costs are increasing, but also that the marginal costs are increasing, at least in the interval of production1. In agriculture, for example, this is often a reasonable short term assumption due to the fixed capacity of farm buildings, the limited possibility of buying up neighbouring farms in the short run, environmental restrictions and so on. Falling (or rising) average costs correspond to the advantages (or disadvantages) of economies of scale. Figure 4.2 illustrates typical textbook assumptions about total costs, marginal costs and average costs. DKr.



Total costs c j q j

Production q j

DKr.

Marginal cost c j ' (q j )

Average cost c j (q j )

Production q j

Figure 4.2 Primary producers' production costs

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Practical production decisions

Methods for determining the cost functions

Processing

PETER BOGETOFT AND HENRIK B. OLESEN

Naturally, a number of more detailed production decisions lie behind this summarised description of primary production. For example, a pig producer must decide which feed and what other inputs to use, given prevailing market prices, etc. The pig producer must also decide how to organise his herd, given the availability of piggery buildings, the rules for the storage and distribution of manure, available land and so on. Depending on the time horizon, costs can either be defined narrowly, so as to include only variable costs, or broadly, so as to include the expense of capital and financing costs. In practice there are at least 4 ways to estimate the costs. It is possible to model all the detailed production decisions by using a traditional production theory, for example by formulating a linear programming model2, where the facts concerning the farms are combined with market information and knowledge on growth, disease, etc. Solving the model for the minimum costs associated with a given quantity gives the cost function. It is also possible to use internal accounts to make cost calculations based on the previous performance of the farm in question, taking into account the skills of the farm management. This corresponds to the principle used by Danske Slagterier (The Danish Federation of Pig Producers and Slaughterhouses) in establishing the production costs of piglets and slaughter pigs for use in the recommended prices for piglets3. It is also possible to establish how the primary producers themselves evaluate their marginal costs by using interviews, for example, by asking producers how they would change their production given an increase in the price paid4. In this way it is possible to calculate their marginal costsM. Finally, it is possible to describe the relationship between production levels and costs by using statistical methods. Statistical analysis can be done using a cross-section or panel data about comparable farms, for example data from De Danske Landboforeningers (The Danish Farmers' Union) accounts database, data from experimental stations and suchlike5. The production and marketing conditions of the cooperative can likewise be described in a number of different ways. For our purpose it is sufficient to have a summarised description of how the revenue (prior to the payment to members); i.e., gross (sales) revenues minus processing and storage costs, depends on the total production received by the cooperative6.

SINGLE PRODUCT PAYMENT SCHEMES

Revenue

The cooperative's revenue function =

Marginal revenue

115

gross revenues - sales costs - processing costs – storage costsM.

We use the term revenue for the cooperative’s gross revenue minus processing and marketing costs, because we analyse the cooperatives from the producers’ perspective. The revenue in the cooperative is the same as the members' sale revenues, because of the principle of balanced budget. Instead of the revenue function, or derived from it, it is possible to determine the marginal revenue; i.e., the increase in revenue when one additional unit of the primary product is produced The marginal revenue of the cooperative =

Average revenue

the additional revenue obtained from the processing and sale of one extra unitM.

We also use the term 'average revenue'; i.e., the average revenue per unit of primary product The average revenue in the co-operativeM = total revenue divided by the total units of the primary product produced.

The price paid to members

The average revenue corresponds to the price per unit which the members receive in a traditional payment scheme in which each unit is paid the same price. In the literature7 it is often assumed that product processing is a simple matter in which one unit of primary product gives one unit of final product. For example this could refer to a slaughterhouse which merely sells carcasses (in pairs). In this case the average revenue will simply be the difference between the sales price and the average processing costsM; i.e., The average revenue of the co-operative =

=

the price paid to the members (incl. supplementary payments) in a traditional co-operative the market price – the average processing costs of the cooperative.

These general formulas enable us to handle complicated processing and market conditions without significantly complicating the presentation of the arguments.

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Typical assumptions

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In economic literature it is typically assumed that revenues increase as production increases, but at a decreasing rate. This means that the marginal revenue falls (at least in the interval of production). This can be the consequence of production without benefits from economies of scale. Another possibility is that while the cooperative does have economies of scale in production, there is decreasing return on the market. That is, the production advantages are outweighed by the price reduction necessary to sell larger quantities on the market (i.e., a market with so-called imperfect competition with a falling demand curve). This is the expectation of the Danish pig industry for special production which is sold on 'thin' markets8. DKr.

Revenue R Q

Production Q

DKr.

Average revenue R Q Marginal revenue R' Q Production Q

Figure 4.3 A cooperative's revenue functions

SINGLE PRODUCT PAYMENT SCHEMES

A summary of complicated relations

The possibility of determining the revenue function

Cooperatives ought to know their revenue function

Decisions of cooperatives

117

As with an individual farm, a number of complicated processing and marketing activities are hidden behind this summary. The description of revenue is further complicated by the fact that it summarises both income and costs, whereas the description of the farm situation concerns costs only. A cooperative slaughterhouse, for example, must decide week by week, or even on a daily basis or by the hour, how the pigs received are to be butchered, processed and sold, whether as carcasses, sides, hams or as more processed products. These decisions must be taken in the light of current market prices in a number of international markets, and with reference to existing contracts, rules for working hours, machine capacity and so on. The same range of techniques used for modelling the cost conditions of individual farms, can be used to derive a summarized description of the revenue function. For example, detailed production and marketing models can be formulated as linear programming problems. Revenue estimations can also be based on internal accounting data and detailed studies of processes, and statistical estimations of cross-section and panel data. Similarly, interviews can identify the management’s expectations of changes in revenues for given changes in the production volume9. It is to be expected that cooperatives possess good knowledge of their revenue function. However, the opposite view is met within cooperative circles on the grounds that it is not the objective to optimise the size of the firm10, but to earn as much as is possible on the primary products received. The objection to this could be that cooperatives should be able to see the relationship between the primary products supplied and the revenues achieved during different periods. This was the basis for the National Pricing System's continuous adjustments of the base price for pigs11. Moreover, cooperatives must consider the revenue potential from different quantities of primary products, in order to make optimal processing decisions. Above we have omitted any detail about the cooperative from the summarised description. However, sometimes it can be beneficial to describe some of the more detailed arrangements or decisionsM of a cooperative, for example the allocation of the sales to different markets, the choice of marketing strategy, the choice of the amount held in reserve, etc.

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Mathematical representation In the description of a cooperative, two types of variable are included, on the one hand the individual members' production decisions q j = member j's production and on the other hand a variable or vector to describe the decisions of the cooperative V = (part of) the decisions of the cooperative

The costs for producer j with a production of q j can be described by Total production costs

c j (q j ) Marginal costs dc j (q j ) dq j

c j '(q j ) #

c j (q j ')  c j (q j ) , for small  q j ' q j q j ' q j

Average costs j

c (q j )

c j (q j ) qj

In interviews the marginal costs can be estimated by asking about it directly. Alternatively, one can ask about production growth

q j ,new  q j which would be caused by a price increase from p new

to p . Using this together with the fact that it is optimal for the member to produce until marginal costs becomes equal to the price received, we can establish two points on the marginal cost curve

c j '(q j ) # p current and c j '( q j , new ) # p new The cooperative's revenue with a total supply of Q units, where Q q1  q1  ...  q n , can correspondingly be described by Total net revenue R (Q )

SINGLE PRODUCT PAYMENT SCHEMES

119

Marginal revenue R '(Q )

dR  Q dQ R(Q ')  R(Q) # , for small  Q ' Q Q ' Q

Average revenue

R(Q )

R(Q) Q

We use the symbols P (Q ) for the members' revenue per unit in a traditional cooperative, i.e.

P (Q )

R (Q )

If the traditional cooperative has an 11 ratio between primary production and processed production, the price to producers can be considered as the final goods price minus the processing and marketing costs P (Q )

Pmarket (Q)  C coop (Q)

When summarising the cooperative's decisions with the vector V , it is natural to consider the revenue as functions of both Q and V ; i.e., the total revenues, marginal revenues and average revenues become R(Q, V) , R '(Q, V) wR / wQ and R(Q, V) .

If we assume, as is often prescribed, that the cooperative should try to get the most possible out of the primary products supplied, the result is R (Q )

max R (Q, V) V

i.e., the standard revenue function gives the highest possible revenue for a given supply of primary products12. We have previously referred to the fact that this may not be the optimal policy in a situation with partially autonomous members - in certain circumstances it can be worth threatening to make sub-optimal decisions. Technically this corresponds to the cooperative being able to affect the shape of R(Q) through the choice of V ; it is not always an advantage for this to be as large as possible for all possible values of Q. In a traditional cooperative the revenue is allocated in proportion to the total number of delivered units; i.e., producer j receives

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x j ( q1 ,.., q n , V)

qj R(Q, V) Q q j R(Q, V) q j P(Q, V)

where V is the cooperative's production and marketing plan.

4.2 The traditional payment scheme

Profit

A traditional cooperative allocates the revenues in proportion to the quantities delivered. This can also be expressed by saying that the price paid is equal to the cooperative's average revenue. The members each seek to maximise their profits; i.e., they maximise the expression Profit

The autonomous solution

= =

sales revenue - production costs price x quantity - production costs

The individual member maximises his profit by increasing his production until his marginal cost equals his marginal revenue. In a traditional payment scheme his marginal revenue is equal to the cooperative's average revenue, corrected by what he gains or loses because his production marginally changes the average revenueM. This solution, which corresponds to the situation in a traditional cooperative, is often called the autonomous solution because the individual member behaves autonomously. Figure 4.4 illustrates this solution for the individual member. DKr.



Marginal cost c j ' q j

Marginal payment P Q  P' Q ˜ q j

j Production q

Figure 4.4 The autonomous solution

Production q j

SINGLE PRODUCT PAYMENT SCHEMES

Approximation of the autonomous solution

121

The individual member thus produces up to the point where his marginal costs equal his marginal revenue; i.e., the average revenue adjusted by what he loses by the lowering in the average revenue of the cooperative. This last part (adjusting to make up for what he loses by changes in the average revenue of the cooperative) is nearly 013 in cooperatives with reasonable numbers of members. Therefore, if we ignore this element, we get the following simple approximation of the autonomous solution The marginal costs of the producer

Average revenue of the cooperative

=

In this model the producer will increase his production, as long as his costs for producing an extra unit are less than the cooperative's average revenue. Mathematical representation We consider the cooperative described above, in which each of the n producers produces q j units, j=1,..,n, so that altogether Q = q 1 + q 2 + ... + q n units are supplied to the cooperative. Producer j’s costs are c j (q j ) . The cooperative's revenue before payment to members is R (Q) , and P(Q) = R(Q) is the average revenue on the total supply Q . In a traditional cooperative, revenue is allocated in proportion to the quantities supplied. The j'th producer will therefore choose a production level which corresponds to

Max j q

qj n

∑q

n

R (∑ q k ) − c j ( q j ) k =1

k

k =1

or n

Max P (∑ q k ) q j − c j ( q j ) j q

k =1

Note that, the optimal production level for producer j depends on the production levels of the other producers, since these affect his payment. Therefore, in order to determine the production level in a traditional cooperative, it is necessary to find equilibrium. Technically this situation corresponds to a Cournot equilibrium between a number of producers in a market. The first order condition for the optimal solution is

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c j '(q j ) = P(Q) + P '(Q)q j

(4.1)

for all producers j = 1,.., n . The equilibrium is found by solving these equations simultaneously. The often used approximation to this problem corresponds to solving c j ' ( q j ) = P( Q )

(4.2)

for all producers j = 1,.., n . Of course, if the cooperative sells in a perfectly competitive market and there is not economies of scale in processing, P’(Q)=0, and the two solutions coincide.

4.3 The wise chairman’s solution The best conceivable solution

In order to assess the traditional payment scheme, it is convenient to compare it to a benchmark like the best conceivable solution. We shall refer to this as the solution of the wise chairman, an analogy of what is sometimes called the central planner’s solution in general economic texts. In fact, it is our firm belief that a wise chairman in a cooperative can have an important impact on the outcome and contribute to the cooperation approximating the central planner’s solution. An important task of chairmen, at least in Danish agricultural cooperatives, has been to explain to the members the positive and negative synergies amongst them, and to appeal to the members to think in cooperative terms as opposed to in individual terms. As we shall see, it is precisely the ability to restrain the pursuit of individual private interests that allows the above cooperative solution to be improved on. Before turning to the wise chairman’s solution in the present situation, let us define it in more general terms using the terminology of Chapter 3.

4.3.1 Wise chairman in general The theoretical optimal solution

In theory, and without reference to the experiences of Eastern Europe, a central, well informed and disinterested planner can create the best system. Instead of a planner, we shall here talk about the wise chairman, as explained above. Formally, the wise chairman’s solution is defined as the solution to an optimisation problem under constraints M

SINGLE PRODUCT PAYMENT SCHEMES

Maximize (subject to)

The problem for the wise chairman

Principal-agent theory

Uncertainty

123

Integrated Profit Technical Applicability Balanced Budget Individual Rationality Incentive Compatibility The problem for the wise chairman is to find a plan for the production level of the individual members as well as for the cooperative's processing and marketing, which gives the highest possible integrated profit. At the same time there must be a payment scheme which gives a balanced budget, and which ensures that the members want to stay in the cooperative. Lastly, the autonomous members should not want to deviate from the production planned by the wise chairman14. This definition of the ideal result for a cooperative is largely in line with the standard problem in the literature on principal-agent theory15. This gives a considerable theoretical basis for the design of payment schemes. The principal-agent literature contains a large number of conclusions about what payments will depend on, how strong the incentives should be (in other words how big the penalties and rewards should be), how the information system (for example the accounting systems) can improve payment schemes, how a communication process, for example an annual budgeting procedure between the principal (in this case the cooperative) and the agents (in this case the members), can help, and so on. In this present book we draw on the general lessons from this literature, but do not enter into it in any great detail. The aim of this book is to focus on the interaction between the internal payment schemes, the members and the market, and for this purpose, the literature dealing with principal-agent theory is only one part, albeit an important part, of the picture, cf. Chapter 1. The principal-agent literature has the most to offer in the study of the individual member's contractual relations with the cooperative. In Bogetoft and Olesen (2004) we give a holistic approach to contract design in agriculture based on this literature, and we illustrate the applicability of this framework in the analysis of a series of actual contracts between producers and processors. A synthesis in terms of ten rules of thumb is presented in Bogetoft and Olesen (2002). In the principal-agent literature, the problem is often further complicated by a certain amount of 'background noise' in observing producers’ inputs. It is thus not possible to determine with certainty what inputs the individual producers use or what their costs are16. It is naturally relevant to include this kind of uncertainty in the problem for the wise chairman, and we return to this question below. Among other

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The upper limit for profit

Cost of more requirements

PETER BOGETOFT AND HENRIK B. OLESEN

things, we discuss the significance of risk and risk sharing between the members. However, for the present, we suppress uncertainty and asymmetry of information in order to simplify the presentation17. With this simplification in mind, it is not too complex to describe the solution to the problem for the wise chairman in a standard setting; i.e., in the context of the standard cooperative model. We shall do so momentarily. The wise chairman’s problem as defined above does not include all the elements usually used to define a cooperative. It includes a minimum of conditions, thus giving an upper limit for what can be achieved in a cooperative by a suitable design of payment scheme. In this way the problem gives a useful measure of how well different payment schemes may function. If additional conditions or rules are included, the value of the problem; i.e., the integrated profit, will fall. The fall in the integrated profit thus represents the cost of the supplementary rules. We can, for example, see what the traditional proportional rule costs in the form of reduced integrated profitM. We do this below. We could also require open and voluntary membership, where it is accepted that members can leave and join. We could thus model missing membership as a supply of 0 and a payment of 0. This would mean that individual rationality must hold when production (and payment) is positiveM. In the same way we could calculate the cost of requiring equality in some other manner (for example as set out in Section 2 above), or a requirement that certain conditions, for example parts of the marketing plan, should be decided by majority vote. Mathematical representation We can summarize the wise chairman's problem more technically as follows n

R (q1 ,.., q n , σ) − ∑ c j (q j )

Max 1 n 1

σ , q .., q , x ,.. x n

j =1

s.t. n

∑x

j

( q1 ,.., q n , σ) = R (q1 ,.., q n , σ)

∀q1 ,.., q n , σ

BB

j =1

x j ( q1 ,.., q n , σ) − c j ( q j ) ≥ π j

∀j

IR

x ( q ,.., q ,..., q , σ) − c (q ) ≥ j

1

j

n

j

j

x j (q1 ,.., q j ',..., q n , σ) − c j (q ' j ) ∀j , q ' j

IC

SINGLE PRODUCT PAYMENT SCHEMES

125

where BB is the balanced budget constraint, IR is the individual rationality constraint, and IC is the incentive compatibility constraint. The wise chairman's problem is seemingly a very complicated problem. Not only must production, processing and marketing plans be chosen, but also payment schemes (i.e., functions) are in the choice set. Given the apparent complexity, it is worth noting that when there are a finite number of possibilities for production, processing and marketing, the problem is actually reduced to an ordinary linear programming problem. Therefore, in some situations it is possible to solve the problem by using standard programmes, and just as importantly, it is always possible to find an arbitrarily good approximation to the problem by using a standard programme. If one wishes to calculate what the traditional allocation rule would cost in the form of a lower integrated profit, this can be done by adding the following conditions x j ( q 1 ,.., q n ,σ ) =

qj R( q 1 ,.., q n ,σ ) ∀q 1 ,.., q n ,σ Q

Traditional allocation rule Open membership can be modelled by replacing the traditional conditions for individual rationality with the following conditions x j (q1 ,.., q n , σ ) ≥ 0 ∀q1 ,.., q n , σ

[

q j x j (q1 ,.., q n , σ ) − C j (q j ) − π

[

j

]≥ 0

x j (q1 ,.., q n , σ ) x j ( q1 ,.., q n , σ ) − C j (q j ) − π

j

]≥ 0

∀j , Open membership The idea behind this model is that j=1,…, n now represents potential j 1 n j j j members. If x ( q ,.., q ,σ ) − C ( q ) − π < 0 then producer j will not choose to be a member. The last two conditions now ensure that j 1 n q j = 0 and x ( q ,.., q ,σ ) = 0 , in other words, non-member j delivers no production and receives no payment. Producer j has a preference (at least weakly) for membership if x j ( q1 ,.., q n , σ ) − C j ( q j ) − π j ≥ 0 . In this case there are therefore no limits on x j ( q1 ,..,q n ,σ ) and q j , apart from the usual IR and IC conditions. Note that IR is immediately satisfied in this case and that is precisely why the producer chooses to be a member.

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Example: In the example from Chapter 3.5 with the two pig producers who form a sales company, the wise chairman's ideal solution could be that revenue should always be shared equally. In this case the payment to the two producers in each of the four instances would be Producer 2 Producer 1 Production 5,000 Production 10,000

Production 5,000 (5, 5) (6.3, 6.3)

Production 10,000 (6.3, 6.3) (7.5, 7.5)

Table 4.1 Payment with equal allocation and the resulting profits would be Producer 2

Production 5,000

Producer 1 (5-3, 5-2) = (2, 3) (6.3-6, 6.3-2) = (0.3, 4.3)

Production 5,000 Production 10,000

Production 10,000 (6.3-3, 6.3-5) = (3.3, 1.3) (7.5-6, 7.5-5) = (1.5, 2.5)

Table 4.2. Profit obtained with equal allocation We see that the only Nash equilibrium exists when both producers produce 5,000 pigs. Since this maximises the integrated profit, and further since the solution gives a balanced budget, is individually rational and incentive compatible, the equal allocation is the solution to the wise chairman's problem.

4.3.2 Wise chairman in standard cooperative setting

Wise chairman’s objective

We can now return to the problem of finding a benchmark for the traditional payment in the context of the standard cooperative model defined by the cost and revenue functions from Section 4.1 The wise chairman will maximise the total profit which the members can obtain. Thereafter he allocates this total profit appropriately between the members. It can also be said that the wise chairman attempts to create as large a cake as is possible to be shared between the members. The wise chairman thus maximises the integrated profit; i.e., Integrated profit

=

the cooperative's revenue - the members' total production costsM.

SINGLE PRODUCT PAYMENT SCHEMES

Chairman’s optimal solution

127

The integrated profit is maximised when all the members produce so their marginal costs are equal to the cooperative's marginal revenue. The wise chairman therefore ensures that they will all produce, as long as their marginal costs can be covered by the cooperative's marginal revenue. This condition is satisfied when every single member produces until his marginal costs equal the average revenue of the cooperative, adjusted by what he and all the other members gain or lose because his production alters the average revenueM. The adjustment is almost always significant, even in cooperatives with many members. This adjustment is the difference between the autonomous solution referred to above, and the wise chairman’s solution here. Individual members do not take into account how their production affects the price which others obtain. This is part of the equation for the wise chairman. It means that he takes the negative synergies between the producers into account. Mathematical representation The wise chairman solves the following problem n

n

j 1

j 1

Max R (¦ q j )  ¦ c j ( q j ) 1 n q ,.., q

or equivalently n

n

n

j 1

j 1

j 1

Max P (¦ q j )¦ q j  ¦ c j ( q j ) j q

The first order condition for this problem is c j '(q j )

P (Q )  P '(Q )Q , for all j 1,.., n

(4.3)

The optimisation criteria in the wise chairman's solution is equivalent to c j ' (q j )

R' (Q) , for all j

1,.., n ,

which also corresponds to what is found directly from the first formulation above. Below we also use the producers' minimal total costs, which we refer to as Call (Q ) . This indicates the minimal production costs associated with the production Q. With the determination of Call (Q ) it is assumed that Q is allocated between the individual producers in the most effective way; i.e., so their marginal costs are the same.

128

The aim of the cheapest possible production

PETER BOGETOFT AND HENRIK B. OLESEN

It is helpful to introduce the producers' minimum total costs. These indicate the total primary production costs when the total production is allocated between the individual producers most effectively. The associated marginal production costs are particularly easy to work with. They are found by making a horizontal aggregation of the individual marginal cost curves (as an optimal allocation corresponds to all producers having the same marginal costs) and constitutes what, in a market for primary products, will be the aggregated supply curve. Minimum total production costs =

primary costs when the total production is allocated as effectively as possible

Marginal total production costs =

the primary producers' aggregated supply curve

The wise chairman's solution is illustrated in Figure 4.5 DKr.

Producers’ aggregated supply Call ' Q

c1 ' c 2 ' c 3 '

Marginal revenue R' Q

1

q q

2

q

3

Q

1

1

q  q ...q

n

Production q j

Figure 4.5 The wise chairman's solution If we consider a large cooperative, in which the adjustments to the average revenues18 of the autonomous solution can be ignored, we can * illustrate the autonomous solution Qtrad .coop corresponding to a * traditional cooperative and the wise chairman's solution Qwise chairman in

the same diagram, as illustrated in Figure 4.6.

SINGLE PRODUCT PAYMENT SCHEMES

DKr.

C

Producers’ aggregated supply Call ' Q

D

E

B A

129

F

Average revenue R Q Marginal revenue R' Q

O

Qwise chairman Qtrad. coop

Production Q

Figure 4.6 Production with traditional payment and with a wise chairman

Over-production

The illustration in Figure 4.6 corresponds to what is found in the traditional literature19. Strictly speaking it is a bit misleading because it is based on an approximation of the traditional payment scheme. The approximation does not take account of the fact that an individual producer can influence the cooperative's average revenue. This is equivalent to the members being in perfect competition with each other. When account is taken of the effect that an individual member can have on the average revenue, the difference between the wise chairman's solution and the traditional solution is less. This can be quite significant, especially in small cooperatives with a steep demand curve20. Figure 4.6 shows the situation when the marginal revenue is below the average revenue in the relevant production area. In this case the traditional cooperative produces too much, Qtrad.coop, as opposed to Qwise charman. This is the over-production problem in traditional cooperatives which was introduced in Chapter 2 under the heading of the quantity control problem. We can even measure the problem. In the wise chairman's solution the producer surplus is equal to the area OCDF. In the traditional cooperative the producer surplus is only equal to the triangle OBE. The difference between these areas equals the loss due to the failure of quantity control.

