Farmers cooperatives and competition: Who
wins, who loses and why?1
Brent Carney, David Haines and Stephen P. King
Monash University
Melbourne, Australia
January 16, 2015
1 Contact
details: Department of Economics, Monash University, Caulfield East,
Victoria, Australia; E-mail: [email protected]
Abstract
Farmer-owned processing cooperatives are common in agricultural industries,
but they differ from standard profit maximizing firms. The farmers who
supply a cooperative are also the shareholders and a cooperative aims to
maximize the overall return to its suppliers. So the presence of a cooperative
can alter both market pricing and structure.
In this paper, we develop a simple model to analyze the market impact of a
farmer cooperative. We show how a cooperative can intensify the competition
between processors for farmers’ produce. This benefits farmers although the
size and distribution of these benefits depend on any price discrimination and
whether the cooperative reduces the viability of profit maximising processors.
Our model captures both the coordination and free rider problems faced
by farmers. Farmers face a coordination problem because their supply decision to the cooperative depends on current pricing and future dividends.
These dividends depend on the aggregate supply decisions of all farmers. We
show how this may lead to multiple equilibria and how the management of
a cooperative can design payments to avoid ‘undesirable’ outcomes.
Farmers face a free rider problem because farmers who do not supply the
cooperative gain through increased competition. This raises the possibility
of market instability, where a cooperative is desirable overall to farmers, but
the cooperative’s shareholders may find it in their own interest to change
it to a profit maximizing processor. We show that the market has two stable outcomes, one where there are only profit maximizing processors, and a
second where a cooperative coexists with profit maximizing processors.
Farmer cooperatives and competition
1
1
Introduction
Farmer-owned processing cooperatives are common in agricultural industries
in many countries.1 For example, fruit growers may cooperatively own a
juicing or a canning company,2 dairy farmers may cooperatively own a milk
processor,3 or sugar farmers may cooperatively own a mill.4
Despite their prominence in agricultural production, farmer cooperatives
have received relatively little attention in the economics literature.5 In particular, the impact of farmer cooperatives on competition in agricultural
markets, and the stability of different institutional structures, are key issues
in ‘mixed’ markets where some processors are cooperatives while others are
standard, proifit-maximizing businesses. In this paper, we consider these
issues of competition and structure.
Cooperatives operate quite differently to standard profit maximizing firms.6
So, the presence of a cooperative in a market for agricultural produce will
alter farmers behaviour and competition between other processors.
First, the farmers who supply the cooperative are also the owners of the
cooperative and receive any profits as dividends. If a farmer sells her produce
to a profit-maximising processor, then she simply receives the ‘farmgate price’
set by that processor. If, however, the farmer sells to a cooperative processor,
she will be paid for her produce in two ways — first through the farmgate
price set by the cooperative and second through a dividend paid ex post by
1
For example, Cogeca, 2010 provides a comprehensive overview of agricultural cooper-
atives in Europe.
2
For example, Ocean Spray in the US
3
For example, Fonterra in New Zealand or Land O’Lakes, Inc. in the US. “Land
O’Lakes, Inc. is a growing, farmer-owned food and agriculture cooperative doing business in all 50 states and more than 60 countries. (Land O’Lakes, Inc. 2013).
4
For example, in India, cooperative sugar mills are common, for example, accounting
for over 50% of sugar processing in the state of Maharashtra. See Damodaran, 2014.
5
Sexton 1990 is a notable exception.
6
This has been recognised by competition authorities and the courts in a number of
jurisdictions. For example see Commission of the European Communities, 2008, at paragraphs 101-103.
Farmer cooperatives and competition
2
the cooperative. For example, in 2014 Fonterra had “a final Cash Payout
[to its supplier-shareholders] of $8.50 comprising the Farmgate Milk Price of
$8.40 per kgMS and a dividend of 10 cents per share”.7 Further, a farmer’s
shareholdings in the cooperative are usually proportionate to the amount
of produce supplied by that farmer. This mix of payments complicates the
farmer’s decision. A farmer must predict the likely profit (and dividend) for
a cooperative processor if she is to compare the alternative options for selling
her produce. But the dividend will depend in part on the behaviour of other
farmers, leading to a potential coordination problem.