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PETER BOGETOFT AND HENRIK B. OLESEN

4.4 Production of special pigs – an example To illustrate the solutions in a traditional cooperative and in a cooperative dictated by the wise chairman, we consider the following example. The actual numbers in this calculated example do not reflect the real world, but they are on the other hand not entirely unrealistic. Example: We will now consider a small production of special pigs within a cooperative. The revenue of special pigs falls from 1,000 DKr. per pig to 500 DKr. per pig as the production increases from 0 to 400,000. This means that P (Q ) 1.000 

1.000 Q 800.000

Let n be the number of pig producers who can supply this special pig. We assume that the producers have the same constant costs c per pig; i.e., c j ( q j ) cq j We assume that the cost per pig, c, is 600 DKr. Solving the above first order conditions (4.1). (4.2) and (4.3) gives the resulting production levels

Production of individual producer q j Total production Q Average revenue P(Q) Profit of the individual producer ( P( Q )  c )q

Total Profit

Traditional cooperative slaughterhouse

Wise chairman's solution

Approx. of cooperative slaughterhouse

800 1.000  600

800 1.000  600

800 1.000  600

n 1

2n

n

160.000

320.000

320.000

n n 1

1.000  600n

1.000  600

n 1

2

800

(1.000  600) ( n  1)

2

2

800

800

(1.000  600) 2 4n

600

0

j

128

n ( n  1) 2

128

1 4

0

Table 4.3 Traditional payment versus wise chairman's solution

SINGLE PRODUCT PAYMENT SCHEMES

A monopolist

The more producers the greater the problem

Optimal with just 1 member

131

It is worth emphasising three conclusions based on the above example. The wise chairman behaves like a monopolist with n production units. Under his leadership all members must nearly halve their production. On the other hand, they obtain a significantly better price and resulting profit. Figure 4.7 below shows how the producers' individual and collective profit depends on the number of members. The figure likewise shows the individual production levels. The number of producers is decisive to the problem of overproduction. Firstly, it affects the quality of the approximation. This is because a relatively large special producer has significant influence on the revenue of a cooperative, which it recognises and therefore adjusts quantities downwards relative to the approximation21. Secondly, the number of producers affects the gains achieved by having a wise chairman. The larger the firm, the more the wise chairman will improve the situation, measured, for example, by total profit. We can also see that the optimal size of a cooperative in a thin market is one member. In that case, he operates like a monopolist which is also the solution recommended by the wise chairman. The more members there are, the greater the internal competition will be, and the lower the profit, unless the cooperative either changes its policy of free delivery rights or the principle of proportional payment. In Section 4.6 we discuss the various possibilities of doing this.

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PETER BOGETOFT AND HENRIK B. OLESEN

Total in 1.000 pigs per producer 180 160

Approximation. of cooperative

140 120 Traditional. cooperative

100 80 60 40 20

Wise chairman 0

5

10

15

20

Number of special producers

Profit per producer, 1.000 DKr 35.000 30.000 25.000 20.000 15.000 10.000

Wise chairman

5.000

Traditional cooperative 0

2

4

6

8

10

12

14

16

18

20

Number of special producers

Total profit in millions of 35

Wise chairman

30 25 20 15

Traditional cooperative 10 5

0

5

10

15

Number of special producers

Figure 4.7 Comparison of traditional cooperative and the wise chairman's solution

20

SINGLE PRODUCT PAYMENT SCHEMES

133

4.5 Optimal, under- or over-production Traditional payment scheme not always problematic Constant average revenues

Before we look in more detail at the problem of over-production and its possible solutions, it is worth emphasising that a cooperative does not always lead to over-production. On the basis of the analysis in Figure 4.6 it is possible to construct Table 4.4 From the table it can be seen that the production is optimal in a cooperative when the marginal average revenue is 0; i.e., when the average revenue is constant. This is sufficiently important to be formulated as a proposition. Average marginal revenue

Total production

Problem in a traditional cooperative None (optimal production)

P' ( Q ) 0

Qtrad .coop

P' ( Q ) ! 0

Qtrad .coop  Qwise chairman

Under-production

P' ( Q )  0

Qtrad .coop ! Qwise chairman

Over-production

Qwise chairman

Table 4.4 A cooperative's production relative to the optimal production Proposition 4.1 Optimality of traditional payment. When the average revenue is constant, a cooperative with a traditional payment scheme is an optimal way for the members to be organised.

Increasing average revenues

For example, this could be the case if the cooperative sells its final goods on perfectly competitive markets, and if there were no significant advantages or disadvantages to economies of scale in processing. This is not an unrealistic characterisation of the original situation in the Danish pig industry. We now look at a situation with increasing average revenues22. In this case the usual payment principles lead to under-production. Such a situation can arise, for example, if the company has advantages from economies of scale in processing, and the final goods are sold on markets which are not sensitive to quantity. Increasing average revenues give an economic rationale for open membership in cooperatives. It is even worth while for existing members to give new members slightly better terms, because their

134

Decreasing average revenues

More detailed discussion

Other solutions

PETER BOGETOFT AND HENRIK B. OLESEN

extra production will benefit existing members through the increased average revenues. When the average revenues are increasing, cooperation is worthwhile - there are positive gains from cooperation. This is an example of positive (intra-product) synergy between members. It leads to under-production because individual members do not gain all the benefits from their contributions. By increasing his production, a member increases the price which all members obtain, but as he can only gain from the increased revenues on his own production and not on the whole of the production, he under-produces. This is an example of the general problems of co-ordination and motivation described in Section 2.5. The last example is the situation where there are decreasing average revenuesM. With the usual payment principles such a situation leads to over-production. This is the situation illustrated in Figure 4.6. Decreasing average revenues and the associated over-production will occur, for example, when the company operates close to its capacity limit and therefore has declining returns to scale in processing. However, it is more relevant to think of situations with a 'thin' market or a 'niche product,' which can only be sold in larger quantities if the price is sufficiently reduced. Decreasing average revenue is an example of negative (intraproduct) synergy. The individual member does not carry all the losses associated with the fall in revenues caused by his production, so he over-produces, cf. Section 2.5. Below in Section 4.6, we discuss a number of solutions to the problem of over-production. Our detailed analysis in the next section concerning the situation with decreasing average revenues can easily be applied in parallel to the situation with increasing average revenues. We conclude this section with two further results from cases with constant average revenues. In this situation the traditional system is optimal, as stated above. The traditional payment scheme is, however, not the only scheme which leads to an optimal solution. The corresponding solution is also achievable if we have several investorowned processors that compete for the producers' production23. Alternatively it is possible to obtain optimal production levels even if the full profit does not accrue to the producers themselves. This is possible with only a single buyer (processor) of primary products who enters into contracts for supply prior to the start of production. The benefit of such contracts is that there is neither so called double marginalisation, nor the hold-up problem which otherwise hampers this form of organisation24.

SINGLE PRODUCT PAYMENT SCHEMES

135

We can summarise these two observations as follows Proposition 4.2 With constant average revenues and perfect information, a cooperative is not the only optimal form of organisation. Asymmetrical information

Above it has been assumed that the producers have full information about everyone's production costs. If this assumption is changed, so that the individual producer's private production costs are known only to himself, he will naturally try to exploit this in negotiations with a buyer or an investor-owned processor - or indeed with a cooperative. For example he will pretend to have higher production costs than he actually has, and therefore demand higher payment for his production. Ultimately this will lead to loss, since a profit maximising processor will respond by not trading with producers who have relatively high costs. The processor will make fewer but to him more profitable deals with producers with relatively low costs (who can no longer pretend to have high costs if they hope to make sales). If, on the other hand, the company is cooperatively owned and uses proportional payment, there will not be a similar limitation of production. The cooperative sharing of profit can in this case be the only optimal solution. This situation and these results can be summarised as follows Proposition 4.3 When only the individual producer knows his production costs, and when the average revenue in the company is constant, the traditional cooperative payment scheme gives the only optimal allocation of profits. Other payment schemes lead to underproduction or to a sub-optimal allocation of production (Bogetoft, 2005). This result shows that with asymmetric information about farm level production costs, the only way to ensure maximal integrated profits may be to organize processing as a cooperative. This gives an information economic rationale for cooperatives. In Bogetoft (2005), it is shown also that the relative advantage of cooperatives (compared to investor owned processors) is greatest, when the cost uncertainty is large and when profitability is limited; i.e., when the average revenue (sometimes also called the net marginal product) is small compared to the primary production cost. In these cases an investor owned processor tends to ration away more aggregate profit value to gain private value. Since the agricultural

136

PETER BOGETOFT AND HENRIK B. OLESEN

sector may have these properties, these results may in part explain the apparent success of cooperatives among farmers. When the average revenue is declining, for example because the downstream market becomes less competitive or the processing costs increase rapidly, the advantage of the cooperative is reduced since the quantity control problem of the cooperative becomes more significant. Mathematical representation The fact that traditional payment schemes lead to optimal production, under-production and over-production respectively when P '  Q 0, P '  Q ! 0 and P '  Q  0, can be seen in a direct comparison of the first-order conditions (4.1) and (4.3) for the autonomous solution and the wise chairman's solution. The situation with increasing average revenues (positive synergy) corresponds to the case with a convex revenue function or, in particular, a super-additive revenue function; i.e., an earnings function satisfying R (q A  q B ) ! R(q B )  R(q B )

for arbitrary quantities q A and q B . If the market price is constant, this means that the firm's cost function Cfirm ˜ is sub-additive C firm ( q A  q B )  C firm (q A )  C firm ( q B )

This is a reasonable assumption, because the two productions can share a number of relatively fixed costs, e.g. administration costs. Increasing average revenues lead to under-production with a traditional payment scheme, because the individual member only obtains the gain P '(Q)q j from the increased production, and not the whole of the gain, P' (Q)Q . The situation with falling average revenues (negative synergy) corresponds to a concave revenue function or, in particular, a subadditive revenue function, so R(q A  q B )  R (q A )  R(q B )

for random quantities q A and q B . If the market price is independent of volumes, this corresponds to the firm's cost function Cfirm ˜ being convex, or at least super-additive C firm ( q A  q B )  C firm (q A )  C firm ( q B ) .

SINGLE PRODUCT PAYMENT SCHEMES

Hold-up

137

Example In this example we illustrate the use of (long-term) sales contracts as alternatives to the cooperative form of organisation when there is symmetrical information, and we show that there is no adequate alternative in cases with asymmetric information. We present the problem as a question of making some (specific) investment in the farm. The hold-up problem can also be reformulated as a question about production. We do this later, in the case with asymmetric information. Suppose that a producer can produce up to 5,000 special pigs at a cost of 500 DKr. each. The value of the pigs at the processing and marketing stage is 1,000 DKr. The producer has the possibility of investing in new pigsty systems, long-term feed supply contracts and so on. The investment represents 300 DKr. per pig, but thereafter the variable costs are only 100 DKr. per pig. Seen in isolation the investment looks like a good idea. Below we look at various scenarios that differ in relation to two circumstances. The first circumstance is the bargaining power. We assume that in some cases the processor is the only buyer and that he has many producers to choose from. He therefore has considerable bargaining power, and he takes all the potential gains from the trading relationship for himself. In other cases, we assume that the producer and the processor have equal bargaining power, and that they therefore share the gains from the trading relationship equally. The other circumstance concerns the timing of the negotiation or the length of the contract. In a simple case the negotiations concerning price and quantity take place after the investments have been carried out, but before the production takes place. This is a short contract or ex post negotiations. In other cases, negotiations will concern future conditions for supply and will take place before any investment is made. This is a long contract or ex ante negotiations. The outcome of the different cases can now be calculated as in Tables 4.5 and 4.6 below. In all cases the production level is 5,000 special pigs. The prices and profits are given on a per pig basis.

138

PETER BOGETOFT AND HENRIK B. OLESEN

Short contract, no investment Short contract, With investment

Price

Producer's profit

Processor's profit

500

0

1.000- 500=500

100-100-300 100

1.000-100=900 =-300

Long contract, no investment Long contract, With investment

500

0

1.000-500=500

100+300

1.000-1000

=400

300=600

Table 4.5 The processor has all the bargaining power When the processor has all the bargaining power, the result will be as in Table 4.5. Thus, for example, if an investment is made prior to there being a contract, it only costs the producer 100 DKr. to produce a pig, and since the processor has all the bargaining power, he pays precisely the 100 DKr. When the bargaining power is allocated equally, the result is as given in Table 4.6. Price Short contract no investment Short contract With investment Long contract, no investment Long contract With investment

500+½(1.000500)=750 100+½(1.000100)=550 500+½(1.000500)=750 100+300 +½ (1.000-100300) =700

Producer's profit

Processor's profit 1.000-750=250

550-100300=150

1.000-550=450

750-500=250

1.000-750=250

700-100300=300

1.000-700=300

Table 4.6 The producer and the processor have equal bargaining power In both instances the producer will not invest with a short-term contract. Economists say that the hold-up problem leads to underinvestment in specific assets. On the other hand, with a long-term contract the producer is willing to invest.

SINGLE PRODUCT PAYMENT SCHEMES

139

In practice this means that producers will not invest unless they are assured of a reasonable market for their products. If the producers own the processing firm themselves, as in a cooperative, they will naturally also make investments. The above shows that long-term contracts can solve the hold-up problem as can cooperatives. This conclusion is a classic result in the literature of new industrial organisation25. We have seen that a cooperative can solve the problem, but that it is not the only possible solution to the hold-up problem. In practice there are other problems associated with long-term contracts, and other factors suggest that a cooperative is the only realistic solution to the hold-up problem. Firstly, long contracts can be renegotiated. If the producer expects that the contract will be renegotiated once the investments have been made, then we are back to the situation with the short contract, where there is underinvestment due to fear of a hold-up. Secondly, long-term contracts cannot solve all the potential conflict between the producer and the processor - especially if there is asymmetric information. We now assume that the production costs are unknown to the processor, and we simplify the problem by disregarding the possibilities for making investments. It is not necessary for demonstrating the argument in this case. It is assumed that the processor only knows that the costs lie somewhere between 0 and 1,000 DKr. per pig, and that all these values are equally probable. It can be shown26 that a processor holding all the bargaining power will give the producer a 'take-it-or-leave-it' offer; produce at price p or not at all. The processor finds the optimal price offer by maximising his expected value, in other words the probability that the producer will accept (here p/1,000) multiplied by the resulting profit 1,000-p; i.e., p max (1.000  p) ˜ p[0,1000] 1.000 The solution to this problem is p = 500 This means that there will only be trade with half of the producers, those with the lower costs. Since all the producers in this example have costs which make production profitable, there is a real economic loss associated with this 'rationing'. Thus there is a real economic loss associated with having an investor-owned processor.

140

PETER BOGETOFT AND HENRIK B. OLESEN

There is no problem in carrying out the right level of production in a cooperative, because the producer himself is the owner. Therefore, in this example, a member of a cooperative always produces because his primary production costs are at all times lower than the net value at the processing and marketing stage.

4.6 The problem of over-production and some possible solutions

Explaining the problem

Competition between members

Problematic price signals

We have shown above that a traditional cooperative over-produces when average revenues decrease. In this section, we look more closely at the cause of this problem and its possible solutions. The analysis in Section 4.3 and especially in Section 4.5 gives a simple explanation of the problem. On the last units produced, from Qwise chairman to Qtrad.coop. , the marginal revenues are lower than the marginal costs. These units are thus produced at an actual loss. The units are produced because it is worthwhile for the individual producer to produce due to the proportional payment scheme. It can also be argued that the traditional payment scheme causes too much competition between members. When, in the traditional payment scheme, one producer increases his deliveries, he also reduces, even if only marginally, the average revenues. A rational producer naturally takes the price fall that he imposes on himself27 into account. This has almost no influence, however, on his production level, since he does not take into account the typically much larger effect of the price fall on other members28. The other members behave in the same way, and the result is increased production, so that the average revenues and the price paid to producers fall. If the producers could control this tendency to push volumes up and prices down, everyone would gain. This requires that the payment to the producer per additional unit should more accurately reflect what that unit actually brings to the cooperative. In other words, each additional unit ought to be paid according to its marginal revenue and not according to the average revenue. In lay man terms, the problem with the present system is that the price signal to the supplier does not reflect the company's actual revenue on the last unit supplied. The cost and market conditions of the cooperative are not accurately enough transmitted to the members via the payment scheme. And naturally, without relevant signals about costs and the market, the producers cannot behave appropriately.

SINGLE PRODUCT PAYMENT SCHEMES

141

Although the traditional scheme does not give sufficient signals regarding revenues, this is not to say that there is a total absence of such signals from the payment schemes used in practice. In Denmark the price for pigs is adjusted, for example by paying supplements or by making deductions for lean meat percentage and slaughter weight, just as weekly adjustments are made which reflect the current revenue possibilities29. These adjustments attempt to send signals about revenue potential to producers, to encourage the right kind of production at the right time. In this sense the pig industry is in fact very actively sending revenue signals. We will now discuss how over-production can be reduced. To start with we follow the traditional approach and assume that we want to reduce and allocate production to maximise integrated profits, as in the plan of the wise chairman. Let Q* Qwise chairman be the total production, and let P* R' ( Q* ) be the resulting marginal revenue on the last produced unit. Figure 4.8 below, which is a simplified form of Figure 4.6, summarises the situation. DKr. Producers’ aggregated supply Call ' Q

P Q * Average revenue R Q

P* Marginal revenue R' Q

Q*

Production Q

Figure 4.8 Reduction of production Proposed solutions

Over time many practitioners30 as well as theoreticians31 have proposed more or less speculative suggestions for reducing the overproduction problem. Some of the suggestions are based on contracts or quota-like supply rights, while others are based on price plans which give individual producers an incentive to produce up to but not beyond the optimal quantity. Quantity control and price control are the traditional economic means of coordinating in decentralised organisations32. Quantity control can obviously work. Price control, on the other hand, has to be understood broadly to be generally successful. A single fixed price is often insufficient, but generalized

142

Pricing plans

PETER BOGETOFT AND HENRIK B. OLESEN

price controls, where the price per unit can vary according to the quantity (for example in the form of a volume bonus) under a payment or price plan, work. The control of the volume of production by autonomous decision-makers via different pricing plans is illustrated in Figure 4.9. A general price plan with an associated marginal pricing plan is illustrated in the top two diagrams. A contract specifying a production right, and a production obligation, corresponds to an extreme payment function in which over-production and under-production are severely penalised. This is illustrated in the next two diagrams. A quota-based two-price system is a kind of hybrid of the classic quantity and price control. It corresponds to a unit-based linear payment plan, and thus to a step-wise marginal price plan. This is illustrated in the next two diagrams. A fixed unit price supplemented by a fixed premium or bonus corresponds to linear (or more specifically affine) payment plans, where the incremental payment is constant, as illustrated in the two lowest diagrams in Figure 4.9 DKr.

q j*

DKr.

DKr. Marginal payment

Payment

Production q j

Payment

q j*

DKr.

Production q j

Marginal payment

a' a'

q j*

Production q j

q j*

Production q j

SINGLE PRODUCT PAYMENT SCHEMES

DKr.

DKr.

Payment

143

Marginal payment

pˆ

bˆ 1

aˆ

bˆ pˆ 1 Production q j

q j*

DKr.

Payment

q j* DKr.

1

Production q j

Marginal payment

~ p

~ p

~ b

q j*

Production q j

q j*

Production q j

Figure 4.9 Payment schemes reducing over-productionM

Room for manoeuvre with payment schemes

All the payment schemes shown, and many others, can be used to ensure the optimal production volumes. The primary requirements are that the scheme should ensure individual rationality and incentive compatibility, as discussed in Chapter 3. In the mathematical section below, there is a presentation of the resulting requirements for the parameters of the pricing planM. In the next section we discuss in detail both these requirements and a number of other possibilities. Thus we look at contract production, two-price payment schemes, marginal price schemes, cost-based schemes and schemes with quota-based marginal prices. There is generally some room for manoeuvre in the choice of a pricing scheme. This is so regardless of whether we restrict ourselves to a given class, for example two-price payment schemes, or whether we consider alternative schemes from different classes. A cooperative focusing on efficiency and the maximization of aggregate profits thus has some degree of freedom within which it can take account of other relevant criteria, e.g. the equal treatment of members. What choices should be made within this scope for manoeuvre depends on which criteria one wishes to consider in the actual situation.

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PETER BOGETOFT AND HENRIK B. OLESEN

Mathematical representation We now formalise the use of payment and marginal pricing plans for controlling production volumes. x j  q1 ,...., q n represents the payment to member j when n

members produce q 1 ,...., q n . Also c j q j represents member j’s production costs and S j represents his profit from the best alternative to membership of the cooperative. Finally, q j* , j 1,..., n represents the optimal production level in the wise chairman's solution. We can simplify the notation if we introduce xˆ j q j as the symbol for the payment to member j, given that the other members – j implement their part of the q* plan, i.e.







x j q j , q  j* .

ˆx j q j

The general payment plan is thus x j ˜ , and the payment plan 'in equilibrium' is xˆ j ˜ . The marginal payment plan is correspondingly wx j wq j and wˆx j wq j . If x j is not differentiable, then the marginal payment can instead be approximated with







x j q j , q  j  x j q j  1, q  j



with production levels q j , q  j . In equilibrium we get the marginal payment







ˆx j q j , q  j  ˆx j q j  1, q  j



j

at the production level q . To ensure the desired production levels, the payment scheme must be individually rational for every member j; i.e.,





ˆx j q j*  c j q j* t S

j

(IR)

and the payment scheme must also be incentive compatible xˆ j  q j*  c j  q j* t xˆ j  q j  c j  q j for all q j

(IC)

These are the general requirements we impose on the payment schemes and marginal price curves. The second system (next below the top) in Figure 4.9; i.e., the system based on supply rights and obligations, has the following IR and IC conditions a ' t c j q j*  S j (IR)

SINGLE PRODUCT PAYMENT SCHEMES





a' t c j q j*  c j q j

145

(IC)

All contracts with supply rights and obligations for volumes q j* and with payment a' , which satisfy these inequalities, will implement the optimal production level. Note how the inequalities in IR and IC leave some room for manoeuvring. In the third scheme in Figure 4.9; i.e., the quota-based price scheme, the IR and IC conditions give the following restrictions on the parameter values j c j q j*  S ˆp t (IR) j* q

ˆp t P* , bˆ d P*

(IC)

where P* is the company's marginal revenue at the optimal production levels. Again, as long as these constraints are fulfilled, the quota-based price scheme will work to implement the wise chairman’s quantities. In the last scheme in Figure 4.9; i.e., the fixed price scheme with a fixed basis payment, the requirement is that ~ b t c j q j*  S j  P* q j*

(IR)

~ p

(IC)

P*

The requirements for the parameters described above leave a certain freedom in the choice of parameters. This illustrates the freedom in the choice of pricing plans. Which payment plan should be used depends on what is desired from the scheme apart from efficiency.

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PETER BOGETOFT AND HENRIK B. OLESEN

4.7 Balanced budget and the allocation of profits and losses

A frequently disregarded problem

Another important quality of a payment scheme is that, as referred to in Chapter 3, it should produce a balanced budget (BB); i.e., the requirement that a payment scheme should leave neither a surplus nor a deficit. We believe that the balanced budget condition or the zero profit constraint has caused some confusion both in the literature and in practice. There is frequently no discussion33 or only superficial discussion, about how this condition should be satisfied, including how any eventual surplus or deficit should be allocated between the members, once it has been ensured that the payment scheme satisfies the requirements for voluntary participation (IR) and incentive compatibility (IC). The discussion is important since a wrong allocation of the surplus can destroy the production incentives. The balanced budget condition is also important, since at the very least a budget deficit should be avoided. Even this is overlooked from time to time34. Last but not least, the question of allocation is important, indeed vital, because it deals with the treatment of members, including satisfying the basic principle of equality. In this section we deal with the requirement for a balanced budget, including the allocation of any surplus or deficit. We focus on the interaction between the incentive structure and the market situation. It is assumed that there is a tentative payment scheme, which satisfies the IR and IC conditions. The remaining budget surplus (whether positive or negative) isM Surplus

=

net earnings of the cooperative - sum of the tentative payments to members

We will now discuss how to allocate this (positive or negative) surplus; i.e., the extra profits or losses compared to what the IR and IC scheme has handled; i.e., the non-allocated profit or loss. Mathematical representation In the preliminary payment scheme, with preliminary payments of ~ x j ( q 1 ,.., q n ) for j 1,.., n , the (positive or negative) surplus is n

Surplus ( q1 ,..., q n )

R (Q )  ¦ x j (q j ,..., q n ) j 1

where Q

q 1  ....  q n is the total production.

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The next question is how the surplus should be allocated. In the following we allocate H j q 1 ,...., q n to member j, j=1,…,n, where n

¦ H  q ,...., q j

j 1

1

n

Surplus  q1 ,..., q n

We frequently refer to the supplementary payment to member j as being H j , and the question is, how such a supplementary payment function should be designed.

4.7.1 Allocating the surplus independent of production

Fixed shares allocation

In the literature it is usually said that the surplus does not distort incentives as long as an individual producer's share of the surplus is not affected by his own actions. This can be achieved by sharing the surplus equally, or according to the provision of capital or more generally, according to some fixed weighting. Supplementary payments do not distort incentives, if and only if the marginal supplementary payment to an individual member is zero, so that the production-dependent allocation of the surplus does not affect the behaviour of individual producers. Thus, the supplementary payment to an individual member may not be affected by marginal changes in his production. This applies only occasionally since any change in production affects both the cooperative's revenues and costs, and therefore the supplementary payments to individual members, even when a fixed weighting is used. The logic of using fixed shares for allocating surpluses is that these shares do not depend on the actions of the members and therefore do not affect their incentives. This is true only if the tentative payments are changed by precisely the same amount as the cooperative’s revenues when the individual production level is changedM. Unfortunately this is not an easy problem to solve, and in fact it is impossible to solve the problem generally for all revenues and cost functions, cf. Chapter 3. Even though fixed allocation of surpluses cannot entirely create a balanced budget without damaging the incentives, it does achieve part of the aim as it is at least possible to prevent someone getting a bigger slice of the cake by increasing his production. It is an interesting theoretical question, which we leave for later analysis, if the use of the one-man-one-vote principle, as distinct from the one-dollar-one-vote (or one-pig-one-vote) principle, increases economic efficiency. This seems to be possible because at least a part of the surplus (which

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members can decide to pay into reserves or towards other common purposes) is thereby not allocated according to turnover. The conclusion is thus that we cannot hope to find a method which allocates the entire surplus without ever affecting the incentives. We must therefore give up part of one criterion in order to achieve the other. On the other hand it is possible to achieve much in this way. It is in fact possible for the supplementary payments to affect incentives without affecting the equilibrium. It is also possible to ensure supplementary payments which do not disturb incentives and which give a balanced budget in equilibrium. We look at these possibilities below. Mathematical representation In a system where the surplus is allocated according to fixed weights or fixed shares, the supplementary payment to member j can be described as n

O j ( R(Q)  ¦ ~x k (q 1 ,..., q n )) for all q

H j (q 1 ,..., q n )

k 1

where O1 ,..., On is the n producers' weighting and O1  ...  On 1 . Supplementary payment does not influence producer j's behaviour if wH i / wqi 0 , i.e. if35 n

R ' (Q )  ¦ w~ x k (q 1 ,..., q n )) / wq j

0 for all j

k 1

which states that when the individual production levels are changed, the revenue and the sum of payments to members in the ~x - system are changed by the same amount

4.7.2 Allocating surplus without affecting the equilibrium Fixed weighting

We consider a general marginal pricing system in which the members receive a price per unit equal to the cooperative's marginal revenue at *

the optimal production level Q . This is clearly a suitable system because it ensures the optimal production level by means of one common price. We can call this model the general marginal pricing system. In fact, this system has already been illustrated in the diagrams at the foot of Figure 4.9. The only immediate problem with this scheme is that it seldom produces a balanced budget. For example, if the cooperative’s average revenues decrease, it generates a surplus. This corresponds to the shaded area in Figure 4.8. However, the problem with the budget surplus can easily be solved. If the surplus is allocated according to fixed weights, the surplus (or deficit) will be allocated in all situations, and it will be an

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equilibrium for the members to choose optimal production levelsM. This is sufficiently important to be formulated as a proposition. Proposition 4.4 The general marginal pricing system, supplemented by fixed weights for the allocation of budget surpluses or deficits, can implement the wise chairman's solution. It is relevant to make two further comments about this system. Firstly, in the general marginal pricing system, supplemented by fixed weighting for the allocation of supplementary payments, individual members can affect the supplementary payment, but this only distorts the incentives outside the equilibrium. Secondly, the system can appear to be unfair, unless the weighting is chosen carefully. The surplus allocated independently of production volumes can be quite large. This means that a small producer with a high weighting can be paid a lot in relation to a large producer with a low weighting. But, if the weighting chosen is close to or equal to the relative shares of production in the wise chairman's solution, the members get exactly the same payment in equilibrium as they get under a proportional payment scheme supplemented with direct quantity controls. Such an allocation would certainly seem fair in many circumstances. Mathematical representation The payment plan for the general marginal pricing system is linear, with unit prices equal to the marginal revenue in Q * , i.e. x j ( q1 ,.., q n )

P* q j

It is now assumed that the surplus is allocated according to fixed weightings §

n

·

§

n

·

H j (q1 ,..., q n ) O j ¨ R(Q)  ¦ ~x k (q1 ,..., q n ) ¸ O j ¨¨ R(Q)  ¦ P*q j ¸¸ k 1 j 1 ¹ © ©

¹

for all q. In this system it is an equilibrium for members to produce the optimal j* quantities, since for q j q it applies that

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w ª¬ x j (q 1* ,.., q j ,., q n* )  Hi (q 1* ,.., q j ,., q n* ) º¼ / wq j P*  O j ( R '(¦ q k *  q j )  P* ) kz j

if q j  q j*

*

­! P ° * ® P ° P* ¯

if q j

q j*

j

if q ! q j*

if R' ' Q  0 . Since member j's incremental costs are c j q j

­ P* ° * ® P ° ! P* ¯

if q j  q j* if q j

q j*

if q j ! q j*

the payment scheme gives incentives to move towards the equilibrium. Assume that O j q j* Q* . The resulting payment to producer j in equilibrium will be n q j* § · ~ x j (q 1* ,..., q n* )  * ¨ R (Q)  ¦ ~ x k q 1* ,..., q n* ¸ Q © k 1 ¹ j* q P * q j*  * R (Q)  P *Q * Q









q j* R(Q) Q* in other words, the company's revenues are allocated in proportion to the quantities supplied, as in the proportional payment scheme.

4.7.3 Unbalanced budget outside equilibrium Another possibility for securing efficiency while complying with the requirement for a balanced budget is for the cooperative to threaten to operate with slack. This means that if there is over-production, the revenues available for allocation will be reducedM. Figure 4.10 below shows how the company's net revenues, with associated payments, can appear if the company use slack threats.

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151

DKr.

Slack '

Revenue R Q  '

Production Q

Q* DKr.

Producers’ aggregated supply Call ' Q

Average revenue R Q Marginal revenue R' Q Q*

Production Q

Figure 4.10 Threatening with slack

The interpretation of slack …

The idea of this scheme is to allocate the revenue in proportion to the quantities supplied, as in a traditional scheme. When there is overproduction there will be a reduction of revenue, or at least in that part of the revenue that is paid out. It is clear that if there is sufficient slack, it is possible to implement the desired production plan. There are several ways of ensuring the necessary reduction in revenue. One possibility is to give (more) slack to the employees of the cooperative. This can be done, for example, by using wages agreements with high overtime rates.

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… giving money away

… reserves

… limiting the capacity

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Members can also improve their revenue by promising to give money away in certain circumstances, because such a promise has a disciplinary effect in making members eliminate their over-production. In equilibrium it is never necessary to give money away. The reduction in revenue can also be obtained by allowing, or even expecting, the cooperative’s management to take non-revenuemaximising actions when there is over-production. The explanation can be that there are not the resources to handle the growing volume of production with the same effectiveness as before (a little more is required, in fact a discreet fall in effectiveness). A variation of this idea is that it may be worth employing less skilled people in the management who, in situations of over-production, do not make the best decisions. This corresponds to the economists' idea that 'lazy managers' can be advantageous in certain markets36. Another and more realistic implementation of the slack model is that an undertaking is given in advance to make extraordinary reserves and consolidation in cases of over-production. Apart from seeming a little artificial, the problem with this approach is that it is not secure against renegotiation. The members have an ex post incentive to have the whole surplus paid out, and as they have the decision-making power, it should not be difficult for them to reach agreement on surplus payouts. A third possibility is to limit the capacity of the capital equipment, etc. This might increase the expense of dealing with quantities above the optimal level. In this way the cooperative’s revenue function is changed, and it becomes possible to use the traditional cooperative principle. If the initial payment plans are linear with a unit price equal to the marginal revenue at the optimal production level, then the payment in equilibrium will correspond to payment in proportion to the quantities supplied. The above solutions imply that when there is over-production, there is a surplus which is just not allocated to the members. A related possibility is to guarantee equilibrium supplementary paymentsM. This corresponds to working with a deficit outside the equilibrium, but to do so in order for there to be a balanced budget in equilibrium. One way to achieve this is to use the above tentative plan with unit prices equal to the marginal revenue at the optimal production level, and issuing guarantees of supplementary payments as they ought to be in equilibrium to individual members. It is immediately clear that this gives each producer the right incentives as well as giving a balanced budget in equilibrium. The

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scheme also has the effect of the total revenue being allocated in proportion to the quantities delivered. A third advantage is that the scheme does not give perverse incentives outside the equilibrium, in contrast to the scheme with fixed weightings in the previous section. The incentive for the individual producer to fulfil his part of the optimal production plan is thus unaffected by what the others do37. In terms of game theory this means that dominant strategy equilibrium is implemented, and not only a Nash equilibrium. The disadvantage is that there will be a deficit in the cooperative if anyone over or underproduces. This does not happen with the scheme discussed in the previous section. Of course, in theory, no-one will deviate and therefore the deficit problem will not arise. These observations are sufficiently important to be summarised in a proposition. Solutions

Proposition 4.5 The traditional payment scheme supplemented by extraordinary reductions in revenues or guaranteed supplementary payments, can solve problems of over-production and lead to the same payments in equilibrium as the proportional payment system. With guaranteed supplementary payments the incentives for the individual producer are independent of the production levels of others; i.e., the desired outcome is implemented in so-called dominant strategy equilibrium.

Both of the systems, revenue reductions via slack or guaranteed supplementary payments, work well as indicated by Proposition 4.5. This attractive outcome, however, builds on an assumption of perfect information. The system designer must know costs and revenue functions to determine the desired equilibrium quantities. This may not be realistic as already discussed. Moreoever, there can be no noise or uncertainty in the implementation of the plan. In reality, uncertainty and random variations in outputs cannot be avoided, and some modification is needed. It may for example be necessary to have a zone around the planned quantities which do not lead to any changes in payments, but in the end, simple random effects will trigger slack or deficits in some situations. This is similar to the wellknown problem of cartel maintenance under uncertainty. From time to time, a penalty phase, e.g. a price war, breaks out because of random variations and not because of deliberate actions by any partners, cf. e.g. Tirole (1988).

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Mathematical representation A payment scheme in which the management uses slack can be written as ­ j R Q if Q d Q * °q Q ° x j (q1 ,..., q n ) ® °q j R  Q  ' otherwise °¯ Q

A payment scheme with fixed unit prices and guaranteed supplementary payments looks like this x j (q1 ,.., qn ) and H j (q1 ,..., q n )

P* q j q j* ( Surplus( q1* ,..., q n* )) Q*

for all q j

The resulting payments correspond, in equilibrium, to payment in proportion to the quantities delivered x j ( q 1* ,.., q n* )

~ x j ( q 1* ,.., q n* )  H j ( q 1* ,.., q n* ) P* q j*  q j* Q*

q j* Q*

P( Q

*

)  P* Q*



R( Q* )

4.7.4 Transfer surplus to others

The public debate

Transfers create inefficiencies

More practically minded economists, including people in industry, have often suggested that the surplus which arises through marginal price payments38 should be transferred to other product groups in order to ensure profits in a thin market; i.e., in a market with declining average net revenue. This transfer may in practice be motivated as a contribution to the cooperative39, as being a fair division of surplus or simply a way to pay for using company resources. Either way, it may be politically advantageous to transfer from the special producers to the ordinary producers. Unfortunately, it is not in general a good idea economically to transfer profit from one producer group to other producers as a way of avoiding over-production. The problem is that if the profit is shared among other producers in proportion to their production, then they

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155

will achieve the wrong revenue signals. This can easily result in just moving the inefficiency around, by moving over-production from one area to another. Note namely that there may well be over-production of a product which has constant marginal revenue. Over-production is not in itself conditioned by decreasing marginal revenue. Overproduction occurs when the marginal costs exceed the marginal revenue at the resulting production level. This can be expressed as a proposition. Proposition 4.6 Transferring profit to other branches of production, to be allocated according to turnover and without quantity control, leads to loss of efficiency.

Figure 4.11 below shows the problem of moving inefficiency from one area to another. In the figure, the additional revenue from a special production (Market A) is transferred to the producers of a standard product (Market B). Even though the standard product is sold under perfect competition, the transfer results in inefficiency in Market B.

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DKr.

Call ' Q A

Market A C B

Settlement price A

D

Average revenue R QA Marginal revenue R' QA Production Q A

Q A*

DKr.

Marginal cost c ' q1

Settlement price Loss

Optimal production

Actual production

Average revenue = marginal revenue

Production q1

Figure 4.11 Transfer of profits between product types

Link profit and quantity control

We see how the profit which is transferred in order to reduce inefficiency in Market A, merely turns up to a greater or lesser extent in Market B. The profit which is transferred corresponds to the area ABCD in Market A and the area EFGH in Market B. The optimal production in Market B is Q*B , but because of the transfer the ~ production becomes QB . To the extent that a niche product is subject to strict quantity control, it is most efficient to allocate the profit to that product. In this way, the inefficiency in the standard market is avoided.

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Synergies and transfers across product groups

157

This is not to say that there should never be any profit transfer from one group to another. We shall study this in greater detail in the next chapter. For now, however, we note that synergies between the two productions, either in terms of production or sales, may motivate transfers. Another motivation may be to share risks.

4.8 Fair and 'natural' profit allocations

The marginal payment scheme

Which unit should be paid first?

In the previous section we discussed how a surplus can be allocated without distorting the individual members' incentives to implement their part of an optimal production plan. In this section we discuss how the surplus can be allocated, to achieve other desirable goals. We focus on allocation principles which can be clearly perceived as being fair. To motivate the discussion, we note that proportional payments may lead to over-production as we have seen, but that this does not imply that this principle should be abandoned per se. There is a general need for different requirements to be balanced against each other. This section illustrates further the potential down-side of departing from the principle of proportional payment. As emphasised in Section 4.5, one explanation for the problems of proportional payment in the case of decreasing marginal revenue, is that individual producers do not receive price signals reflecting the cooperative's marginal revenues. This problem can be solved by the marginal price system where the price paid is equal to the cooperative's marginal net revenue of the actual production quantity. This also generates a surplus for allocation. One idea for the allocation of revenues which sends producers relevant signals regarding revenues, is to give different payments for different products, so that each unit is paid according to its marginal revenue for the cooperative40. The problem is that there are no reasonable and objective criteria for deciding which units, e.g. which pigs, have generated the greatest marginal revenue (the 'first' units); in other words, which units should be paid on the basis of the first part of the revenue curve. Figure 4.12 illustrates the problem.

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DKr. Revenue R Q

Marginal revenue on ”last units”

Marginal revenue on ”first units” Production

Q

Figure 4.12 The revenue curve of a cooperative

4.8.1 Aumann-Shapley prices Average marginal revenue

The same price as with proportional payment

Fulfilling monotonicity …

Since all producers can claim to have delivered the "first" units, which have generated the greatest marginal revenue, it is natural to make payments on the basis of a price corresponding to the average marginal revenue of the cooperative. With Aumann-Shapley prices each unit is paid on the basis of the average marginal revenueM. There is a parallel to Aumann-Shapley prices in the case of heterogeneous products, where revenues are divided between different producer groups - the so-called 'Shapley value', which we describe in Chapter 5. Using Aumann-Shapley prices achieves full allocation of revenues41. Unfortunately, however, it turns out that Aumann-Shapley prices give the same prices as the proportional principle in traditional cooperatives. This means that there is no progress made on the quantity control problem. This resultM, on the other hand, means that we can use the theoretical characteristics of Aumann-Shapley prices to describe the qualities of the proportional payment principle. Aumann-Shapley prices, and thus the proportional payment principle, fulfil the requirement for monotonicity. The price paid per unit will rise if there is a shift in the cooperative's revenue function R, so that the marginal revenue increases at all levels of productionM. This corresponds to the requirement for coalition-monotonicity, cf. Chapter 3. This situation is illustrated in Figure 4.13.

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159

DKr. High revenue R Q Low revenue Rˆ Q

Production Q

Figure 4.13 Increase in a cooperative's marginal revenues at all production levels

The consistency requirement is satisfied

The additivity requirement is satisfied

Moreover Aumann-Shapley prices, and thus the proportional payment principle, are consistent42. This means that the allocation to individual members is the same regardless of whether the earnings are allocated to all producers at once, or whether they are allocated between producers groups first. The latter case can occur when a cooperative with a number of processing plants first allocates the revenues to the producer groups who have delivered to each plant, after which the payment is shared among the individual producers in the groups. Consistency thus helps to reduce the influence problem as there is no reason to argue about which procedure to use for the allocation of revenues, cf. Section 3.7. The additivity requirement is likewise satisfied by AumannShapley prices. This means that there is the same allocation regardless of whether incomes and expenditures are allocated separately or together, as the resulting net income. This reduces internal conflicts in cooperatives and increases transparency, as it becomes possible to present the accounts of the business in which the incomes and revenues are allocated, to all groups according to the proportional principle (or by means of Aumann-Shapley prices).

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Mathematical representation The average marginal revenue of a cooperative, and thus the AumannShapley price, can be formally represented as Q 1 p ³ R' u du 0 Q where R(Q) is the total revenue of the cooperative when there is a total supply of Q units. By using Aumann-Shapley prices a full allocation of revenues can be achieved (Moulin, 1988) since pQ

³

Q

0

R' u du

RQ  R0

RQ

A simple reformulation of this gives p

RQ Q

which is, in fact, the settlement price in the proportional principle.

4.8.2 The serial principle

No penalty because larger producers overproduce

The serial principle can be used as an alternative to Aumann-Shapley prices. Consider again as a motivation the problem of over-production, cf. Section 4.5. It would seem unfair for one member to receive a lower payment just because other members over-produce. On this basis it seems reasonable to allocate revenues so the producer with the lowest production is initially given his share of the revenues, which the co-operative would have had if everyone had produced as little as him. Producer 1 is the producer who has the lowest production. The payment to producer 1 would be as followsM. Net revenue if all produced the same as producer 1 Number of producers

All producers receive the payment paid to producer 1 as their basic payment. Likewise it is reasonable that producer 2, who has the next lowest production, should not be penalised because other producers have produced more than him. Producer 2 should therefore have the same payment as producer 1, plus his share of the amount by which the net revenue would increase if all but producer 1 increased production from the level of producer 1 to the level of producer 2. Producer 1 has not contributed to this increase in revenue, thus he should not receive a share of itM. Continuing next to producer 3 and so on, we get an allocation of the revenue according to the serial principle.

SINGLE PRODUCT PAYMENT SCHEMES

Two basic ideas

161

The serial principle is constructed from two basic ideas. Firstly, all producers should be treated equally, so that producers of equal size should obtain the same payment. Secondly, the payment to a given producer should not depend on the production level of producers who have greater production43. Example We consider the example of a small cooperative slaughterhouse with four members, in which the revenue from a slaughter pig falls from 1,000 DKr. for the sale of one pig to 500 DKr. in the case of a production of 5,000 pigs. In other words, the per-pig revenue to the slaughterhouse is 1,000 DKr. - 0.1 DKr. multiplied by the number of pigs produced. The four producers supply 100, 500, 1,500, and 3,000 slaughter pigs, respectively. The serial principle says that producer 1 must not be affected by the fact that the others produce more than him. He should therefore collect a quarter of the revenue which the slaughterhouse would receive if all members produced as little as him; i.e., if the total production were 4 x 100 pigs = 400 pigs. Likewise, producer 2 must not be penalised because the others produce more than him. He should therefore obtain the basic payment (the amount paid to producer 1) plus one third of the amount by which the revenue would increase if production increased from 400 pigs to 3 x 500 pigs from producers 2 to 4, plus 100 pigs from producer 1; i.e., 1,600 pigs in total. Producer Production Total production inhgp Price inhgp Revenue inhgp Basic payment Add. payment to Prod.2, 3,4 Add. payment to Prod. 3,4 Add. payment to Prod. 4 Total payment Payment per pig

1 100

2 500

3 1.500

4 3.000

400

1.600

3.600

5.100

960 840 640 384.000 1.344.000 2.304.000 96.000 96.000 96.000

490 2.499.000 96.000

384.000

320.000

320.000

960.000

352.000

352.000

704.000

195.000

195.000

1.091.000 363

2499.000

320.000

96.000 960

416.000 832

896.000 597

Table 4.7 Example of the serial principle

Total 5.100

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PETER BOGETOFT AND HENRIK B. OLESEN

The procedure is laid out in the Table 4.7 above, where inhgp means “if none had greater production” Advantageous for small producers

The example shows that the serial principle gives widely differing unit prices to producers. Thus, large producers will presumably consider the introduction of the serial principle in a cooperative to be unfair. But the serial principle can be combined with the traditional payment scheme. It is possible to allocate quotas to producers, corresponding to their existing production levels, with payment being made on a proportional basis. Then it could be decided that any expansion of production should be paid in accordance with the serial principle. In this way producers could be given better incentives to choose the optimal production levels, as their marginal revenue would more accurately reflect the cooperative's marginal revenues. Mathematical representation Let j=1 be the producer with the lowest level of production q 1 . If all n producers merely produce q 1 the cooperative's earnings will be R (nq 1 ) . Payment to producer j=1 is therefore x1 =

( )

R nq 1 n

Producer j=2 with the next lowest production level q 2 should not be disadvantaged because other producers have produced more than him. If there are no producers who have produced more than q 2 the cooperative's earnings will rise from R (nq 1 ) to R ((n − 1) q 2 + q 1 ). These additional earnings should be divided between the remaining n-1 producers. Therefore producer 2 receives the following payment x2 =

( )

(

) ( )

R nq 1 R ( n − 1) q 2 + q 1 − R nq 1 + n n −1

When this payment rule is generalised so as to apply to all producers, we can formulate the payment to the j'th producer as j

xj =∑ k =1

R(q k ) − R(q k −1 ) n +1− k

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163

where producers are ranked according to their production so that q 1 ≤ q 2 ≤ ... ≤ q n ,

and where

q k = q 1 + q 2 + ... + q k −1 + (n + 1 − k )q k

is the total production for producers below k plus q k for each of the other producers. The principle is illustrated below in Figure 4.14 in which the segmented linear curve is the payment plan x j (⋅) for a random producer. DKr. Revenue R (Q )

(

R (n − 1)q 2 + q 1

)

( )

R nq 1

nq 1

(n − 1)q 2 + q1

Production q j

Figure 4.14 Illustration of the serial principle The combination of proportional payment and serial payment can be formulated as follows Let q j be the quota allocated to producer j, j=1,…n, and let the total quota be q 1 + q 2 + .... + q n = Q . Production variations from the quota are referred to as d j = q j − q j . Such a deviation leads to a change in the revenue of D(d j ) = R(Q + d j ) − R(Q ) . The price paid to producer j is now

x j ,comb =

( )+

R Q Q

j

∑ k =1

D ( d k ) − D ( d k −1 ) n +1− k

where d k = d 1 + d 2 + ... + d k −1 + (n + 1 − k )d k .