Second, a cooperative does not profit maximize. Rather its objective is to
maximize the return to its farmer-members. For example, “[a]s a cooperative,
it is our primary responsibility to deliver value to our member-owners”.8 This
means that a cooperative will tend to intensify competitive pressure more
than an equivalent profit-maximizing processor. If this competitive pressure
results in higher prices for farmers, then all farmers gain, not just those that
supply the cooperative. This can create a free-rider problem. All farmers
benefit from a cooperative even though only the farmers who supply the
cooperative bear the costs of operating the cooperative.
Both the coordination problem and the free rider problem may create
issues of institutional stability.
In this paper we develop a simply model of imperfect competition to capture the interaction between three agricultural processors. Using this model
we compare the competitive outcomes when one of the processors is a cooperative rather than a profit maximizer. In the absence of price discrimination,
we show that the presence of a cooperative may intensify competition and
benefit all farmers. However, a cooperative may intensify competition too
much. if a cooperative processor makes one of the other processors unviable,
then some farmers may receive a lower (net) price for their product. Further,
if profit-maximising processors can price discriminate, then this may result
in no gain to farmers who are ‘captured’ by the profit maximising processors,
but intensify competition even more for farmers who can potentially supply
7
8
Fonterra Co-operative Group Limited, 2014, at p.14.
Land O’Lakes, Inc. 2013 at p.7.
Farmer cooperatives and competition
3
the cooperative.
Our model formalizes the free rider effect, in the sense that we show that
some farmers who do not supply the cooperative gain from the presence of
a cooperative. Further, we show that when exit does not occur, the gains to
farmers, in total, outweigh the profit that a profit maximising cooperative
would otherwise receive. This raises the possibility of institutional change. If
the market has three profit maximzing processors, can an entrepreneur turn
one of these into a cooperative processor and make a net gain? We show that
the free rider problem makes such institutional change impossible. Indeed, if
an entrepreneur tried such a transformation, the result would be no change in
prices and gain for any market participant. In this sense, a market structure
with three profit maximizing processors is ‘stable’.
The free rider effect also raises the possibility that a cooperative could
be transformed into a profit maximising processor by an entrepreneur. After
all, each farmer who is a shareholder in the cooperative can be compensated
for any loss in competition when the entrepreneur buys her shares. Further,
because non-member farmers also face less competition, the entrepreneur
may be able to get agreement from cooperative members by sharing part
of the resulting profit gain. Assuming that the entrepreneur must pay all
farmer members of the cooperative at the same price for their shares, we
show that an entrepreneur cannot strike a deal with at least fifty per cent
of farmer-members to transform a cooperative. The profits that accrue to
the entrepreneur are not sufficient to compensate the farmer-members of the
cooperative. In this sense, a market structure with one cooperative and two
profit maximizing processors is ‘stable’.
Our model also captures the coordination problem faced by farmers. However, we show that the managers of a cooperative can overcome this problem
if (a) its farmer-shareholders are covered by limited liability, so any dividend
cannot be negative, and (b) the total payment to farmers is biased towards
the farmgate price. In such a situation, a cooperative can commit to high
ex ante price to avoid the coordination issues that may lead to a low ex post
dividend and total payment.
Some of the literature has argued that (consumer) cooperatives “have
Farmer cooperatives and competition
4
coordination and governance costs that a [profit maximizing] firm does not
face”.9 However, it is far from obvious that the farmers, as shareholders in
a cooperative processor, would face higher coordination or governance costs
than the (dispersed) shareholders in a profit maximizing processor.10 Hence,
we assume that a processors efficiency is not determined by its ownership
structure. That said, we allow for each of the three processors to have different fixed costs of operation.
2
The model
A unit mass of farmers is uniformly distributed around a circle of unit circumference. Each farmer can produce one unit of a well-specified, identical
product at a cost c and can sell his or her product to a processor. A processor can use the product to make a final output. For example, the farmers’
product may be raw milk that is sold to a dairy processor, grain that is sold
to a mill, or vegetables sold to a cannery.