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4.9 Information needs

Departures from the traditional scheme increase information needs

When designing a payment scheme, it is important to bear in mind how much information is needed for the scheme to operate. It can be necessary to compromise on efficiency if that reduces the information needs and creates an administratively simpler system. The traditional payment scheme is certainly attractive from the point of view of information needs. It merely requires a cooperative to calculate its revenues; i.e., the value of the members' deliveries ex post. The various modifications described above, for solving the problems of efficiency and balanced budgets when there are decreasing marginal revenues, requires much more information. For example, the marginal price system requires information regarding revenues at differing production levels, and about producers' costs at different production levels. Only then can the optimal production levels and the relevant marginal prices be determined. The differences should not be exaggerated. It is not only the information needs of the cooperative that are important. The members also need information in order to make decisions about their production. From the members' point of view the marginal price system or the quota based system is very convenient, since they need not speculate so much about the expected payment under these systems. Below we look at some of the methods for reducing the information needs of the cooperatives and of the producers.

4.9.1 Usual techniques and inertia Usual estimation methods

Inertia and continuity

In Section 4.1 we analysed how the revenues of cooperatives and the costs of the individual producers can be mapped using traditional production theory, revenue and cost estimations, interview research and statistical methods. These methods can help the cooperative delineate its need for information, since the precision of the estimated functions, etc. depends on how much information is collected as well as on the techniques used. Investments by individual producers are often made on a reasonably long-term basis, typically 10 to 20 years in the pig industry for example44. This does not mean that there cannot be substantial new investment and restructuring in the shorter term, as for example in more recent times with higher pig prices. However, the longer investment horizons mean that there is capital equipment whose

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existence hinders rapid changes in cost structures. The cooperative will build up knowledge about these conditions. Therefore it is not necessary to calculate from scratch when designing a payment scheme. Cooperatives possess a lot of both verifiable and non-verifiable information45. The information needs of the individual members are naturally also important. A large part of the producers’ information-related costs are directly related to the cooperative’s information collection procedures, as the producers must supply data regarding their farms for the cooperatives to use in calibrating the payment schemes.

4.9.2 Auctions The cooperative's information need is reduced

Information and markets

Members' information needs increase

Another thing which can reduce a cooperative's need for information is to base the payment scheme on tradable production rights or similar instruments. In such a situation it is not necessary for a cooperative to know how cheaply the individual producer can produce in order to enter into reasonable contracts with individual producers. It is sufficient that the cooperative knows or has a reasonable idea about the total production cost function Call (Q ) . By setting this against the revenue curve, the cooperative can set the total production level which maximises the integrated profit. The allocation of the total production in the form of production rights can then be made via an auction. There are frequent proposals for auctions, tradable production rights, etc. in the literature46. The popularity of these proposals is more or less implicitly based on the general economic theory about the market's ability to make an optimal allocation of resources. One should beware of simple arguments that the market mechanism will be beneficial in every situation. The market mechanism can involve significant transaction costs, especially when there are only relatively few participants in the market. Buyers and sellers must find each other, they must consider what they are willing to pay or what they can demand, they must negotiate the terms of trade, etc. This can lead to sub-optimal deals, there can be delays and opportunities missed while attempts are made to re-allocate resources. In reality the advantage of the auction mechanism for a cooperative is probably primarily that it transfers the costs of gathering information from the cooperative to the individual members. In order for a producer to know how much he can bid for a production right, he needs a lot of information. He needs to know not just how his own production costs will develop, including the costs of feed-stuffs, etc., he must also have an expectation about the cooperative's revenue

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function; i.e., he must be able to forecast the developments of the cooperative's costs and sales. The allocation of production rights via an auction can also give rise to certain logistical problems. If production rights are solely allocated to the producers who made the highest bids, there is a risk that there will be an inappropriate geographical spread of production, in which small size special production is distributed throughout the country. This will lead to the cooperative having high transportation costs, if the cooperative continues to pay these costs. Lastly, it should be observed that it is important how the auction is organized. Some auctions, notably second price auctions, are easier to bid in as they have dominant strategy equilibriums and it may therefore be possible to bid without collecting information about the other bidders. The design of auctions has a very large literature and some of the basic results are by now text book material. An analysis of a presumably suboptimal actual milk quota exchange (auction) is Bogetoft, Nielsen and Olesen (2003).

4.9.3 Iterative methods Linking information collection and optimisation

Budgeting

The problem of collecting information can be helped through iterative planning methods47. It is not necessary to know the revenue functions and the production cost curves of the aggregated production, Call (⋅) in detail, in order to establish the optimal production level. It suffices to know the function relatively precisely, close to the optimal production levels. The iterative planning method links together information collection and optimisation so that the information is reduced to what is necessary for solving the optimisation problem. It is problematic for the production planning of a cooperative to lack information about the individual members' cost functions. In an iterative procedure the cooperative asks a number of questions, either concerning the costs at different production levels, or regarding the expenditures required to increase production to given production levels. In this way the cooperative can iteratively build up sufficient knowledge about the local cost structures in order for an optimal production plan to be determined. If there is a similar lack of information about revenues, then information can be obtained iteratively from the processing and sales departments. This can occur parallel to the collection of information about the primary production costs. These methods have a practical counterpart. They correspond largely with the (iterative) budgeting process used in virtually all businesses. The theoretical literature draws attention to a number of

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different methods for posing questions and organising the collection of information. The literature also contains the results of the expected consequences of the procedures and the likely improvements to be obtained from continuing to gather information48. In this way the theoretical literature gives a more rational basis on which to organise the collection of information. Price control systems often lead relatively quickly to sensible solutions, even though they may not necessarily be optimal solutions. For cooperatives this means that it can be both difficult and unsuitable to use specific contracts with quantity restrictions, unless they have good knowledge of the production costs of the individual farms. It may be better to control the total supply through a pricing system similar to the marginal price system described above. If the marginal costs are underestimated for one producer whilst overestimated for another, this is balanced out relatively easily in a price control system but not in a rigid quantity control system. A price control system is thus probably more robust in the face of wrong information about an individual farm than a quantity control system is. Price controls can also give more reasonable incentives than quantity controls in relation to general variations in costs49. If the producers' production costs fall, then in a price control system the producers will automatically have an incentive to increase their production. This will not be the case with a quantity control system. It is likewise relatively easy to adjust the incentives using a price control mechanism when the revenue situation of the cooperative changes. An example of this is the pricing under the National Pricing System in Denmark, which was adjusted every week50. With a quantity control system it is also possible to adjust the quantities as a reaction to changed conditions for revenues or costs, but it is more difficult. To make the correct adjustment the cooperative must calculate what the optimal quantities are in every situation, because it is necessary to take into account that both the cooperative's revenues and the producers' costs can change simultaneously. In practice this means that far fewer adjustments are made in schemes using quantity controls than in those using price controls.

4.9.4 Manipulation and asymmetric information A particular problem in information collection is the opportunity for strategic behaviour and the manipulation of information. For example, it is not certain that all producers find it in their interests to disclose exactly how cheaply they can increase their production.

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The manipulation of information is well known in the literature on planning in decentralised systems, as well as by everyone who has been involved in practical budgeting in organisations. There is a comprehensive literature on budgeting processes, and more generally on information collection in situations with strategic behaviour51. This topic is not dealt with in more detail here because it becomes less relevant when there are large numbers of producers, as well as because in principle dealing with information problems follows the same pattern as dealing with production incentives which is discussed above52. A simple mechanism called relative performance evaluation, or more specifically yardstick competition, should also be mentioned, because it can eliminate strategic behaviour and because elements of yardstick competition can be found in many settings. In Denmark, for example, The National Pricing System for special pigs based on the additional cost reimbursement principle, for example, requires elements of yardstick competition, as we shall see in Chapter 5. The same is true for many of the contracts observed in Danish agriculture, cf. Bogetoft and Olesen (2004). Yardstick competition is especially applicable when the producers are assumed to have more or less the same cost structure53, that they know while the cooperative does not. Assume that the actual costs of the individual farm depend on how hard the individual producer works to reduce his costs. By paying a producer a cost allowance based on the actual costs of others, the cooperative can motivate producers to take reasonable cost reduction measures on their farms, while making a fair and reasonable payment to all producers, which at least covers their costs. Under yardstick competition the cooperative guarantees to cover the individual producer’s actual costs, plus a percentage of what he saves relative to the cost normM in advance. It can be shown that each producer has a personal interest in minimising costs if he receives a sufficiently large share of the cost savings. Figure 4.15 below illustrates a cost reimbursement system based on yardstick competition.

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DKr.

Cost norm



cˆ j q j

Actual cost



cj qj

qj

Production q j

Figure 4.15 Cost reimbursement based on yardstick competition. All have their costs covered

It can be shown that the cost norm in equilibrium is very precise. If all members produce the same quantity, no-one will be paid more than their costs. In equilibrium all producers minimise their costs and are paid their minimal costs, neither more nor less. If producers produce varying quantities some of them will be paid more than their costs. However, it can be shown that even in this situation, the system minimises the amount that needs to be paid to motivate participation. Yardstick competition thus makes it possible to ensure that every producer receives reasonable payment, but that none can exploit his private knowledge about costs structures to obtain an exceptionally large share of the common revenue54. Example: Consider the situation in which three producers each produce 1,000 pigs under a yardstick contract. The payment under the contract consists of

production costs + 50 per cent of cost savings in relation to the others. The three producers all have minimum production costs of DKr. 500 per pig. However, in reality they produce at Producer A DKr. 500 per pig Producer B DKr. 600 per pig Producer C DKr. 700 per pig

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The norm against which producer A is compared is the lowest production costs for B and C, which is DKr. 600. So producer A is paid DKr. 500 (his production costs) + (DKr. 600 - DKr 500)/2 = DKr. 550 per pig. Correspondingly, producer B gets DKr. 600 + (DKr. 500 – DKr. 600)/2 = DKr. 550 per pig, but as his actual costs were DKr. 600 he makes a loss. He will therefore work to reduce his costs. The payment to producer C is DKr. 700 + (DKr. 500 – DKr. 700)/2 = DKr. 625 per pig, which gives a deficit of DKr. 75. He will also have an interest in reducing his costs. Mathematical representation Yardstick competition can be formulated in the following way. Each of n members supplies q 1 ,.., q n products to the cooperative. (q j , c j ) is producer j's actual production and costs. cˆ j ( q j ;( q k ,c k ), k z j ) are the costs which it is estimated, on the basis of data from the other producers. Under yardstick competition producer j‘s payment is thus ~ x j (q 1 ,..., q j ,..., q n )

c j  D j ˜ [cˆ j (q j ; ( q k , c k ), k z j )  c j ]

= the actual costs + share D j of the cost savings.

4.9.5 Decisions at farm level Price or quantity control

Establishing an equilibrium

Direct contract production with fixed production procedures and norms probably has the least information requirements for the individual producer, once he has chosen his product type. If price controls are used instead of contract production, for example a marginal pricing scheme, the individual producer must think about his production planning and how to optimise his production quantity. If price controls are supplemented by profit sharing, where the producer's total payment, inclusive of supplementary payments, depends on the production level of others, this naturally increases his need for information. Depending on the principles used by the cooperative for paying for special products, the producer can have a very large information requirement when choosing between different product types. It is easiest for a cooperative to design a payment scheme which gives the right incentives to members, as long as everyone behaves as required, that is, a scheme which leads to a reasonable Nash

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equilibrium, cf. Section 3.3. However, it is not necessarily the most effortless for the members to operate under such a system. Individual members can be spared many considerations and a considerable amount of information collection if the payment scheme implements dominant strategies, in which the individual producer's choice of action does not depend on what others do. The system of marginal price payments combined with guaranteed equilibrium supplementary payments has this attractive characteristic55.

4.10 Summary

Main theme traditional payments and quantity control

Alternative systems

Optimal marginal pricing scheme

In this chapter we have analysed a number of economic models which illustrate the applicability of different payment schemes for cooperatives. The main discussion has been about how the traditional payment principle (with allocation of revenues proportionate to the quantities delivered) operates under different assumptions about processing and marketing conditions. We have shown that if the marginal revenue is constant, the traditional principle results in efficient production levels. This is the great strength of cooperative organisations, as this means that they do not suffer from loss of production or lack of investment which threatens other arrangements because of the hold-up problem. If the marginal revenues are decreasing (or increasing), the traditional payment principle however results in over-production (or under-production) and it can be necessary to adjust the payment principles. In this chapter we have discussed the use of contract production with direct quantity control, a two-price system, Aumann-Shapley prices and the serial principle. In particular we have paid attention to simple price systems in which price reductions are used to control production volumes. However this often generates a surplus in the cooperative which must be allocated. There must therefore be additional rules for supplementary payments, which achieve a balanced budget without disturbing the production incentives too much. We have considered the marginal pricing scheme which ensures that the integrated profit is maximised. We have shown how marginal pricing, supplemented by various supplementary payment schemes (partly depending on production and partly on equilibrium quantities, breach of budgetary limits outside the equilibrium, guaranteed supplementary payments and so on) can lead to efficient production

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levels in a cooperative. At the same time we have shown that the transfer of profits from niche production to standard production does not solve the efficiency problem – but may indeed aggravate it. We have focussed on a situation with homogeneous primary products. Even in this situation there are a number of intra-product synergies between producers, and the exploitation of these is decisive for the efficiency of a cooperative. We have looked particularly at economies of scale and market synergies. In this chapter we have emphasised that the schemes must result in efficient production while taking due account of individual rationality, incentive compatibility and balanced budgets. We have also discussed the need for payment schemes which are fair, and which do not have excessive information needs. In the following chapter, we will do a systematic evaluation of six payment schemes on the basis of a broad spectrum of such criteria.

Notes Noter 1

If the capacity limits are reached this means that the costs will be much greater. See Hazell and Norton (1985). This is also the idea in the KVL model of different branches of industry, cf. e.g. Andersen et al (1979). 3 See Danske Slagterier (199a), as well as Chapter 6. 4 In Scandinavia this method has been used, for example, in connection with Skaane Dairies' assessment of a new payment scheme, cf. Anderson (1998). 5 This method has recently been used for constructing a simulation of the milk producers' response to changes in the payment principles; cf. e.g. Nielsen (1998). There is a particular problem in making comparisons when using purely sample data. In such cases the result can be a series of observations from different short-run cost functions. Theoretically it is possible to observe one point of each cost function, the point where the marginal costs equal the price paid. It is then possible to say that the producers' different production levels reflect their different short-term cost curves. We still think it is possible to use sample data because primary producers have presumably not had entirely homogeneous price expectations or sold at identical prices. 6 This summarised description of the revenue situation of the slaughterhouses can easily be developed as a model which applies when the cooperative receives products of different types. This could be a slaughterhouse receiving slaughter pigs of different types, cf. Section 2.4.2 on special pigs. In situations where there are different primary products then a model will express the cooperative's revenues as a function of a production vector, i.e. R(q). When the activities of the slaughterhouse are expanded to include more product types there can be positive synergies between the product types. This means that the profits of the cooperative exceed the profits which the product types could achieve in separate firms. In the general economics literature positive synergies between product types are called economies of scope. Synergies can occur as a result of production gains from co-operation in processing or as a result of co-ordinated marketing. Bogetoft (1996) gives an analysis of synergies in cooperatives. 2

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7

In the literature the abbreviations NRP, NMRP and NARP are used for net revenue product, net marginal revenue product and net average revenue product respectively. 8 Cf. Claudi Lassen (1997). 9 Danish examples of such descriptions are, for instance linear programming models of slaughterhouses by Christensen and Obel (1976), Fertin (1985), Rasmussen (1992) as well as Rasmussen and Thomsen (1991). The problems with using sample data are illustrated by Asmild & Bogetoft (1998) and Winther (1997). 10 This is due to the open production rights which mean that the slaughterhouse cannot control the supplies of primary materials. 11 See Danske Slagterier (1999b). 12 It is also possible, in accordance with the classic production theory, to model the earnings potential as a quantity corresponding to all the levels on the R(Q) curve. It is also possible to consider V as a one dimensional slack variable which indicates how much the actual revenues fall below the maximum obtainable. 13 The example in Section 5 illustrates the difference between the precise and the approximate solution for different sizes of co-operative. 14 Note that we have implicitly included physical applicability via the cost and revenue functions as explained above. 15 See for example Bogetoft (1994). 16 In the literature this is called asymmetric information. 17 A principal-agent model of a cooperative with asymmetrical information (private knowledge) is analyzed in Bogetoft(2005). The introduction of uncertainty and risk aversion can take place within a standard principal-agent model with hidden actions, cf. for example Bogetoft (1994) 18

j

i.e. P ' (Q ) q . An illustration corresponding to Figure 4.6 is standard in most presentations of the theory of cooperatives, see e.g. Corbia (1989) and it is based on Helmberger (1964) and LeVay (1983). 20 However, cf. the example in Section 4.5. Technically speaking this approximation corresponds to a Cournot equilibrium in an oligopoly situation approaching a perfect competition equilibrium 21 One possibility is for a co-operative to split up the membership into smaller groups, perhaps with 10 producers in each, which are allocated parts of the market, possibly using the quota based marginal payment scheme discussed below. In this way strategic behaviour, possibly helped by social pressure, could presumably reduce the over-production problem significantly. 22 I.e. P' (Q) ! 0 . 23 We disregard the increased transaction costs which are to be expected in this and in the following example. 24 Cf. e.g. Tirole (1988). 25 Cf. e.g. Tirole (1988) and Hart (1995). 26 Cf. e.g. Antle and Eppen (1985) and Tirole (1988), or for more general cases Antle, Bogetoft and Stark (1999). 19

j By way of P' ( Q )q in (4.1). I.e. via P' ( Q )Q in (4.2). 29 The national pricing system is described in Chapter 2. 30 See for example Andelsbladet (1998) and Danske Andelsselskaber (1996). 31 Fulton (1998), Lopez & Spreen (1985), Sexton (1986), and Zusman (1982). 32 See e.g. Diricks and Jennergren (1979). 33 See e.g. Søgaard & Just (1995). 34 See for example Bogetoft (1998) in which it is demonstrated that a marginal price system proposed by Danish and Swedish milk producers would normally result in a budget deficit. 35 For the sake of simplicity it is assumed they can be differentiated. 27 28

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PETER BOGETOFT AND HENRIK B. OLESEN .

See e.g. Tirole (1988) on the signalling of market behaviour. It can be objected to this system that it does not provide any guidelines as to how payment should be arranged outside the equilibrium. Members will always receive the residual earnings of the company in their capacity as owners. There is therefore a need for further rules which lay down how the residual earnings should be dealt with once the members have received their guaranteed supplementary payments. This can be done by using the slack model described above or by including a third part which ensures a balanced budget outside the equilibrium. The latter method is described in Tirole (1988) as well as Holmström (1982). j 1 n * j 38 This payment scheme appears as x (q ,.., q ) P q . 39 In Denmark, for example, Bent Claudi Lassen, the then chairman of The Federation of Danish Cooperatives and now the chairman of The Federation of Danish Pig Producers and Slaughterhouses, has expressed the view as follows "It is obvious that the rest of the members of the cooperative have a claim to part of the profit if the 'special group' uses the assets of the concern.", see Jyllands-Posten (1998) This point of view seems to be shared by a researcher on cooperatives, Søren Svendsen, who has said "The collective membership must obviously have its share of the profit. That's logical.", see Jyllands-Posten (1998). 40 This assumes that there are no fixed costs or similar, i.e. R(0)=0. 41 Moulin (1988). 42 Moulin (1988). 43 There is a formal description of the characteristics of the serial allocation principle in Hougaard (1998). 44 See Andelsbladet (1998). 45 See Bogetoft (1994) on the use of non-verifiable information in contracts. 46 Lopez & Spreen (1985) is an example of a more theoretical approach, while there is a more practically oriented approach in the proposal in Søgaard & Just (1995), suggesting that co-operative slaughterhouses can control quantities of special products by means of production rights sold at auction. 47 See e.g. Dirick and Jennergren (1979), Heal (1973), Johansen (1977, 78), Meijboom (1987) and Obel (1981). 48 See e.g. Dirick and Jennergren (1979), Heal (1973), Johansen (1977, 78), Meijboom (1987) and Obel (1981). 49 See Milgrom & Roberts (1992) for a more detailed discussion of the robustness of price controls contra quantity controls. 50 Cf. Section 2.6.1. 51 See e.g. Bogetoft (1994) and its references. 52 The individual member shall 'merely' be given an incentive to report his true costs rather than a false cost level. 53 The case of differences in the cost structure is dealt with in the general literature under the heading of relative performance evaluation, see, e.g. Holmström (1979, 1981). For a textbook approach see Kreps (1990). 54 The basic model of yardstick competition is Schleifer (1985). A yardstick-based cost re-imbursement system which is based on linear programming and which allows production of multiple products by each producer is developed in Bogetoft (1997, 2000) and Agrell, Bogetoft and Tind(2005). 55 Also the suggested marginal pricing system for milk production, in which marginal prices depend on quotas, has these characteristics in a modified form, cf. Bogetoft (1998). 37

5 Producer groups as units for analysis

Six schemes

Criteria

Multi product payment schemes In this chapter we analyse a series of payment schemes aimed at multi product cooperatives. The schemes are defined and exemplified using a common example. Moreover, they are evaluated using the multiple criteria approach suggested in Chapter 3 The payment schemes analyzed in Chapter 4 were primarily aimed at cooperatives with a single product line. We now focus on schemes for multi product cooperatives. Of course the distinction is not that precise. The single product schemes may be used in a multi product cooperative to allocate inside a producer group. Also, the multi products schemes are sufficiently general to be applicable in single product cooperatives. To simplify the exposition, however, we consider the producer groups to be the primary players in this chapter1. For instance, when we analyse whether a payment scheme leads to a solution in the core, we check whether producer groups or coalitions of producer groups have an incentive to leave the cooperative. We analyse no less than six different schemes. The first is based on the idea of equal gross margins in different product lines, the second on equal returns on capital and the third involves a combination with production quota. They all have a background in Danish agriculture but are of course applicable and used more generally as well. The last three are classical schemes from cooperative game theory, namely the socalled ACA, Nucleolus and Shapley methods. The six schemes are analysed using the multiple criteria evaluation framework from Chapter 3. We focus on nine of the properties (criteria) that we consider to be of particular interest, namely Efficiency, Core solution, Information needs, Total monotonicity, Coalition monotonicity, Investment, Risk, Consistency, and Additivity.

5.1 A general example Example to illustrate the properties

A formalisation of the criteria and of the payment schemes which we analyse, can easily lead to a highly complicated notation. Therefore, we supplement the analysis with a simple example, which illustrates the properties of the payment schemes. The example is only for the purposes of illustration, and the figures used do not give a realistic picture of actual conditions in the pig industry.

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Example This example concerns a cooperative slaughterhouse which produces multi-pigs, UK pigs and organic pigs. The revenues of the cooperative are DKr. 800 million. The stand-alone revenue for the product types are DKr. 200 million for multi-pigs, DKr. 100 million for UK pigs and DKr. 300 million for organic pigs. If two of the producer groups get together in a cooperative, they can obtain revenues of DKr. 500 million, regardless of which two product types are involved. There is production of 700,000 multi-pigs, 100,000 UK pigs and 200,000 organic pigs. The producers' costs are DKr. 600 per multi-pig, DKr. 700 per UK pig and DKr. 750 per organic pig. The capital requirements are DKr. 1,000 per multi-pig, DKr. 2,000 per UK pig, and DKr. 3,000 per organic pig. It is assumed that the interest rate is 5 per cent per year. The assumptions in this general example are summarised in Table 5.1 below. From time to time in this analysis, it is necessary to modify this example to emphasise particular points in the individual payment schemes. Product type (Coalition S)

Standalone revenue (100 million)

ProUnits produced duction (100,000) costs per pig qi (DKr. 1,000)

R(S)

ci Multi-pigs (M) UK pigs (E) Organic pigs (O) Two product groups together Total Cooperative

Production costs excl. financing (DKr. 1,000)

Capital require ment per pig (DKr. 1,000)

c~i

k i

2 1

7 1

0.60 0.70

0.55 0.60

1 2

3

2

0.75

0.60

3

5 8

Table 5.1 Assumptions used in the general example

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5.2 National pricing system: Equal gross margins The same gross margin

Payment

In this section we analyse the principles previously used for paying special producers in Danish cooperative slaughterhouses2. Until 1999 the Pricing Committee of The Federation of Danish Pig Producers and Slaughterhouses set the weekly price and the supplements which could be paid to special producers. The policy of the Pricing Committee regarding special production was that3 "the price paid for special breeds or suchlike must be approved by the Pricing Committee, and any supplementary payment may only correspond to the extra costs of the production concerned". Thus, the payment was determined so there was the same gross margin on all types of pigs. First the supplement corresponding to their additional costs was paid to the special producers. Then the remainder was allocated in proportion to the quantities delivered4. In other words, the payment for traditional products wasM The revenues of the cooperative - supplements paid to special producers The total quantity supplied The special products were paid with the same amount as the traditional products, with the addition of the supplement which corresponded to the additional production costs. It only makes sense to aggregate different product types if the products are comparable. For example, this payment scheme would not be applicable for allocating revenues for products as different as pigs and milk. The system cannot be used by cooperatives with widely differing product types, unless there is agreement on a fixed conversion factor between the different product types. Example In the general example the supplement for UK pigs is 0.7 - 0.6 (thousand DKr.) and the supplement for organic pigs is 0.75 - 0.6. The total supplements paid to the special producers is therefore 1 ˜  0.7  0.6  2 ˜  0.75  0.6 0, 4

Payment for the three kinds of pig would thus be yM

8  0.4   0.6  0.6 0.76 (1.000 kr.) 10

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yE yO

8  0.4   0.7  0.6 0.86 10 8  0.4   0.75  0.6 0.91 10

This represents a total payment to the groups of 5.32 to the producers of multi-pigs, 0.86 to the producers of UK pigs and 1.82 to the organic producers. Mathematical representation In a cooperative with producer groups i=1,…, m, each producing q i products of type i, the payment according to the principles of the National Pricing System is º ªm Rq  «¦ ci qi  c1Q » ¼  c  c ¬i 1 yi 1 i  Q  supplement payment basic payment

where y i is the payment per product unit (e.g. per pig or per kg of milk) to producer group i. Q q1  ...  q m is the total quantity delivered5 to the cooperative, while the vector q  q1 ,...q m indicates the total of each of the different product types which the cooperative receives. R(q) is the total revenue of the cooperative. Group 1 is the producers of the standard product (the product type with the lowest production costs). We assume that there are constant marginal costs, so c1 is the production cost per product in group 1. The production costs in group i for producing qi are c1 qi . In the calculations for this payment scheme the production costs include the financing costs. The equation m

¦ ci i 1

 c1 q i

m

¦c q i

i

 c1Q

i 1

therefore consists of the total supplements which the cooperative must pay to the special producers i=2,…m, before the remainder of the revenues can be paid out in proportion to the quantities supplied.

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5.2.1 Efficiency and incentives

Distortions of production

To evaluate the efficiency of a payment scheme, we compare the productions which the payment scheme result in with the efficient productions (first best); i.e., the production plan which maximise the integrated profit. The payment scheme based on the National Pricing System distorts the production quantities by equalizing the gross margins. In the efficient production plan, the gross margins on the different products are seldom equal. For special products sold on thin markets, the cooperative can obtain higher earnings by limiting production quantities. The principle of uniform gross margins for all product types deprives the cooperative of the possibility of controlling supplies of special products via price signals. Production quantities of special products therefore have to be controlled via contracts6, so as to implement optimal (efficient) special production. However, this generates more revenue for the cooperative which must be allocated to the members. When this allocation is made in proportion to the quantities delivered, this distorts production levels of the different product types which are not subject to quantity controls, cf. also Chapter 4 and the discussion herein of alternative ways to allocate a surplus. The situation is shown in Figures 5.1 and 5.2, which consider the production of special products i, which are sold in a thin market with a falling demand curve, and standard product 1 which is sold under conditions of perfect competition. The optimal production level lies where the marginal costs equal the marginal revenues, cf. Chapter 4. In the figures, we disregard possible synergistic effects between the two productions.

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DKr. Marginal cost c ' qi

Profit Fortjenest e Fortjeneste

Average revenue R q1

Marginal revenue R' q i Production q i

* Optimal production q i

DKr.

Marginal cost c ' q1

Average revenue = marginal revenue

* Optimal production q1

Production q1

Figure 5.1 First best production In the figures, it is assumed that the production level of special pigs is controlled by contracts. This makes it possible to obtain the optimal production volume of special products. The special production generates a surplus (the grey area). Under the National Pricing System, part of the surplus would be transferred from special production to standard production. This sends the wrong earnings signals to the standard producers as shown in Figure 5.2., so there is a distortion of the production volumes of the product types which are not subject to quantity control.

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DKr. Marginal cost c ' qi

Fortjenest Fortjeneste Profit e

Settlement price

Marginal revenue R' q i

* Optimal production q i

Production q i

DKr.

Marginal cost c ' q1

Settlement price Loss

Optimal production

Actual production

Average revenue = marginal revenue

Production q1

Figure 5.2 Production under the National Pricing System

5.2.2 The core Cooperation is not always beneficial

One of the more important criteria for evaluating a payment scheme is whether or not it supports cooperation. In a scheme based on the National Pricing System, payment to a producer group depends only on the revenues of the cooperative and the production costs. Payment is thus not dependant on the alternative revenue possibilities of individual producer groups, e.g. the stand-alone revenue from UK pigs, so the payment scheme does not guarantee that the resulting allocation of the cooperative's revenues belongs to the core. There will be situations

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where producer groups will have an incentive to leave the cooperative, and where other groups will be subsidised. This reflects what has been seen in practice in the pig industry. Exports of live pigs for slaughter in Germany7 show that, at least in the short term, payments to some pig producers are lower than their revenue potential outside the cooperative, so the export of live pigs demonstrated that the principles of the National Pricing System did not fulfil the conditions of the core8. Example The calculations in our example illustrate that the scheme does not ensure a core solution. Thus, the payment scheme results in a price for organic pigs of DKr. 910 per pig. The organic producers can obtain payment of DKr. 1,500 per pig on a stand-alone basis. Organic pig producers thus have an incentive to resign from the cooperative. The problem arises because the National Pricing System only takes account of the production costs, while the potential stand-alone profits are determined by sales options as well as by the production costs.

5.2.3 Information needs The information needs of the cooperative

The information needs of the producers

Simplicity is clearly one of the great strengths of the scheme. In order to calculate the payment, it is only necessary for the cooperative to know the total revenues and the additional production costs of special production. This is no great problem in practice, because there are large quantities of accounting information available in agriculture, so it is relatively easy to make the cost calculation9. To find the optimal level of special production the cooperative must know the cost functions of the primary producers, as well as how the prices in each market depend on the volumes. Only if the cooperative has this information, is it possible to fix production quantities through contracts, so the integrated profit is maximised (given the limitations of the scheme). Since the gross margin is the same for all product types, it does not matter to the individual producer which product type he chooses – at least in theory. It follows that the producer does not need special insight into market prospects for each product type before making his choice. He only needs a general evaluation of the prospective revenues of the cooperative.

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5.2.4 Monotonicity Reasonable dynamic properties

Weak incentives for producer groups

Monotonicity is an important characteristic for evaluating a payment scheme. Monotonicity ensures a reasonable adjustment of payments when market conditions change. This is important in the pig industry, for example, because the market conditions for different product types are constantly changing. In a payment scheme based on the National Pricing System, an increase in the cooperative's revenues would lead to higher payments for all producer groups. The scheme also ensures that a producer group would always be rewarded, if it contributes to improvements in the cooperative so total monotonicity is satisfied. The scheme likewise is coalition monotonic, because the payment to a producer group could only fall if the revenues of the cooperative fell. This is because payment is independent of the revenue possibilities of possible sub-coalitions of producer groups, for example an independent slaughterhouse for organic pigs. However, the payment scheme provides only weak incentives for individual producer groups to improve their revenue. This is because payment to individual groups is dependant on the development of the total revenues of the cooperative. Growth in the revenues of the cooperative are allocated in proportion to the volumes delivered. This means that if, for example, organic pigs are the cause of the revenue growth, organic producers receive only part of the growth, corresponding to their share of the total volumes. If organic pigs only constitute 5 per cent of the total deliveries, the organic producers only receive 5 per cent of the growth in revenues they have created. The example given below shows that the payment scheme for individual producer groups gives only a weak incentive for individual producer groups to develop the sales value of their own products. Example The situation can be illustrated by making a modification to the general example. Assume that there is an increase in demand on the English market, so that revenues increase by 1 in all coalitions which include UK pigs. Thus the stand-alone revenues for producers of UK pigs increase from 1 to 2, and the revenues of the cooperative for all three product types increase from 8 to 9. In this situation the new price paid per UK pig would be y ENEW

9  0.4   0.7  0.6 0.96 10

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PETER BOGETOFT AND HENRIK B. OLESEN

On this basis payment for UK pigs only increases by DKr 100 per pig, from DKr 860 to DKr 960, and payment to producers of UK pigs increases by only DKr 10 million, in spite of the fact that the revenues for all coalitions with UK pigs increase by DKr 100 million.

5.2.5 Investments

Risk of hold-up

The cooperative should pay for general investments

It is important that a payment scheme should lead to sensible investments so future earnings potential is protected. The supplement paid to special producers is seldom set for more than a few years ahead10, so a pig producer investing in production equipment with a longer life-span risks a weakening of his position when a new supplement is determined. Traditionally there is no hold-up problem in cooperatives because the producers themselves own the company. With differentiated production there is a risk that the traditional pig producers will exploit the specific investments of the special producers to hold-up the special producers. This can happen when there are changes to the supplementary payments for special producers. A payment scheme based on the National Pricing System has similarities to yardstick competition, which is described in Section 4.9.4. In contracts of this type, an individual participant has an incentive to do better than the others in his group, but for the group as a whole, there is no incentive to do better than other groups. In a payment scheme this means that the individual producer has an incentive to reduce his production costs in relation to the others in his producer group, but that the producer group as a whole will be worse off by reducing its production costs11. In the next example, the organic pig producers are worse off because of cost savings. The reason is that the cost savings are shared between all producer groups, while the reduction of the supplementary payment affects them fully, so a producer group has no incentive for investing in measures to reduce the general costs of the particular product type. Nor does an individual producer have any incentive for undertaking general investments (for example developing a more rational pig-pen system), because the gains of such an investment would be a public good benefiting all producers - the free rider problem12. The result is that the investment costs, for general measures which can reduce cost levels, must be borne by all producers in common. In the Danish pig industry this is the task of The Federation of Danish Pig Producers and Slaughterhouses13.

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185

Example Assume that production costs fall from 7.5 to 7 for organic pigs so §

m

·

the cooperative's supplementary payment ¨ ¦ ci q i  c1Q ¸ to special ©i

1

¹

producers falls from 0.4 to 0.3. The price paid for organic pigs will then be 8  0.3 y*O   0.70  0.6 0.87 10 This means the profit per organic pig will fall from (0.93-0.75) = 0.18 to (0.87-0.7) = 0.17.

5.2.6 Risk Good risk sharing

The payment scheme has good risk sharing on the income side. This is because variations of income for a single product type are shared between the producers of all product types. The scheme also gives good risk sharing for variations in production costs, for example via factor prices which can affect a single product type. This payment scheme (as the other schemes looked at in this analysis) gives no security when it comes to production risks; i.e., uncontrolled variations of production volumes of an individual producer (or of a whole producer group). This is because payment is based directly on the volume produced. A producer who, for one reason or another, suffers from a fall in production has to bear the full consequences of this.

5.2.7 Consistency and additivity No conflict about accounting principles

A payment scheme based on the National Pricing System limits conflicts about accounting principles. This is because the payment scheme is both consistent and additive. Payment does not depend on whether the allocation is done hierarchically, or whether payment is allocated to all producer groups at the same time. Likewise payment is the same regardless of whether there is consolidated allocation of the cooperative's revenues, or the sales revenue and processing costs are allocated separately.

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5.3 Payment scheme for piglets: Equal returns on capital Same return on capital

Payment

In the Danish pig industry the allocation of revenues between producers of piglets and producers of slaughter-pigs is usually based on the capital involved14. Producers of piglets and slaughter-pigs often use the estimated piglet price as the price guide for contracts between them. The calculation of the estimated piglet price is made by The Federation of Danish Pig Producers and Slaughterhouses, and it is based on the principle that "producers of piglets and of slaughter-pigs should have the same return on capital invested in production equipment" (Danske Slagterier, 1999). The principle for piglet pricing can be used as a basis for a payment scheme for cooperatives with differentiated primary products. Payment per product unit is determined as followsM: The production costs of the relevant product, excluding financing costs, are paid as the basic payment. Thereafter the remaining surplus (i.e. the cooperative's revenue minus the total production costs) is allocated in proportion to the capital investment. In this case the capital investment and the production costs used are the average norm for capital requirements and production costs per unit of the product type in question. So payment is not directly based on the actual costs and the actual capital investment of the individual producer. This fully corresponds to the principles of the piglet pricing system. Mathematical representation Based on an equal return on capital the payment per unit is as follows

yi

m ki ª º Rq  ¦ c~i qi »  c~i « K¬ 1 i ¼ return to capital

where y i is the payment per unit of product type k, k i is the capital requirement associated with the production of product type i, K is the k

total capital requirement, i.e. K

¦k q i

i

, R(q) is the total revenue of

i 1

the cooperative, q is the cooperative's production vector, c~i is the production costs per unit of product type i exclusive of financing

MULTI PRODUCT PAYMENT SCHEMES

187

costs (as opposed to ci which was the production costs including financing costs). Example In the general example, the total capital investment is 15 and the total direct costs are 5.65, so payment to the producers of multi-pigs, UK pigs and organic pigs is yM yE yO

1 >8  5.65@  0.55 0.707 15 2 >8  5.65@  0.6 0.913 15 3 >8  5.65@  0.6 1.07 15

This corresponds to a total payment to the producer groups of 4.95 for multi-pigs, 0.91 to the producers of UK pigs and 2.14 to the organic producers.

5.3.1 Efficiency and incentives Inefficiency caused by transfers

To a great extent, this payment scheme matches the National Pricing System. This means that in this scheme too, there is inefficiency, because the profits from special production are shared among all product types. This leads to increased production of the product types which are not subject to quantity control. For example, high profits on organic pigs can result in over-production of multi-pigs, because the profits on organic pigs increase the payment for multi-pigs.

5.3.2 The core Not always in the core

As with the National Pricing System, payment to the individual producer does not depend on the alternative income options for the individual producer groups. Hence, the payment will not always be in the core. Cooperation based on the payment scheme for piglets can therefore lead to situations in which some producer groups or coalitions of producer groups are subsidised, while others have an incentive to leave the cooperative. This situation is well known from the Danish market for piglets. In the second half of the 1990’s there were wide variations in the market price for piglets. This meant that a large number of existing contracts were terminated, because the official piglet prices varied too much from the alternative revenue options of the producers. This resulted in a considerable loss to the industry of the benefits of cooperation15.

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PETER BOGETOFT AND HENRIK B. OLESEN

5.3.3 Information need Easy to obtain information

One advantage of the payment scheme is that it is based on information about the cost conditions of producers, which are relatively easy to obtain and use in cost calculations. The assessment of capital investment is sometimes more difficult. It is also necessary for the cooperative to gain knowledge about market conditions in order to plan the optimal production levels for special products. When individual producers choose between different product types, they are, in principle, guaranteed the same return on capital, regardless of which product type is chosen. This means that the individual producer does not need to have an in depth knowledge about the sales prospects for the individual product types. On the other hand, he always needs to make an overall assessment of the revenue potential for the cooperative's products. He also needs to make an overall assessment of the capital and production costs. Only then can he evaluate whether it is worthwhile investing in the production of the cooperative's products.

5.3.4 Monotonicity Requirements satisfied

Higher revenues in the cooperative result in higher payments to all producers. Thus the payment scheme is total monotonic. Payment is independent of developments in all sub-coalitions, so the requirements of coalition monotonicity are also satisfied, since payment to one producer group can fall only if the total revenues of the cooperative fall.

5.3.5 Investments General investments should be made in common

Independent weighting

This payment scheme suffers from the same weaknesses in investment incentives as the National Pricing System. Thus a producer group does not have an incentive to reduce its production costs through general measures, such as the development of new pig-pen systems or improved breeding, etc. This particularly applies to cost reductions due to lower capital intensity. If a producer group saves on capital, it will obtain a smaller share of the cooperative's revenues; therefore it can be an advantage for a producer group to use a lot of capital. These results are shown in the next example. The problems of investment incentives disappear if a basis for weighting individual product types is used, which is independent of capital and costs. The idea of a weighted payment schemeM is that each product of a given type corresponds to a specific number of standard products.

MULTI PRODUCT PAYMENT SCHEMES

189

A weighted payment scheme is in many ways similar to a payment scheme based on capital investment. The weighted payment scheme thus x does not always belong to the core x is monotonic x is consistent and additive Adjusting the weighting is problematic

The question is how the weighting should be decided. Initially the weighting will be based on costs and capital. But it can upset investment incentives if the weighting is subsequently changed to reflect actual cost and capital conditions. This would mean that an investment in the development of cheaper production methods could result in the product of a producer group being given a lower weighting, and therefore a lower share of the revenues. However, producers have an incentive to invest if the weighting is kept more or less constant. Example We start with the general example in order to show the characteristics of the piglet pricing system. We assume that capital investment in the production of organic pigs falls from 3 to 2 so the total capital invested falls from 15 to 13. This means that the payment per organic pig falls from y OBEFORE

3 >8  5.65@  0.6 1.07 15

to y OAFTER

2 >8  5.65@  0.6 0.96 13

The profit (price paid minus production costs inclusive financing costs) per organic pig falls from (1.07-0.75) = 0.32 to (0.96-0.7) = 0.26. In other words, the organic producers would be worse off because their production is less capital intensive. Mathematical representation In the weighted payment scheme each product of type i z 1 corresponds to vi products of type 1. Also, v1 1 . The payment scheme is then

yh

vh m

¦v q

i i

i 1

Rq

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PETER BOGETOFT AND HENRIK B. OLESEN

5.3.6 Risk Poor risk sharing

An increase in the cooperative's revenues will primarily benefit capital intensive producer groups. Correspondingly these groups are hit the hardest when revenue falls. From a risk perspective this is bad, because the producers with the most capital tied up in production, also have the greatest risk. Typically the least well established producers are the most sensitive to variations in income, and will primarily bear the risk associated with the revenues of the cooperative.

5.3.7 Consistency and additivity Satisfies the requirements

Allocating individual items of income and expenditure in proportion to the capital costs gives the same payment to individual producers as if the revenue were allocated using the same principle. The payment scheme is therefore additive. Mathematical representation The payment scheme is consistent. This can be seen by looking at the payment allocated to producer group h by a hierarchical system. First we look at the payment to group J which includes h. The group's capital costs per unit are calculated as

¦k q ¦q i

kJ

i

iJ

i

iJ

Group J is therefore allocated the following payment per unit

yJ

kJ K

N ª ~ º « Rq  ¦ ci q i »  i 1 ¬ ¼

¦ c~ q ¦q i

i

iJ

i

iJ

This payment is now allocated to the individual product groups within J. Producer group h receives

xh



ª º « » kt « § k J · ~ q »  c~  y q c ¸ ¨ ¦ i ¦ J i i» h ki qi « © K iJ ¹ ¦  iJ  » «

iJ  « Payment to group J prod. costs » in group J ¼ h ' s share ¬

MULTI PRODUCT PAYMENT SCHEMES

xh

191

ª º ~q · « » § c ¦ i i m ¨ kJ ª ¸ » ~ kt « º iJ ~ ~ ¸  ¦ ci qi »  ch «¦ qi ¨ « Rq  ¦ ci qi »  ki qi « iJ ¨ K ¬ i 1 i J ¼ ¦ qi ¸ ¦

 » J i J © i prod. costs » « ¹ group J Payment to group J ¬ ¼ m kh ª º Rq  ¦ c~i qi »  c~h K «¬ i 1 ¼

which is the payment which group h would receive if the revenues were allocated simultaneously to all groups.

5.4 The premium-pig system: Quota and premium products

Parallels with agricultural policy

Balanced budget and efficiency

In this section, we propose a variant of the marginal pricing system from Chapter 4. It consists of using marginal pricing for the payment of different product types, while using a supplementary rule for allocating the residual revenue to owners of special premium rights. In the pig industry context, the system implies that producers receive some payment for the products they deliver, as well as a supplement for “premium pigs”. The producer must own premium rights in order to supply premium pigs. The payment scheme is described in detail below. Many measures of agricultural policy seek to ensure higher prices by reducing production. There are parallels between this and the issues of quantity control in cooperatives16, enabling the utilisation of past experience of various agricultural policy instruments as a source of inspiration for new payment schemes. One of the themes in this book is that individual members can cause harm to a cooperative by pursuing their own interests. Giving individual members the same interests as the cooperative, can solve the problem. In Chapter 4 we analysed various suggestions as to how a cooperative can achieve efficiency and a balanced budget simultaneously. Californian milk quotas are a practical example of a similar mechanism which ensures both efficiency and a balanced budget17. This quota arrangement is also an example of an agricultural policy instrument which can inspire payment schemes in cooperatives. The quota arrangement is described in the box below. The Californian milk quota is broadly reminiscent of a proposal made in the Danish and Swedish dairy industries that the price paid

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PETER BOGETOFT AND HENRIK B. OLESEN

should depend on the extent to which a producer uses his milk quota18. The main difference is that the Nordic proposal is based on a direct and detailed signalling of revenue potential, while the Californian scheme only uses two prices, similar to the premium pig scheme. The premium pig scheme described here has been developed with the aim of dealing with differentiated products.

Californian milk quotas

The payment scheme

Example In the USA the milk market has been regulated since the 1930’s in order to ensure high prices for farmers. Outside California, American farmers receive one average price for all their milk (a pool price for drinking milk and industrial milk). This means that the higher price for drinking milk leads to greater milk production19. California uses a two-price system. There is a high price for the milk supplied which does not exceed the producer's quota (called 'quota milk'), and a lower price for the remaining milk. Broadly speaking, until 1997 the price of quota milk corresponded to the price the processors had to pay for drinking milk, while the lower price corresponded to the price for milk for industrial use. Since 1997, quota milk has been paid a fixed supplement20. If the milk quota is not fully used, the quota owner gets no return on the unused portion of the quota, as it is not permitted to lease quota out. Quotas can be freely sold, so there is an incentive to sell any unused quota. The total milk quota in California is considerably less than the total production, so there are always farmers who are interested in buying more quotas. In this way, practically no farmer owns more quota than he uses. This means that the marginal price to producers; i.e. the price paid on the last milk from a farm, is the low milk price, so the high price for drinking milk does not lead to increased milk production in California. Producers are free to choose their production level. The Californian milk quotas do not directly regulate production volumes. The milk quotas are merely a method for implementing a dual price system.

A cooperative can copy the principles of the Californian milk quota by introducing a two-price scheme in which producers with special premium rights receive a supplement for part of their production21. Producers can in effect buy and sell rights to part of the cooperative's supplementary payments.

MULTI PRODUCT PAYMENT SCHEMES

Payment equal to marginal revenue

Allocation of surplus

Rules of the scheme

193

In order to ensure that members have the right production incentives, the additional payment which a producer gets from supplying an additional unit, must correspond to the cooperative's marginal revenue for that unit. Expressed more formally, the producer's marginal payment must be equal to the cooperative's marginal revenue (marginal price)22. This means, for example, that the price for a UK pig should correspond to the amount by which the cooperative's revenue would increase with the production of one more UK pig. There will normally be a surplus in a cooperative if the marginal price is used for payment23. The surplus (or deficit) which arises under marginal pricing does not distort the incentives, if it is allocated as supplementary payments without direct reference to production. If premium rights to supplementary payments are freely traded, the rights are similar to shares in an investor-owned company. There is, however, the important difference that the members; i.e., the producers, still have the right to make decisions in the company. Schemes based on marginal prices and the disposition of surplus via premium rights, are not tenable if the rights are held by non-members. In such a situation, the members would have a strong incentive to change the payment scheme or to manipulate information to ensure a price above the marginal price24 for themselves. The scheme would also be very difficult to sustain, if there were substantial conflicts of interest within the membership; thus it is desirable to design a system ensuring the members reasonably homogeneous interests. This will be the case if all members have the same relationship between the total of premium rights and their production. Regulating the trading of premium rights can ensure this. A cooperative slaughterhouse can implement a premium pig scheme by using the following rules 1. The price for each type of pig shall be the marginal revenue for the relevant type of pig. 2. Members are free to choose their own production levels. 3. If marginal pricing leads to a surplus, this shall be allocated according to the deliveries of premium pigs. The number of premium pigs delivered by a producer is the number of premium rights he owns, though not exceeding the number of pigs that are in fact delivered, regardless of type. 4. If marginal pricing leads to a deficit, this shall be allocated in proportion to the premium rights. 5. The cooperative determines the total number of premium rights as

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PETER BOGETOFT AND HENRIK B. OLESEN

6. 7.

8. 9.

Supplementary payment, regardless of product type

Applicable to other cooperatives

a percentage of the total number of pigs slaughtered in the previous year (e.g. 80 per cent). Increases or decreases of the total number of premium rights are allocated in proportion to the premium rights owned. Premium rights can be sold if the producer has more premium rights per pig produced than the average for all the members of the cooperative. All members are entitled to buy additional premium rights. Premium rights cannot be leased.

We justify each of these rules in the following section. The scheme distinguishes between different kinds of pigs when the marginal prices are set, but not when supplementary payments to owners of premium rights are set. A producer's supplementary payment per premium pig is thus independent of the kind of pig he produces. Nor is the total of a producer’s premium pigs dependent on which kind of pig he produces. The only relevant numbers are the total of premium rights owned and the total number of pigs delivered. The scheme, as described, is most applicable to cooperatives where the different product types are comparable. However, it is possible to link the rights to the turnover, rather than to the number of units delivered, so the principles of the scheme can be used in cooperatives with very different kinds of products. There would be a number of start-up problems when introducing such a scheme in a cooperative. A key initial question would be how the premium rights should be allocated. One obvious possibility is to allocate the rights in proportion to the producers' past deliveries25. To ensure an effective allocation of premium rights, it would be appropriate to allow free trading of rights immediately after the initial allocation of the premium rights. This will avoid members being locked into a situation where they have too many rights in relation to their production. Mathematical representation Imagine a cooperative slaughterhouse with producer groups i=1,…m, in which each produces qi pigs of type i. The basic payment per pig of type i pigs is

~y i

dR q dq i

Once the basic payment has been made there is residual revenue in the company of

MULTI PRODUCT PAYMENT SCHEMES

Rˆ

195

dR q qi R q  ¦ ~ yi qi R q  ¦ i 1 dq i i 1 m

m

If this residual revenue is positive when the revenue function is concave, it will be allocated in proportion to the total of premium pigs. The total of premium pigs for producer j, who produces type i pigs is zj

­° qij ® j °¯v

for v j t qij for v j  qij

where qij is the total number of pigs delivered by producer j and v j is the total of premium rights owned by producer j. This means that the supplementary payment per premium pig is m

ˆy

Rq  ¦ ~y i qi i 1

z

when z is the total number of premium pigs, i.e. n

¦z

z

j

j 1

z i is the total of premium pigs delivered by the producers in producer group i. It is assumed that each producer only delivers pigs of one type. z i is therefore given by

zi

¦z

j

hvor S i

^j  N | q

j i

`

!0

jS i

The total payment to group i is then

xi

~y q  ˆy ˜ z i i i

If the residual revenue is negative, it is allocated in proportion to the premium rights, i.e., proportionately to v j . In this case the total payment to group i becomes  x ~ y q  y˜v i

i

i

i

where vi is the sum of the premium rights in group i and

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PETER BOGETOFT AND HENRIK B. OLESEN

m

 y

Rq  ¦ ~ y i qi i 1

n

¦v

j

j 1

The total of premium rights v is determined as a percentage of the previous year's production. This means that this year's total of premium rights v T is determined by last year's production Q T 1

vT

w ˜ Q T 1

where w is an expansion factor w t 1 or a contraction factor w d 1 . Expansions or contractions are allocated in proportion to the individual members' premium rights. This means that the number of premium rights v j ,T for producer j in year T are

v j ,T

v T  v T 1 j ,T 1 v v T 1

The maximum number of premium rights which a member can sell is ­ v  ½ Max ®0, v j  q j ¾ Q ¯ ¿ 

where q j is producer j's actual production of pigs. We have assumed that the cooperative has information about members' actual production, and not just information about their deliveries. Example Table 5.1 does not show the marginal revenues of the different types of pigs. If it is assumed that the marginal revenue corresponds to the production costs per pig; i.e., 0.6 for multi-pigs, 0.7 for UK pigs and 0.75 for organic pigs, the basic payment will be ~ yM

0,6 (1.000 kr.)

~ yE

0,7

yO

0, 75

The residual revenue of the cooperative is R

8  7 ˜ 0.6  1 ˜ 0.7  2 ˜ 0.75 1.6

(DKr. 100 million)

MULTI PRODUCT PAYMENT SCHEMES

197

It is assumed that the number of premium pigs is 80 per cent of the pigs delivered in all groups; i.e., that the producers of multi-pigs have delivered 5.6 premium pigs, the producers of UK pigs have delivered 0.8 premium pigs and the organic producers have delivered 1.6. This results in a payment to each of the groups as follows: 5.32 to the producers of multi-pigs, 0.86 to the producers of UK pigs and 1.82 to the producers of organic pigs. This is exactly the same payment as under the National Pricing System. This is due to the assumption that the marginal revenue is equal to the production costs, and the premium rights are allocated in proportion to the deliveries.

5.4.1 Efficiency and incentives The premium pig scheme gives all members the right incentives since the last pig delivered is paid according to its marginal revenue. The payment scheme is thus designed to lead to first best production levels. However, a completely efficient solution is only achieved if no producer has more premium rights than the number of pigs he produces. If this is not so, then increased production will be paid for at the premium pig rate, which means it will be paid more than the marginal revenue. Since a member does not receive any return on the last premium rights if he has more rights than his pig production, he has incentive to sell his surplus rights26. The rule for determining the total number of premium rights, to e.g. 80 per cent of the previous year's production, should ensure that producers with surplus premium rights always have a right to sell these, and that there will always be potential buyers. The rules should therefore mean that no producer owns more premium rights than the number of pigs he produces27. The figures below show how the scheme works in a simple cooperative slaughterhouse with two types of pig: standard pigs which are sold under conditions of perfect competition, and special pigs that are sold on a thin market. The figures show that the production quantities are optimal.

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PETER BOGETOFT AND HENRIK B. OLESEN

Kr. Marginal cost c ' qi

Profit

Settlement price

Premium Marginal revenue R' q i

Number of primium rights v i

Optimal production q i*

Average revenue R q i Production q i

DKr.

Marginal cost c ' q l

Premium

Number of primium rights v i

Average revenue = marginal revenue

Optimal production q i*

Production q l

Figure 5.3 Payment and production with a premium pig scheme

Premium payments contra basic payments

For the scheme to work it is important to establish an effective market for the premium rights. The most effective market would presumably be for the cooperative to set up a central exchange for premium rights, where members could send their offers of buying or selling. There is a fundamental problem in the payment schemes which can involve large influence costs. This problem is an internal conflict between the desire for a high basic payment and a high premium payment28. There are two basic possibilities for limiting these influence costs.

MULTI PRODUCT PAYMENT SCHEMES

Use a technical calculation

Create homogeneous interests

Price control or quantity control

199

Firstly, the scheme provides clear rules about how the payment should be determined. The basic payment is determined by the marginal revenues, and the premium payment acts as a residual payment. This means that as long as the rules are observed, there is no decision to influence. In practice there is a danger that political and other considerations will be taken into account when setting the payment. Thus there will be a basis for costly influencing activities. This suggests that prices in this scheme ought to be set according to technical accounting rules without direct influence from the members. The second possibility for limiting the problem of influence is to try to ensure that members have as homogeneous interests as possible. As long as all the members have the same ratio between their premium rights and the number of pigs they produce, the basis for conflict about high basic price contra high premium payments is minimal. The most extreme conflict of interests can arise between owners of premium rights who have no production and producers without premium rights. To prevent this conflict, we have suggested that the leasing of premium rights should not be allowed. This is also why we suggest limiting the scope for selling premium rights. These restrictions prevent a producer putting himself in a position where he owns no premium rights, and therefore is exposed to too great a conflict of interests in relation to the other members. No member has an incentive to own more premium rights than the number of pigs he produces. The closer the total number of premium rights to the total number of pigs produced is, the more homogeneous the members' interests will be. The more premium rights there are, the more equally they will be distributed across the membership. It is important that the total number of premium rights does not exceed the total number of pigs produced. If this is not the case, it will be impossible to sell surplus premium rights. This will undermine the requirement for efficiency, the fact that no producer should own more premium rights than the number of pig he produces. In Section 4.9.3 it was argued that price controls are more robust than quantity controls. This payment scheme uses price controls and the members themselves determine their production quantities. The premium pig scheme makes it possible to implement efficient production plans, even if the cooperative does not have perfect knowledge of members' production costs. This gives the scheme a certain robustness against misinformation or disinformation about the members. The scheme is also robust towards changes in revenue conditions, because the basic payment can easily be adjusted to always reflect the cooperative's marginal revenue. Such adjustments are much more difficult in a scheme with quantity controls. These qualities of

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PETER BOGETOFT AND HENRIK B. OLESEN

robustness are probably the greatest advantage of using a two-price scheme, as for example the premium pig scheme compared with tradable production rights (or obligations) as used in New Generation Cooperatives, cf. Section 2.3.

5.4.2 The core Not always in the core

Premium rights reduce the problem

An example with figures

A similar rule from Danish Fur Breeders' Association (Dansk Pelsdyravlerforening)

A payment scheme based on premium rights is not always a core solution, since payment does not depend on the producers' alternative revenue possibilities. This problem can be reduced if certain limitations are introduced to the right to trade in premium rights. The surplus which is allocated to premium pigs will be capitalised in the price for premium rights. In the rules formulated above, premium rights can only be sold by producers whose ratio of premium rights to pigs produced exceeds the average ratio in the whole cooperative, cf. rule 6. For example, if the total number of premium rights corresponds to 80 per cent of the total production, a member with a production of 1,000 pigs could sell premium rights until he has 800 premium rights left. A producer choosing to deliver to another company could not sell all his premium rights, as his production would not fall29. The rule restricting the right to sell premium rights makes it less attractive for producers to switch to a competing slaughterhouse, because departing members would lose a return on their premium rights. However, the rules do not prevent members from selling rights as long as they cease production. Example In the general example, the payment to the producer groups is: 5.32 to the producers of multi-pigs, 0.86 to the producers of UK pigs and 1.82 to the organic producers. This is not in the core as both producers of UK pigs and producers of organic pigs would be better off, if they acted independently and received stand-alone revenues of 1 and 3, respectively. Example Danish Fur Breeders' Association30 has a rule which is similar to the above rule, restricting the right to sell premium rights. The equity capital of Danish Fur Breeders' Association is held in personal accounts. A member who wishes to leave can have his equity capital paid to him if certain conditions are satisfied. The member must be at least 67 years old, must have definitively given up fur breeding, and the board must approve the payment. The rule of Danish Fur

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201

Breeders' Association is thus an example of a rule which strengthens the ties between the members and the cooperative, making it easier to ensure that cooperation is worthwhile continuing.

5.4.3 Information needs

Moderate needs for the cooperative

Greater needs for the members

Methods known from the National Pricing System

For a premium pig scheme to work, the cooperative must be able to calculate how much the cooperative's net revenue will increase, if an extra pig of a given type is sold; i.e., the marginal revenue for all product types. The payment scheme thus needs other calculations the payment scheme based on the National Pricing System. This does not mean, however, that there is a need for new information. When cooperative slaughterhouses determine production volumes of special pigs under the National Pricing System, it is necessary to know the marginal revenue of the particular special pig in order to maximise the integrated profit. Moreover effective marketing requires that the cooperative knows how much revenue an extra pig will earn in each market. So the premium pig scheme will presumably not create new information needs for the cooperative regarding revenue possibilities. In the example in the box below we describe how the calculation can be made in practice. In the National Pricing System a cooperative also needs to know the production costs for the special producers, in order to determine the optimal production level of the special products. This information is not necessary in the premium pig scheme. The premium pig scheme imposes a considerable need for information on the members, as the scheme does not give the same gross margin for all product types. This means that the individual member must judge the revenue potentials of the different product types, before choosing to invest in a particular type of production. In addition to this, trading in premium rights creates new information needs. The individual member must thus have an expectation about the returns on premium rights before he decides how much he is willing to pay for such rights. Example Under the National Pricing System supplements and deductions leading to either too high or too low slaughter-weights were determined on the basis of three standard types: lightweight pigs, standard pigs and heavyweight pigs31. Within each group it was possible to calculate what an extra pig could be sold for. This corresponded to the pig's marginal revenue. The calculation was

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made on the basis of the sales value of the particular cuts on the markets where any increased production could be sold. In this way three different prices per kilo are found for lightweight, standard and heavyweight pigs respectively. The prices per kilo formed the basis for supplements or deductions made in relation to slaughter-weights32.

5.4.4 Monotonicity There is no one-to-one relationship between the development of a cooperative's revenues and the development of the marginal prices. In fact, there may be changes in demand which reduce the marginal revenues even if the cooperative's revenues increase. For example, such a situation can arise if demand becomes less sensitive to price; in other words, if small increases in volume require large decreases in price. Owners of premium rights will be the main gainers in such cases. The supplements paid on premium pigs will increase for two reasons. Firstly, the cooperative's revenues increase, and secondly the basic payments to producers fall. For members with few premium rights, the net result can be a loss. Thus the premium pig scheme is neither total monotonic nor is it coalition monotonic. The result shows that in some circumstances, some members have no incentive to invest in measures which will change demand, so the cooperative's revenues increase33. This result also reveals that in certain cases monotonicity can conflict with efficiency.

5.4.5 Investments

Reduces the horizon problem

In general the premium pig scheme gives good incentives for investment. Payment does not depend on capital intensity or production costs. Therefore no member has an incentive to over-capitalise. Also, everyone has an incentive to invest in reducing production costs. Even more importantly, the premium pig scheme reduces the horizon problem, as described in Section 2.4. This is because investments in the cooperative cause the expected premium payments to rise34. If the market for premium rights works properly, the increase is capitalised in the expected premium payments. An individual member will not assess investment projects on the basis of the expected return on the investment during his expected time as a member, he will assess on the basis of the expected return during the whole life of a project. This means that investments are assessed on the basis of the same criteria as in a private profit maximising firm, which normally lead to optimal investment decisions.

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203

5.4.6 Risk Poor risk sharing

There is no levelling out of risk in the basic payment. Thus if the demand for a special product falls, the production of that product type alone suffers the fall in marginal revenue. On the other hand, there is some risk sharing in the payments made for premium rights. In practice the payment on premium rights probably only amounts to a relatively modest portion of the total payment, so the supplementary payments will not share much of the risk. Another problem is that premium rights will be risky because the supplements paid vary from year to year35. In some circumstances the supplement on premium pigs could even be negative. All in all such a scheme will have poor risk sharing.

5.4.7 Consistency and additivity Additivity

Not consistent

Mergers can cause problems

The resulting payment will be the same regardless of whether the cooperative's net revenues are allocated in one step, or whether incomes and expenditures are allocated item by item. This means that the scheme is additive. On the other hand, the payment scheme is not consistent. The rules given above do not propose any procedure for aggregating different product types, which would make it possible to implement a stepwise allocation of the cooperative's net revenues. For example, the scheme does not dictate how to allocate net revenues between multi-pigs and special pigs. The problem being that the marginal revenue of a product depends on which coalition the product is a part of. Therefore it is impossible to carry out a stepwise allocation of the net revenues36. The lack of consistency means that there will not always be agreement about profitable mergers because individual producer groups could be worse off. The problem can arise if the marginal revenue on one product type falls, while the cooperative grows. This will typically happen if the cooperative merges with a competing producer group. This is because the original producers in the cooperative reduce their competitors' revenues when they increase their production. Before a merger this loss is not included in the calculation of the cooperative's marginal revenue, but it is included when the competitors become members of the same cooperative. Example We consider the situation of a merger between the original cooperative consisting of producers of multi-pigs, UK pigs and organic pigs and a cooperative producing outdoor pigs. It is assumed that UK pigs and outdoor pigs are competing products. Because of

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this, the marginal revenue for a UK pig falls from 0.7 to 0.5 when the earnings of the producers of outdoor pigs are taken into account. Outdoor pigs do not compete with either multi-pigs or organic pigs. After the merger, the cooperative's revenues rise from 8 to 10. Producers of outdoor pigs receive payment of 1, so the original producer groups together earn 1 from the merger. For the sake of simplicity it is assumed that the producers of outdoor pigs do not receive premium rights. This means that the residual revenues, after payment of the basic payment, are allocated in the same proportions as previously between the original producers, and the number of premium pigs is still 8. The residual revenue increases from 1.6 to R 10  1  7 ˜ 0.6  1 ˜ 0.5  2 ˜ 0.75 3.1

The producers of UK pigs still deliver 0.8 premium pigs and therefore get a total supplementary payment of 0.31. The total payment to producers of UK pigs therefore falls from 0.86 to 0.5 + 0.31 = 0.81. This producer group therefore has an incentive to oppose the merger, despite it being advantageous to the original producer group as a whole.

5.5 The ACA (Alternate Cost Avoidance) method Who should get the gains from special production?

Payment of incremental revenue

There has been frequent discussion in the Danish pig industry about how to allocate the gains from special production between traditional producers and special producers. In this discussion the principle of the National Pricing System giving special producers supplementary payment relating to their additional costs, has characterised one side of the debate37. In opposition to this, it has been proposed that special producers should be paid the added value; i.e., the incremental revenue, which they generate for the cooperative38. Usually there will be a budget deficit if the cooperative pays each producer group its incremental revenueM; i.e., the amount by which the cooperative’s revenue would fall if the producer in question left the cooperative. In order to base a payment scheme on incremental revenue, a supplementary rule is required to ensure a balanced budget. The ACA method has a proposal for such a rule. The ACA method39 was introduced in the mid-twentieth century and has played a major role in the literature of cost-benefit ever since. The ACA method has also been widely used in engineering circles, where it

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Payment

205

is used to allocate income and expenditure between different projects. On payments in cooperatives, the method states that each producer group shall initially be allocated the producer group's incremental revenue40. Once the incremental revenues have been allocated, there is a residual in the cooperative. According to the ACA method, the residual is allocated in proportion to the difference between the incremental revenue and the stand-alone revenue of each producer groupM. The difference between the amount which the cooperative would lose if a producer group left the cooperative, and the amount which the producer group could earn outside the cooperative, can be interpreted as the producer group's contribution to the total gains from cooperation. A producer group's contribution to the gains of cooperation is thus the incremental revenue minus the stand-alone revenue. The ACA method allocates the gains from cooperation in proportion to each participant's contribution to those gains.

Mathematical representation A producer group's marginal contribution is given by

R N  R N \ i where R(N) is the revenue of the whole cooperative consisting of all producer groups i = 1,…m, and R(N\i) is the revenue which the cooperative would obtain if group i left the cooperative. When all incremental revenues has been paid out there is a residual in the cooperative of R N  ¦ >R N  R N \ i @ iN

The residual sum is allocated in proportion to the difference between the stand-alone revenue and the marginal revenue of each producer group

ri

>RN  RN \ i @  Ri

The ACA method therefore results in the following payment to producer group i

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xi

ª º » ri « R  N  R  N \i  R  N  ¦ ª¬ R  N  R  N \i º¼ » «  ¦ ri « iN » incremental revenue iN residual ¬« ¼»

If the core is not empty the residual sum will be negative or zero. A non-empty core means that the payment to producer group i is less than i's incremental revenue xi d R N  RN \ i for all i  N

Combined with the balanced budget constraint this means that the residual sum is negative

¦x iN

i

R N d ¦ R N  R N \ i iN

Reformulating the payment under the ACA method can help the intuitive understanding of the method.

xi

ª ri º ¦ ri « iN RN  R N \ i  ri  RN  ¦ >RN  R N \ i @  ri » « » r r i N  ¦ i i »¼ iN ¬«

 xi

Ri 

ri ª º RN  ¦ Ri » « iN ¼ ¦ ri ¬ iN

This reformulation shows that the total gains of cooperation RN  ¦ Ri are allocated in proportion to each producer group's iN

contribution to those gains ri . Example In the general example, the incremental revenue of each production type is 3, regardless of which product type is considered. According to the ACA method, the initial payment to each producer group is 3, giving a total payment of 9, and thus a residual in the cooperative of R  N  ¦ ª¬ R  N  R  N \i º¼ 8 - (3  3  3) -1 iN

The contributions to the gains of the cooperative from multi-pigs, UK pigs and organic pigs are respectively rM

>RN  RN \ M @  RN >8  5@  2

1

MULTI PRODUCT PAYMENT SCHEMES

rE

>RN  RN \ E @  RN >8  5@  1

ª¬ R  N  R  N \O º¼  R  N The resulting payments will therefore be rO

xM

RN  RN \ M 

rM ¦ ri

> 8  5@  3

207

2 0

ª º « RN  ¦ >RN  RN \ i @» ¬ ¼ iN

iN

1 > 1@# 2,67 3 1 2  0 xE

xO

3

2 > 1@ # 2,33 1 2  0

3

0 > 1@ 3 1 2  0

5.5.1 Efficiency and incentives Relatively good incentives

With the ACA method, the payment for each product is not directly determined by consideration for efficiency, so the scheme will only rarely implement the first best solution. Payment to a producer group is based on the group's incremental revenue. This does not necessarily mean that the payment reflects the market conditions for the group's products. The incremental revenue may well reflect the market conditions, but the allocation of the residual can change the picture. Below we show that the ACA method is not monotonic. This means that payment to a producer group can fall, even if the market value of the group's products increases. The scheme can therefore give lower payment on a product whose market value has risen, and thus prompt a decrease in production volumes. This is the perverse incentive effect. The most practical way to make a concrete evaluation of the efficiency of the payment scheme is probably by using a simulation model based on the cost and revenue structure in an actual cooperative41.

5.5.2 The core Not always in the core

The ACA does not include information about the stand-alone revenues of all possible sub-coalitions, so for example the coalition between UK pigs and organic pigs is not included in the calculation of the above example. This means that the ACA method does not always give a solution in the core.

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Even though the ACA method does not ensure a solution in the core, it gives an allocation of revenues which is individually rational so that no single producer group will be better off by leaving the cooperative and operating outside it. Only coalitions between several producer groups can have an incentive to leave the cooperative42. The example below illustrates the ACA method's properties in relation to the core. Example We extend the general example so the cooperative also includes production of EU heavyweight pigs. It is also assumed that the standalone earnings in the coalition of UK pigs and organic pigs increase to 6. The data behind this therefore is as follows

Coalition

Stand-alone revenues

Multi-pigs

2

UK Pigs

1

Organic pigs

3

EU heavyweight pigs

2

UK pigs + organic pigs

6

All other coalitions between 2 producer groups

5

All coalitions with three producer groups

8

Earnings with a large slaughterhouse

11

Table 5.2 The data basis illustrating the ACA method vis-à-vis the core Payment to individual producer groups can be calculated from the table below

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Product type

209

Increment Stand-alone Contribution al revenue revenue to gains of cooperative ri R N  R N \ i R(i)

Payment xi 3

1 4

 1

Multi-pigs

11-8=3

2

3-2=1

UK pigs

11-8=3

1

3-1=2

11-8=3

3

3-3=0

3

11-8=3

2

3-2=1

3

Organic pigs EU heavyweight pigs Total Total revenue Total incremental revenue Residual

12

4

3

2 ,75

 1

2 4

0 4

1 4

 1

 1

2,5 3 2 ,75

11

11 12 -1

Table 5.3 Table for calculating payment based on the ACA method UK pigs and organic pigs thus obtain a combined payment of 2.5 +3 = 5.5 by being part of the cooperative. This is less than their coalition stand-alone revenue of 6. This means that producers of UK pigs and organic pigs have an incentive to leave the cooperative and join together.

5.5.3 Information needs Relatively high information needs

Compared with the previously reviewed payment schemes the ACA method requires more information about the revenue function (R). There is a need to know the producer groups’ stand-alone revenue, as well as how the revenues of the cooperative would fall, if a producer group left it. On the other hand, as described here, the ACA method does not require information about the producers' production costs. However, compared with the next two payment schemes, which are more theoretical, the ACA method still has a relatively modest need for information. With the ACA method, the individual producer needs a lot of information in order to choose his product type. In order to form reasonable expectations about a particular product type, there is a need

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to know the incremental revenue and the stand-alone revenues for each product type in the cooperative. The scheme is therefore less transparent for the producers than the preceding payment schemes.

5.5.4 Monotonicity Not monotonic

The ACA method is not totally monotonic. With this payment scheme, a producer group can become worse off if the cooperative earns more. Since the ACA method is not totally monotonic, it is therefore also not coalition monotonic43. The following example illustrates these findings. Example We modify the general example to show the lack of monotonicity more clearly. Assume that the stand-alone revenues before and after some new measure, e.g. better marketing, are

Coalition

Stand-alone revenue before

Stand-alone revenue after

Multi-pigs

2

2

UK Pigs

1

1

Organic pigs

3

3

Multi-pigs + UK pigs Multi-pigs + organic pigs UK pigs + organic pigs Earnings in one big slaughterhouse

4

4

7

7

6

6

8

9

Table 5.4 ACA method's lack of total monotonicity (data) On the basis of these values the ACA method gives the following payments Product type Multi-pigs UK pigs Organic pigs

Payment before44 2 1 5

Payment after 2.75 1.75 4.50

Table 5.5 Payment using the ACA method (example)

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The producers of organic pigs lose by the introduction of the new measure, even though it improves the revenue of the cooperative as a whole.

5.5.5 Investments Problems arising from the lack of monotonicity

Contrary to the previous payment schemes, the ACA method does not depend on the capital investments and costs of the producers. This means that individual producer groups have an incentive to invest in general measures which reduce costs. However, the lack of monotonicity means that a producer group does not always have an incentive to invest in sales promotion.

5.5.6 Risk No clear pattern

There is no clear pattern indicating how a fall in demand would affect payments to particular groups. Therefore, there will not always be risk sharing. On the other hand, the ACA method does not exclude a certain risk sharing as it is not strongly monotonic. To illustrate this in more detail, it is necessary to make consequence calculations (simulations) of specific problems.

5.5.7 Consistency and additivity The requirements are not satisfied

The ACA method is not consistent and this can result in conflict over the priority of the allocation procedure. This problem is seen in the example below. The ACA method also breaches the principle of additivity45. The payment scheme can thus lead to conflicts about how incomes and expenditures should be categorised in the accounts. Example The lack of consistency will be apparent if we consider the 'before' example above. If the revenues are initially allocated between producers of multi-pigs and producers of special pigs, the allocation will be Product Stand-alone Incremental Payment type revenues revenue under the ACA method Multi-pigs 2 2 2 Special pigs 6 6 6 Combined 8 Table 5.6 Payment for multi-pigs and special pigs using the ACA method

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When payment to the producers of special pigs is allocated between UK pigs and organic pigs, the resulting payment using the ACA method is

Product type UK pigs Organic pigs UK pigs + organic pigs

StandIncrePayment Payment with alone mental under the direct allocation revenues revenue ACA method cf. Table 6.5 1 3 2 1 3 5 4 5 6

Table 5.7 The ACA method is not consistent (example) In this example, the producers of UK pigs prefer a hierarchical allocation procedure in which the earnings are first divided between traditional producers and special producers, and thereafter allocated between special producers.

5.6 Nucleolus Puts those who are worst off in the best possible position

This section looks at a payment scheme of a more theoretical origin. Nucleolus is a method for choosing a single point in the core which often has a large number of possible allocations. Using the arguments of fairness and equality, it is reasonable to choose an allocation which puts those who are worst off in the best possible position. In the nucleolus, the payment is set to ensure the greatest possible revenue gain to the coalition whose revenue gain is the least46. Nucleolus is thus a generalisation of the principle of adjusted maximin equality, cf. Section 3.2. For a given coalition the benefit from participating in a cooperative consists of the total payment to the coalition, minus the coalition's stand-alone revenueM. Mathematical representation The benefit of cooperation for coalition S is given by

¦ x R  S i

iS

Coalition S will thus be better off than coalition T if

MULTI PRODUCT PAYMENT SCHEMES

¦x iS

i

213

RS ! ¦ xi RT iT

The nucleolus is found by solving the following optimisation programme max H H , xi

s.t.

¦x

i

 RS t H

for all S z Ø , N

iS

m

¦x

i

R N

i 1

This program maximizes the minimal gains from cooperation across the different coalitions while ensuring that the total revenue is being allocated. If more than one allocation gives the same H , then the nucleolus scheme chooses the one which gives the greatest benefit to the coalition whose revenue gain is the next least. Nucleolus thus has 'tiebreakers' using lexicographic ranking.

Example Nucleolus can be illustrated in the following example

Coalition Multi-pigs UK pigs Organic pigs Multi-pigs + UK pigs Multi-pigs + organic pigs UK pigs + organic pigs Combined total

Stand-alone revenues 2 1 3 5 5 5 8

Conditions xM  2 t H x E 1 t H xø  3 t H xM  xE  5 t H xM  xO  5 t H

xO  xM  5 t H xM  xE  xO

8

Table 5.8 Conditions for determining the nucleolus Using the balanced budget constraint, we see that the conditions for the coalition of multi-pigs and UK pigs are the same as the condition for organic pigs, so that x M  x E 5 and xO 3 . This means that these coalitions do not gain any revenue from the cooperation; i.e., H 0 . It is

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therefore necessary to maximise the gains of cooperation for the coalition whose revenue gain is next least. This is done by allocating payment of 2.5 to each of the groups of producers of multi-pigs and UK pigs. According to the nucleolus scheme, the payment to producers of organic pigs will thus be 3 (corresponding to 1.5 per pig), payment to producers of UK pigs will be 2.5 (corresponding to 2.5 per pig) and payment to producers of multi-pigs pigs will be 2.5 (corresponding to 0.36 per pig).

5.6.1 Efficiency and incentives Far from efficient

Payment in the nucleolus scheme is not determined by efficiency considerations. Payment to individual producer groups is determined by consideration for the worst off coalitions. This means that a nucleolus scheme will often give poor market signals, and will typically lead to inefficient production. A concrete evaluation of the nucleolus scheme must be based on simulations in a specific context.

5.6.2 The core A core allocation is one in which each producer at least gets his standalone revenue. As a nucleolus scheme tries to give everyone as much as possible in addition to their stand-alone revenue, it does result in allocation in the core. In fact, the aim of the nucleolus scheme is to find an allocation as close to the “centre of the core” as possible.

5.6.3 Information needs Large information needs

Calculate the nucleolus for critical coalitions

One of the greatest disadvantages of a nucleolus scheme is that it has a comprehensive need for information. To calculate the nucleolus in an actual case one needs, in principle, the stand-alone revenues for all 2 m  2 possible sub-coalitions in the cooperative. This means that for a cooperative with just five different product types, it is necessary to know the stand-alone revenues of 2 5  2 30 sub-coalitions. This is a horrendous requirement which it will be difficult to satisfy in practice. It is possible to minimise the information need, if there is prior knowledge about the coalitions' revenue potential. The nucleolus seeks to maximise the gains from cooperation in the coalition which gains least from the cooperation. The nucleolus lays down payments for each individual producer group. A result from mathematical programming implies that the number of coalitions which obtain the smallest gains from the cooperation will never exceed the number of producer groups47. This means that in most cases, it is sufficient to solve the problem for the m most critical coalitions (unless there is no single solution as in the example above). In practice, there are probably prior

MULTI PRODUCT PAYMENT SCHEMES

Not transparent payment

215

assumptions about which coalitions are most likely to be worst off. It should be sufficient to calculate the nucleolus for these coalitions. For example, if the cooperative knows that the coalitions formed by single producer groups are most likely to become critical (binding), it need only find the nucleolus among these coalitions. This will significantly reduce the need for information. The data requirement of the nucleolus scheme will likely lead to many conflicts because the stand-alone earnings are not verifiable for many of the coalitions. When an individual producer chooses which product type to invest in, he needs the same information as the cooperative. A payment scheme based on the nucleolus is therefore not transparent.

5.6.4 Monotonicity Nucleolus is not monotonic

As nucleolus is a core allocation procedure, it is possible to use the general findings about monotonicity. On the basis of Young's proposition about coalition monotonicity, it follows that the nucleolus is not coalition monotonic if there are more than 4 product groups; i.e. Proposition 5.1 If there are more than 4 product groups, nucleolus is not coalition monotonic.

This means that there will be situations in which a producer group will receive a lower payment, even though the stand-alone revenue has increased in all the coalitions which the producer group in question belongs to. Nucleolus can therefore lead to perverse incentives since a producer group may want to reduce the profitability of the coalitions it belongs to. In the case of total monotonicity we have the following result: Proposition 5.2 If there are more than 9 producer groups there are stand-alone revenue functions in which the nucleolus is not totally monotonic (Meggido, 1974)

This means that if there are more than 9 different producer groups in a cooperative, situations can arise in which payments to individual groups fall, despite of increasing revenue in the cooperative.

5.6.5 Investments The lack of monotonicity can ruin a producer group's incentives to invest in marketing measures. On the other hand, nucleolus does give good incentives to invest in measures which reduce production costs. Payment is not affected by such savings.

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PETER BOGETOFT AND HENRIK B. OLESEN

5.6.6 Risk A certain amount of risk sharing

The idea behind nucleolus payment, to ensure the greatest possible revenue gain to the coalition whose revenue gain is the least, means that there is a safety net under the revenues which the individual coalitions obtain from taking part in the cooperative. The gain from participating in the cooperative is the payment to the coalition minus the coalition's stand-alone revenue. Thus, payment to a producer group can go down without the producer group thereby benefiting less from participating in the cooperative, if the producer group's stand-alone revenue falls. The payment to a group normally falls if the demand for the group's products falls, and thus the stand-alone revenue of the coalitions the group belongs to, also falls. Falling demand for a given product type will often hit hardest in a smaller coalition because smaller coalitions have fewer alternative sales channels. This means that the total benefit from cooperation can increase as the consequence of lower demand for a given product type. Falling demand for one product type can thus mean that some producer groups which produce other products, receive greater revenue by participating in the cooperation. However, this is a second order effect which does not normally outweigh the first effects referred to. Altogether nucleolus therefore only gives limited risk sharing.

5.6.7 Consistency and additivity Consistent but not additive

Nucleolus is consistent48, which limits the influence problem. But nucleolus is not additive. This happens – loosely speaking – because the maximin problem is solved under too many side constraints if the procedure is split up and applied to a number of different categories of income and expenditure.

5.7 Shapley

Payment

In the literature on cooperative game theory, Shapley value is often used as an alternative to nucleolus49. Payment according to this system, the so-called Shapley value, is a producer group's expected incremental revenue. The incremental revenue of a producer group joining a given coalition S is the amount by which the coalition’s revenue increases due to the expansionM. Shapley value is calculated as the weighted sum of a producer group's possible incremental revenue to all the coalitions which the producer group could participate in. The marginal

MULTI PRODUCT PAYMENT SCHEMES

217

contribution to a given coalition is weighted with the probability that a random selection of producer groups constitutes the coalition in questionM. The payment scheme is illustrated below using our standard example. Mathematical representation The incremental revenue of group i when participating in coalition S is

RS ‰ ^` i  R S We consider the m! possible arrangements of the m groups and assume that all are equally probable. There are S !m S  1 ! arrangements where producer groups in S are ranked above i, S is the number of producer groups in coalition S. The probability that i is the lowest ranked in coalition S ‰ ^` i can thus be expressed as

S ! m  S  1 ! m! The Shapley value is defined as50

yi

¦

S  N ,iS

S ! m  S  1 !

ª¬ R  S ‰ ^i`  R  S º¼ m!

  Incremental profit Probability of coalition S

Example The general example is used to illustrate Shapley value. Shapley value for multi-pigs is calculated on the basis of incremental revenue to four coalitions, the empty coalition, the coalition consisting of organic pigs alone, the coalition consisting of UK pigs alone and the coalition consisting of UK pigs and organic pigs. The incremental revenue to the first coalition is the stand-alone revenue for multi-pigs, the incremental revenue to the second coalition is the stand-alone revenue for the coalition of multi-pigs plus organic pigs minus the stand-alone revenue for organic pigs, and so on. Shapley value for multi-pigs will therefore be

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PETER BOGETOFT AND HENRIK B. OLESEN

yM

0!3  0  1 ! >2  0@ 1! 3  1  1 ! >5  1@ 3! 3!   Coalition with M alone Coalition with E 

1!3  1  1 ! >5  3@ 2! 3  2  1 ! >8  5@# 2,67 3! 3!   Coalition

Coalition with O with E&O

Correspondingly, Shapley values for UK pigs and organic pigs respectively are yE

0! 3  0  1 ! >1  0@ 1!3  1  1 ! >5  2@ 3! 3!   Coalition with M Coalition with E 

yO

1! 3  1  1 ! >5  3@ 2!3  2  1 ! >8  5@# 2,17 3! 3!  Coalition

 with O Coalition with M&O

0! 3  0  1 ! 1! 3  1  1 ! > 3  0@  > 5  2@ 3!  3!  Coalition with O

Coalition with M

1! 3  1  1 ! 2! 3  2  1 !  >5  1@  >8  5@ # 3,17 3! 3!   Coalition with E

yO

Coalition with M&E

0! 3  0  1 ! 1! 3  1  1 ! >3  0@  >5  2@ 3!  3!  Coalition with O

Coalition with M

1! 3  1  1 ! 2! 3  2  1 !  >5  1@  >8  5@ # 3,17 3! 3!   Coalition with E

Coalition with M&E

5.7.1 Efficiency and incentives Reasonable incentives

Payment based on Shapley value is not determined by consideration for efficiency, and it therefore do not implementing the first best solution. However, the Shapley value is based on the producer group's incremental revenue. This means that the payment to some extent reflects the market signals about the revenue on the product in question. To evaluate the efficiency of Shapley value in a specific case, it is necessary to construct a simulation model.

5.7.2 The core Individual producer groups do not have an incentive to leave a

MULTI PRODUCT PAYMENT SCHEMES

Only individually rational

Most often in the core

219

cooperative because of the Shapley value51. No producer groups earn more by standing aloneM. Shapley value is therefore individually rational for producer groups. Even if an individual producer group is never better off outside the cooperative when the core is non-empty, the Shapley value does not always belong to the core. This is illustrated by the example below. However, Shapley value lies in the core in most situations when the core is non-empty. Moulin (1988) has shown that the Shapley value does lie in the core for so-called convex stand-alone earnings functionsM. Example The allocation calculated in the example box above exceeds the stand-alone revenue of the individual producer groups. Cooperation is therefore individually rational. However, a coalition consisting of multi-pigs and UK pigs is only allocated 2.67 + 2.17 = 4.84, which is less than the coalitions’ stand-alone revenue of 5. This shows that Shapley value is not always in the core. Mathematical representation A necessary condition for the existence of a non-empty core is that the revenues should be super-additive, so RS  R S * d R S ‰ S * for S ˆ S *

Ø.

A special case of super-additivity is that RS ‰ ^` i  RS t Ri

This means that the incremental revenues exceed the producer groups' stand-alone revenues. Therefore payment to producer group i also exceeds producer group i's stand-alone revenue, because payment is a weighted average of all the producer groups' incremental profits. Shapley value is therefore individually rational for each producer group when stand-alone revenues are super-additive.

5.7.3 Information needs Huge information needs

In principle, Shapley value has the same need for data as a nucleolus scheme, so it is not particularly usable in practice. However, the Shapley value depends on the stand-alone revenues of all coalitions not merely in principle but also in practice. This means that, unlike nucleolus, it is not possible to base calculations only on 'critical' coalitions. Therefore, Shapley value requires even more information than the nucleolus.

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5.7.4 Monotonicity Requirement satisfied

All things being equal, an increase in the total revenue of the cooperative means that the Shapley value increases. Thus, the payment scheme is total monotonic. Shapley value is also coalition monotonic. If revenues increase in all the coalitions in which a producer group participates, then all the producer groups' incremental revenues increase and with them Shapley value. This means that Shapley value can never result in lower payment to a producer group whose revenues increase in all the coalitions it is part of. Therefore Shapley value never gives any incentive to resist an increase in revenues.

5.7.5 Investment Good incentives to invest

The cost levels and capital investment in primary production do not affect Shapley value, so the payment scheme does not create disincentives to invest in measures leading to lower production costs. Coalition monotonicity ensures that a producer group has reasonable incentives to invest in the marketing of its products, for example. This is because such investments have positive effects for the revenues in all the coalitions it belongs to. This means that the producer group's incremental revenue goes up, which increases the payment to the producer group.

5.7.6 Risk Poor risk sharing

In Section 3.8.1 we argued that, from a risk sharing perspective, a payment scheme should not be strictly monotonic. A payment scheme is strictly monotonic if an increase in a producer group's incremental revenue never results in lower payment to the group. Shapley value is strictly monotonic52. The example below shows that one producer group can profit from a fall in demand for another producer group's products when using Shapley value. This is bad from a risk sharing perspective. Example A small example with stand-alone revenues and Shapley values shows the problems connected with strict monotonicity. In the example the producers of product A benefit from a fall in the demand for product B.

MULTI PRODUCT PAYMENT SCHEMES

Before Stand-alone Shapley revenues value

Product

Product A Product B Combined

100 100 220

110 110

221

After Product

100 80 210

Standalone revenues 115 95

Table 5.9 Shapley value can give poor risk sharing

5.7.7 Consistency and additivity Additive but not consistent

Shapley value is additive53. This means that allocations made using Shapley value are not altered by allocating incomes and expenditures to producer groups item by item. On the other hand, Shapley values are not consistent, which is shown in the following example. Example The general example is used, with three product types. To start with special pigs (UK pigs and organic pigs) are considered together. Multi-pigs have stand-alone earnings of 2 and special pigs have stand-alone earnings of 5, and the earnings of the cooperative are 8. Shapley values for multi-pigs and special pigs respectively are yM

0!2  0  1 ! >2  0@ 1!2  1  1 ! >8  5@ 2.5 2! 2! Coalition with M

yS

Coalition with S

0!2  0  1 ! >5  0@ 1!2  1  1 ! >8  2@ 5.5 2! 2! Coalition with S

Coalition with M

If the special producers use Shapley values to allocate payment of 5.5 between themselves, then the payment for UK pigs and organic pigs (cf. stand-alone revenues for UK pigs of 1 and stand-alone earnings for organic pigs of 3) will be yU

0! 2  0  1 ! >1  0@ 1! 2  1  1 ! >5.5  3@ 1.75 2! 2! Coalition with E

yO

Coalition with O

0!2  0  1 ! >3  0@ 1!2  1  1 ! >5.5  1@ 3.75 2! 2! Coalition with O

Coalition with E

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These payments should be compared with the payments which the producer groups would obtain if the earnings were allocated directly to all producer groups at once as in the first example. Producers of multi-pigs thus receive 2.67 if the revenues are allocated directly, but only 2.5 if their revenues are allocated in two stages. Producers of UK pigs receive 2.17 if revenues are allocated directly, but only 1.75 with allocation in stages. On the other hand, organic producers get 3.17 with direct allocation and 3.75 with allocation in stages. The organic producers will prefer allocation in two stages, while the other producers will prefer a direct allocation of revenues.

5.8 Summary Six schemes and nine criteria

Necessary to weigh the different criteria

This chapter analyses six different payment schemes for cooperatives with differentiated primary production. The schemes are analysed by evaluation against nine central criteria which are set out in general form in Chapters 3. The different schemes are illustrated by using a common example. The example is based on imagined figures and should therefore not be thought of as a prediction of real prices if a cooperative changes its payment scheme. The calculations made using the sample values do show that the different schemes can lead to very different payments to the individual producers. The figure below shows the payment per slaughter-pig under each of the payment schemes. The analyses of payment schemes show that each of them has its strengths and weaknesses. This emphasizes the general conclusions in the literature that it is often impossible to achieve even a limited number of attractive characteristics simultaneously. For example, it is not possible to find payment schemes which always give a balanced budget and lead to efficient production54. Another example being that it is impossible to achieve coalition monotonicity and a core solution simultaneously55. This means that in choosing a payment scheme it is necessary to weigh the different criteria, and this should be done by reference to a specific context.

MULTI PRODUCT PAYMENT SCHEMES

DKr. per pig 3.000

223

National pricing and Premium pigs Landsnotering Smågrise Piglets

2.500

ACA ACA Nucleolus Nucleolus Shapley Shapley

2.000 1.500 1.000 500 Multi-pigs

UK pigs

Organic pigs

Figure 5.4 Payment per slaughter-pig using different payment schemes56 (example)

The table below summarises how well each payment scheme satisfies the different criteria. Three different ratings are used, as follows: z Criterion not satisfied zz Criterion partially satisfied zzz Criterion satisfied Scheme National Piglet Premium ACA Nucleo- Shapley Criterion Pricing pigs lus Efficiency zz zz zzz zz z zz Core solution z z zz zz zzz zz Information zzz zzz zz z z z needs Total zz zz zz z zz zzz monotonicity Coalition zz zz zz z z zzz monotonicity Investment zz zz zzz zz zz zz Risk zzz zz z zz zz z Consistency zzz zzz z z zzz z Additivity zzz zzz zzz z z zzz Table 5.10 Evaluation of actual payment schemes

224

No unambiguous answer

National Pricing System or premium pig scheme

Combination

PETER BOGETOFT AND HENRIK B. OLESEN

The table clearly shows that all the payment schemes have their good and bad points. No single payment scheme is superior to the others on all criteria. However, the National Pricing System used hitherto in the Danish pig industry scores reasonable well on most criteria, so it is not surprising that the National Pricing System has survived for 100 years. The National Pricing System is superior to the piglet pricing scheme, because it is as good as or better than it on all 9 criteria. The premium pig scheme also scores well on most criteria, so this payment scheme might be an interesting alternative to the scheme used until now. The choice of payment scheme depends on an assessment of which criteria are most important in the actual situation confronting the cooperative. In many situations the need for information is presumably critical, because a scheme can only be used in practice if it is possible to gather the information required. This means that in reality the choice is reduced to a choice between the National Pricing System or the premium pig scheme57. The two criteria which presumably ought to be given greatest weight (after the information needs) are efficiency and a solution in the core. Judged by these criteria, the premium pig scheme is preferable to the National Pricing System. Above we have analysed payment schemes which each allocate payment according to one set of principles. It is, of course, possible to combine different principles. It is possible to allocate one part of the revenues according to one payment scheme (e.g. a fixed percentage of the revenue), while the remaining revenue is allocated according to another payment scheme. For example, 50 per cent of the revenues could be allocated using the National Pricing System, and the rest could be allocated using the piglet payment scheme. Another possibility is to combine payment schemes vertically, using one scheme to allocate revenues between main areas while another scheme is used to allocate revenues within main areas. For example, a cooperative slaughterhouse could make allocations between cattle and pigs by using nucleolus, and subsequent allocation to pig producers, e.g. multi-pigs, UK pigs, etc., could be made using the National Pricing System.

MULTI PRODUCT PAYMENT SCHEMES

225

Notes Noter 1

We assume that production quantities do not depend on which coalition a producer group belongs to. This means that we use payment schemes to allocate the cooperative's net revenues R˜ instead of the resulting profit 3 ˜ , cf. Section 3.7. 2 The National Pricing System (Landsnoteringen) ended on 1st October 1999, but many cooperatives still use the principles of the National Pricing System. 3 The Federation of Danish Pig Producers and Slaughterhouses (Danske Slagterier). See also Section 2.6.1 for a description of the National Pricing System (Landsnoteringen). 4 Cf. the proportional rule described in Section 2.2. 5 In order not complicate the notation unnecessarily the model disregards the fact that different kinds of slaughter-pigs have different slaughter-weights. This omission is not relevant to the theoretical results. 6 To a large extent cooperative slaughterhouses use contract production to control production quantities of special pigs. 7 See Hansen (1997). 8 This assumes that the incremental revenue from the exported pigs exceeds their stand-alone revenue. If this is so, in cooperative game theory this is called super-additive. 9 See Section 4.1 on the calculation of the revenue and cost functions. 10 See Andelsbladet (1997a). 11 The costs included in the calculation of payments are not the actual costs of the actual group in the actual year, but are based on cost estimates, see Danske Slagterier (The Federation of Danish Pig Producers and Slaughterhouses) (1999). A general cost reduction for a product type will affect the cost estimates. 12 See Section 2.4. 13 Danske Slagterier (The Federation of Danish Pig Producers and Slaughterhouses) (1999). 14 The allocation is described in Graversen & Nørgaard (1999) as well as Danske Slagterier (The Federation of Danish Pig Producers and Slaughterhouses) (1999). 15 In reality the loss of the gains of cooperation merely expresses that the core is non-empty. See Graversen & Nørgaard (1999) for a more detailed analysis of the problem. 16 For example a quota scheme can be very similar to production rights in a cooperative, since both methods are based on quantity controls and have the common aim of ensuring better prices for farmers. 17 See Sumner and Wilson (2000) and Sumner and Wolf (1996). 18 See Bogetoft (1998) 19 See Sumner and Cox (1998). 20 In 2000 the supplement was $1.7 per 100 lbs., corresponding to DKr. 0.25 per kg. 21 A two-price system means that an individual producer has only two prices, but the scheme can use different prices for different product types. 22 We have assumed that both marginal pricing and revenues are continuous. 23 This is because the average revenues are often falling, cf. Chapter 4. 24 A similar but much more low key conflict can also arise between the payment of premium rights and production. 25 When introducing quota arrangements the initial allocation is typically based on historical production. To avoid producers having an incentive to increase production in an attempt to obtain a larger quota it is important to use the production levels existing before a decision is made to introduce quotas, and preferably before the time when the issue of quotas has even been seriously discussed. This was the situation, for example, with the introduction of the EC milk quotas. However, there can be problems using historical data for allocating quotas, because there can be significant differences in production

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volumes between the historical reference period and the time when quotas are introduced. See Alston (1992) for a more detailed discussion of the problems of introducing quotas. 26 Experience of the Californian milk quota system shows that farmers sell their quotas so that nearly all have larger production than their quota. Sumner and Cox (1996). 27 This disregards producers who, as a speculation, choose to hold more premium rights than required by their production. 28 This problem is reminiscent of the conflict between the rewards for capital and for raw materials in a food company jointly owned by cooperative members and financial investors. See Hansen (1997) for an illustration of the problems of mixed ownership. 29 The rules also mean that a member cannot sell his premium rights in one year and move to another slaughterhouse in the following year. To enforce this rule the cooperative must be able to monitor not only the producer's deliveries to the cooperative, but his total production. 30 See Danske Andelselskaber, (1998). 31 Karsten Flemin, 2000. See also Section 2.6.1. 32 This approach requires that the last cuts should be sold in markets with perfect competition. Under other market conditions the calculation must take into account that larger sale volumes will push prices down. 33 In other cases the owner of the premium with relatively few deliveries will oppose this. 34 Unless there is a situation in which the marginal revenues increase more than the average revenues, cf. the discussion on monotonicity. 35 This is why the supplements for Californian quota milk are now a fixed amount (Sumner, 2000). 36 It is possible to supplement this with rules which make it possible to determine the marginal revenues for an aggregated product by using the average of the marginal revenues of the products aggregated. However, there is still a basic problem with this approach because the marginal revenue depends on the coalition which the product type is part of. This is illustrated in the following discussion on mergers. 37 This point of view has been supported, among others, by Claudi Lassen, cf. Andelsbladet(1997b), the chairman of The Federation of Danish Pig Producers and Slaughterhouses (Danske Slagterier). 38 This point of view has been argued by Kent Skaaning(1996), chairman of chairman of the Danish Association of Pig Producers (Landsforeningen af Danske Svineproducenter). 39 ACA stands for 'alternate cost avoided'. The method is referred to in many places in the literature on cost allocation, see cf. Moulin (1988) and Young (1985). 40 In other words R(N)-R(N\i). 41 On a theoretical level it is difficult to say anything definite about the criterion as the ACA method is based on traditional cooperative game theory. This theoretical approach does not include the underlying actions (production decisions etc.) but takes as given the resulting earnings of a coalition. However, the efficiency criteria are derived from the tradition of non-cooperative game theory which seeks to analyse what actions individuals take in different situations. To assess the efficiency of the ACA method we have to move from the framework of cooperative game theory over to that of noncooperative game theory. This means that we must try to clarify what actions underlie the revenue levels which cooperative game theory takes as given. 42 In Hougaard (1998) there is a formal proof for these statements about the relationship of the ACA method to the core. 43 Young (1985) gives a more detailed analysis of monotonicity characteristics in relation to the core. 44 Note that this allocation does not lie in the core as the coalition of producers of multi-pigs and of UK pigs has an incentive to leave the cooperative. 45 Moulin (1988). 46 There is a fuller description of nucleolus in Young (1985). 47 2 of the possible coalitions are deducted since neither the empty coalition nor the grand coalition with all the producer groups are included in the calculation.

MULTI PRODUCT PAYMENT SCHEMES

48

227

See Section 3.8.1. This result is shown in Young (1985) among others. 50 For a description of Shapley value see Moulin (1988), Hougaard (1998) or Young (1985). 51 Moulin (1988). 52 Moulin (1988). 53 There is formal proof of this finding in Moulin (1988). 54 Green and Laffont (1979). 55 Moulin (1988). 56 Payment for premium pigs, in the example given for all pig types, is equal to payment under the National Pricing System. 57 Here the payment scheme for piglets is disregarded because it is inferior to the National Pricing System (Landsnoteringen). 49

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(in

Danish;

Erklæring

om

Johansen, L., Lectures on Macroeconomic Planning, Part I: general aspects, North-Holland, 1977. Johansen, L., Lectures on Macroeconomic Planning, Part II: centralization, decentralization, planning under uncertainty, North-Holland, 1978. Jyllands-Posten, Greater Movement in the Co-operative. (in Danish; Mere bevægelse i andelen), Jyllands-Posten, 02-12, 1998a. Jyllands-Posten, Sluggishness is Expensive, (in Danish; Træghed er dyr), JyllandsPosten, 02-12, 1998b. Kalai, E. and Smorodisky, M., Other Solutions to Nash's Bargaining Problem, Econometrica, 43: 513-518, 1975. Knetter, M.M., Price Discrimination by U.S. and German Exporters, The American Economic Review, 79:198-209, 1989. Kreps, D., A Course in Microeconomy Theory, Princeton University Press, 1990. LeVay, C., Agricultural Co-operative Theory: A Review, Journal of Agricultural Economics, 34:1-44, 1983. Lopez, R.A. and Streen, T.H., Coordination Strategies and Non-Members Trade in Processing Cooperatives, Journal of Agricultural Economics, 36:385-396, 1985. Meggido, On the Monotonicity of the Bargaining Set, the Kernel and the Nucleolus of a Game, Mathematics of Operations Research, 9:189-195, 1974. Meijboom, B.R., Planning in Decentralized Firms, Springer-Verlag, 1987. Milgrom, P. and Robert, J., Bargaining Cost, Influence Cost, and the Organization of Economic Activity in: Alt, J. and Shepsle, K. (Eds), Perspectives on Positive Political Economy, Cambridge University Press, 1990. Moulin, H., Axioms of Cooperative Decision Making, Cambridge University Press, 1988. Nash, J.F., The Bargaining Problem, Econometrica, 18:155-162, 1950. Nilsson, J., New Generation Farmer Co-ops, ICA Review, 90:32-38, 1997.

REFERENCES

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Nourse, E.G., The Economic Philosophy of Cooperation, American Economic Review, 12: 577-597, 1922. Obel, B., Issues of Organizational Design: a mathematical programming view of organizations, Pergamon Press, 1981. Porter, P. K., and Scully, G.W., Economic Efficiency in Cooperatives, The Journal of Law and Economics, 30:489-512, 1987. Rasmussen, S. and Thomsen, M.B., A Model for the Optimization of Commodity Usage at Slaughterhouses (in Danish; En model for optimering af råvare-anvendelsen på svineslagterier), Department of Economics and Natural Resources, Unit of Economics, KVL, 1991. Richards, R. J., Klein, K.K. and Walburger, A., Principal-Agent Relationships in Agricultural Cooperatives: An Empirical Analysis from Rural Alberta, Journal of Cooperatives, 13:21-34, 1998. Roth, A.E., Axiomatic Models of Bargaining, Springer Verlag, 1979. Rubinstein, A., Perfect Equilibrium in a Bargaining Model, Econometrica, 50: 97-110, 1982. Salanié, B., The Economics of Contracts, MIT Press, 1997. Sexton, R. J., Perspectives on the Development of the Economic Theory of Cooperatives, Canadian Journal of Agricultural Economics. 32: 423-436, 1984. Sexton, R. J., The Formation of Cooperatives: A game–theoretic approach with implications for cooperative finance, decision making, and stability, American Journal of Agricultural Economics, 68:214–225, 1986. Sexton, R. J., Imperfect Competition in Agricultural Markets and the Role of Cooperatives: A Spatial Analysis, American Journal of Agricultural Economics, 72:709-20, 1990. Sexton, R. J., The Economic Role of Cooperatives in Market-Oriented Economies. Working Paper, University of California, Davis, 1995. Shapley, L., Cores of Convex Games, International Journal of Game Theory, 1:11-26, 1971. Shleifer, A., A Theory of Yardstick Competition, Rand Journal of Economics, 16:319-327, 1985. Skaaning, K., Earmarking of Cooperative Capital is a Necessity (in Danish; Øremærkning af andelskapitalen er en nødvendighed), Andelsbladet, 10, 1996. Soegaard, V. and Just, F., Differentiated Pig Production – Possibilities of Differentiating Production amongst Members of a Cooperative Society (in Danish; Differentieret svineproduktion – om mulighederne for at differentiere produktionen blandt

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andelshaverne), Working Paper, Department of Societal and Industrial Development, Southern Jutland University, 1995. Staatz, J.M, The Co-operative as a Coalition: A Game Theoretic Approach, American Journal of Agricultural Economics, 65:1084-1089, 1983. Staatz, J.M, Farmer Cooperative Theory: Recent Developments, ACS Research Report No. 84, Agricultural Cooperative Service, USDA, 1989. Steff Houlberg, The Statutes of the Steff Houlberg Slaughtery (in Danish; Vedtægter for Steff Houlberg Slagterierne), Steff Houlberg, 1990. Sumner, D. and Cox, T., Fair Dairy Policy, Contemporary Economic Policy, 16:58-68, 1998. Sumner, D. and Wilson, L.W., The Evolution of Dairy Price Policy in California: Our Unique System for Distributing Milk Revenue, Working Paper, University of California, Davis, 2000. Sumner, D. and Wolf C., Quotas Without Supply Control: Effects of Dairy Quota Policy in California, American Journal of Agricultural Economics, 78:354-366, 1996. Sutton, J., Non-Cooperative Bargaining Theory: An introduction, Review of Economic Studies, LIII:709-724, 1986. Tennbakk , B. Marketing Cooperatives in Mixed Duopolies, Journal of Agricultural Economics, 46:33-45, 1996. Tirole, Jean , The Theory of Industrial Organization, The MIT Press, 1988. Torgerson, R.E., Reynolds, B. and Gray, T.W., Evolution of Cooperative Thought, Theory and Purpose, Journal of Cooperatives, 13:1-20, 1998. Vercammen, J., Fulton, M.and Hyde, C., Nonlinear Pricing Schemes for Agricultural Cooperatives, American Journal of Agricultural Economics, 78: 572-84, 1996. Young, H.P., Cost Allocation, in: Young, H.P. (Ed), Fair allocation, American Mathematical Society, 1985. Zusman, P., Group Choice in an Agricultural Marketing Co-Operative, Canadian Journal of Economics, 15: 220-234, 1982.

Glossary ACA method: payment scheme distributing the gains of cooperation in proportion to each producing group's contribution to the gains. Additional payment: see supplementary payment. Additivity: payment is independent of whether the resulting profit is distributed in one step, or whether the incomes and costs are distributed separately. Agency theory: see principal-agent theory. Asymmetric information: when an economic agent has information about costs, activities or other factors which the other agents do not have access to. Aumann-Shapley prices: prices which correspond to the average marginal revenue of the cooperative. Axiom: a fundamental property which is accepted as self-evident. Balanced budget: the requirement that neither more nor less than the net income shall be distributed to the members.

Consistency: payment shall be independent of whether the earnings are distributed to all producer groups at one time, or whether they should first be divided between standard and special producers. Control and motivation problem: the problem of ensuring that the management and members act together for the benefit of the common aims. Cooperative: a business which is owned by its members´, e.g. suppliers, rather than its capital investors. Cooperative game theory: Analytical models that focus on how syndicates of economic agents behave. It is distinguished from non-cooperative game theory by being less detailed in the description and by the agents having the possibility of entering into binding agreements. Cooperative game models must at least describe what the different sub-groups (coalitions) of members can generate for themselves (stand-alone profits).

Coalition: a grouping of producers or producing groups.

Coordination: the organisation of efficient production such that the right goods are supplied at the right time and at the right place, and in the right quantities and qualities.

Coalition monotonicity: profit to a producer cannot fall when the standalone profit increases in all the coalitions he can be a member of.

Core: the distribution of revenue (profits) so that no producer group can be better-off by withdrawing from the cooperative.

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Cournot equilibrium: the prices and quantities which exist in an oligopolistic market in which the participants determine the quantities produced. Diversify: to spread activities across several areas. Dominating strategy equilibrium: a situation in which none of the parties change their behaviour, regardless of what the others do. Efficiency (simple): if the payment system leads to decisions that maximise the integrated profit. Equilibrium: see Nash-, Cournot- and Dominating equilibriums. First-best: the solution that is possible with no asymmetric information and perfect control of every member’s actions. Usually thought of as the situation when the integrated profit is maximised. Free-rider problem: the situation where some members can obtain an advantage from the investment of others, without themselves making a contribution. Game theory: see cooperative and noncooperative game theory. Hold-up problem: the problem that one party, having made a specific investment, is vulnerable in subsequent negotiations, as the other party can threaten to withdraw from the cooperation.

Horizon problem: members do not have an incentive to make investments if the return on those investments will not be realised until after they have ceased to be members. Incentive compatibility: when some behaviour is in the own interest of a party. No member for example can be better-off by changing that part of the cooperative’s production plan over which he has control. Incremental profit (Marginal contribution): the amount by which the total profit of the cooperative will fall if a group of producers withdraws from the cooperation. Incremental profit (marginal contribution) principle: no group of producers shall be given a greater profit than the group's incremental profits. Individual rationality: no member should be able to be better-off by leaving the cooperative. Influence costs: The costs arising because of 1) attempts to influence the decisions of others to serve personal interests, 2) attempts to prevent such lobbying activities and 3) sub-optimal decision-making as a result of such lobbying activities. Influence problem: the problem of trying to limit lobbying costs. Integrated profit: the sum of all the profits, both of the suppliers and of the cooperative. It can be calculated as: the

GLOSSARY

revenues from the sales of finished goods, minus the costs of processing and marketing, and minus the costs of primary production. Investor ownership: ownership of firms by their capital investors. Iterative planning: successive steps of collecting information and making use of it. Linear programming: a mathematical method for maximizing an objective while respecting a series of sideconstraints. Marginal revenue: the additional revenue from an increase of output of one unit. Multi-criteria evaluation: simultaneous evaluation in relation to several aims. Nash equilibrium: a situation in which no individual has any incentive to change his behaviour if none of the others changes their behaviour. National pricing (Landsnotering): a common system for calculating prices for payment on account, used by all Danish meat producers' cooperatives up to 1st October 1999. Net income (revenue): the cooperative society's sales revenue, minus the processing and marketing costs. Net present value: the value of future revenues, corrected for loss of interest.

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New generation cooperatives: the name for a number of cooperatives, notably in the USA, which breaks with some traditional cooperative principles. Most importantly, free entry and delivery rights are abandoned and substituted with tradable delivery rights. NGC: see New generation cooperatives. Non-cooperative game theory: analytical modelling of conflict and cooperation among rational and intelligent individuals. Non-Cooperative game models involve as a minimum, a description of the individuals (players), what they can do (strategies) and what will happen (pay-off) as a result. Nucleolus: a payment system which seeks to give the best possible conditions to the coalition which obtains the smallest gains from the cooperation. Over-production problem: Quantity control problem.

see

Pareto-optimality: a situation in which no party can have improved welfare without it lowering that of another party. Payment system: the rules which determine the distribution of the cooperative’s revenue (net income). It is sometimes used simply as a common term for cost and profit sharing schemes. Personal accounts: part of a cooperative's net assets which is allocated to members, but which has not yet been paid out.

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Perverse incentive: an incentive to work against the common aims. Portfolio problem: Lack of diversification leading to too high risks. Farmers get a bad spread of risks by investing in processing firms. Preliminary payment: preliminary payment made to members before the distribution of supplementary payment. Pricing Committee (Noterings udvalg): the committee set up by the Danish meat producers' organisation, which established national pricing. Principal-agent theory: the theory of motivation when there is asymmetric information. Production plan: a list of the inputs a business must buy and the outputs it must sell. Profit share: a list of the resulting profit which is payable to each member. Quantity control problem: the quantity which the participants in a cooperative choose to produce is not necessarily optimal. The problem arises because the individual member does not take account of how his choice of production quantity will affect other members. Residual earnings: that part of the earnings which remain after all the firm commitments have been met.

Revenue: The cooperative's revenue is gross revenues, minus sales costs, minus processing costs, minus storage costs. Corresponds to the revenue met by the members. Sometimes called net income or net revenue product. Risk sharing: The transfer of risk in order to reduce the problem of uncertainty in regard to revenues or profits. Risk premium: The difference between an expected payment from an uncertain revenue stream and a secure payment which gives the member equal satisfaction (in other words, makes him indifferent as to which of the two alternatives he chooses). Serial principle: a payment system in which producers of the same size are dealt with equally, and where payment is independent of the production level of the larger producers. Shapley: payment is determined by a producer group's expected incremental profit (marginal contribution). Solidity: the net assets as a percentage of the total activities. Special pigs: pigs produced according to special regulations. Stand-alone profit: the total profit which a group of producers can obtain outside the cooperative.

GLOSSARY

Strong monotonicity: exists if payment to a producer group does not fall when the marginal contribution of the producer group grows. Subadditive: the total revenue (profit) falls if two independent producer groups join together.

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Tradable delivery right: rights to supply which producers can buy and sell between themselves. Under investment: when not all investments with positive current value are made.

Superadditive: the total revenue (profit) increases if two independent producer groups join together.

Vertical integration: when several successive stages of production have a common owner or common management.

Supplementary payment: that part of a cooperative’s profits which are not used for re-investment.

Yardstick competition: payment is determined by comparison with the results achieved by a reference group.

The ideal of the wise chairman: the solution which a well-informed and impartial planner would choose for the whole cooperative (primary production, processing and marketing). The payment system for piglets: ensures the same return on invested capital for all producer groups. The stand-alone profit principle: No producer group should receive less profit than the profit which the group could obtain outside the cooperative. Thin market: a market in which additional volumes can only be sold if the price is reduced. In a thin market, the supplier faces a “declining demand function”. Total monotonicity: exists if an increase in the profits of the total cooperative do not lead to a reduction in profits to any of the producer groups.

Index D

A ACA (Alternate Cost Avoidance) 24;204, 205 Accounting principles 94;104;185 Additive Additivity 20;94;102;104;106;159;185; 190;203;211;216;221 Adjusted maximin equality 18 After payment 53 Agency theory 15 Agricultural policy 191 Allocating surplus 147;148;193 Asymmetric information 135;167 Auctions 165 Aumann-Shapley prises 22;158 Autonomy 120 Average costs 112 Average revenue 115;133;134

B Balanced budget Budgeting

18;71;98;106;146;191 166

C Californian milk quotas 192 Coalition monotonicity 88 Collective incentives 106 Consistency 20;92;102;104;106;159; 185;190; 203;211;216;221 Cooperative economics 9 Cooperative game theory 15;49;60 Coordination 26;44;98;107 Core 19;81;85;87;102;181;187;200; 207; 214;218;219 Cost allocation 15 Cross-subsidies 83

Decision rights Democracy Direct equality Dominant strategy Dynamic adjustment

30 19;98;102 18 152 26;104;107;183

E Efficiency and incentives 179;197;207; 214;218 Efficiency 18;60; 65;67;99;103 Efficiency;Pareto-efficiency 106 Electricity companies 27 Equality 18;29;31;33;63;64;98;102;106

F Fair allocation Fixed shares Fixed weighting

157 147 148

G Game theory Goal hierarchy Group incentives Guaranteed supplementary payment

60 97 51;81 152

H Heterogeneity Hierarchy Hold-up Holistic approach Homogeneous Horizon problem Horizontal coordination

49;50 97;107 36;137 96 172;199 202 30

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N

I Incentive compatability 103 Incentives 19 Individual incentives 72;106 Individual rationality 81;208 Influence costs 92;102 Information and markets 165 Information collection 166 Information needs 18;98;99;164;165; 182;188;182;201;209;219 Integrated profit 64 Investments 20;104;184;188;202;211; 215;220 Iterative planning methods 166

L Landsnoteringen Law firms Linear programming

23 27 114

M Management 102;103;112 Marginal costs 112 Marginal payment scheme 22;143;157; 171 Marginal revenue 115;158 Marketing cooperatives 28 Maximin equality 18;102 Median equality 19;102 Median member 63 Membership;closed 34 Mergers 93;203 Monopoly 48;131 Monotonic 20;87;104;106;158; 183;188;202;210;211;215;220; Motivation 44;102;107 Multi product payment schemes 175 Multiple-criteria evaluation 25;35

National pricing system 25;53;177; 201;224 New Generation Cooperatives (NGCs) 33;34 Non cooperative game theory 15;60 Nucleolus 24;212;214;215

O One-man-one vote Over production

98;102 101;129;133;140

P Pareto-efficiency Payment scheme for piglets Premium pig system Price control Principal-agent theory Production rights Proportional payment

60 186 25;191 170;199 101;123 22 21

Q Quantity control problem Quantity control Quota Quota-based prices

21;51 167;199 191 142;143

R Relative performance evaluation 168 Renegotiation 152 Residual earnings 29 Risk sharing 10;101;185;190;203; 216;220 Risk 18;100;184;185;190;203;211; 216;220 Robustness 87

S Serial principle Shapley Side trading

22;160 24;216 31

INDEX

Slack Social capital Stand-alone profit Strong monotonicity Supplementary payment

150;151 29 78;79 89;90 194

U Unbalanced budget Uncertainty Under-investment

150 100;123 36;37;38

V

T Total monotonicity Tradable production rights Traditional cooperatives Traditional payment scheme 171 Transaction costs Transfer of surplus Two-part pricing

245

87 34 30 120;133; 51 22;154 50;143;192

Vertical integration

30

W Weighted payment scheme Wise chairman

188 122;123;126

Y Yardstick competition

48;168