There are three processors, labelled A, B and C, located symmetrically
around the circle. Let x ∈ [0, 1] be a point on the circumference of the circle.
For convenience we consider that processor A is located at x = 0, processor
B is located at x =
1
3
and processor C is located at x = 23 .
For one unit of the input purchased from a farmer, a processor can produce and sell one unit of output. Our aim is to consider the effects of different
institutions on the competition between processors for the farmers’ product,
so we assume that, in the relevant output market, processors have no market
power and are price takers.
Each processor’s cost of transforming one unit of the input into one unit of
output is constant and identical. Denote the output price faced by processors,
less the constant costs of transformation, by F . Thus, F represents the
9
10
Heath and Moshchini, 2014, p.4. See also Innes and Sexton 1993.
As the High Court of New Zealand, 1991 at 102,803, noted “by a system of committees,
meetings and appointment of directors, the suppliers have a very effective day to day
influence on the decision making processes of their their dairy company co-operatives.”
Farmer cooperatives and competition
5
‘break-even’ payment that a processor could make to farmers. Processors
also have fixed costs denoted by Kj , j ∈ {A, B, C}.
Processor payments to farmers may have two components: a farm gate
price denoted by Pj for processor j and a ‘dividend’ denoted by dj . The ‘farm
gate’ price is simply the standard price that the processor pays a farmer for
her produce. While referred to as ‘farm gate’, we assume that the farmers
are liable for any delivery costs so that farmers receive the farm gate price
less any delivery costs. A processor j commits to a specific farm gate price
Pj prior to receiving any product from any farmers.
The ‘dividend’ will refer to a situation where the farmers supply and own
the processor and receive a share of the processor’s profits in proportion to
their sales to the processor. In other words, the dividend is only paid by
a processor that is a farmers cooperative and is paid to farmer members
in proportion to their shareholdings which, in turn, are proportional to the
amount of product each farmer supplies to the processor. We assume that
farmers shares in a cooperative are covered by limited liability so that the
dividend dj cannot be negative. However, a cooperative processor cannot
commit to a dividend before receiving delivery from any farmer.
Processors have one of two alternative organizational forms:
Profit maximizing processor: If processor j is a profit maximising processor then, given the farm gate prices set by the other processors,
processor j will set a farm gate price that it pays farmers, Pj , in order
to maximize its profit. A profit maximizing processor does not pay a
dividend to farmers.
Farmer cooperative: If processor j is a farmer cooperative, then its objective is to maximize its total payment to its farmer members subject to
not operating at a loss. Thus, given the farm gate prices set by other
processors, processor j will seek to maximize the value of Pj + dj that
it pays to its members. Its members will be any farmers who choose to
supply the cooperative.
We are interested in the competitive effects of a cooperative processor on
the payments that farmers receive. Thus, we will assume that processors B
Farmer cooperatives and competition
6
and C are always profit maximizing processors. However, processor A can
either be a profit maximizing processor or a cooperative processor.
If all processors are profit maximizers, then there are no dividends that
are relevant to farmers. The sales to a processor j will just depend on
the farm gate prices set by each of the processors and are given by Qj =
Qj (PA , PB , PC ).
If processor A is a farmer cooperative, then farmers will have an expectation about the dividend that processor A will pay. This expectation is
relevant to each farmers supply decision. Of course, the actual dividend paid
by a cooperative will depend on the funds available for distribution after it
pays its costs. We assume that all farmers have the same expectation, d˜A .
The sales to processor j when processor A is a farmer cooperative will depend
on the farm gate prices set by each processor and the expected dividend that
will be paid by the cooperative processor so Qj = Qj (PA + d˜A , PB , PC ).
The objectives of the management of a processor will differ depending on
its structure. The management of a profit maximizing processor j will set
its farm gate price Pj to farmers to solve:
max Πj = (F − Pj )Qj − Kj
(1)
Pj
In contrast, if processor A is a farmers cooperative, its management wishes
to maximize the total payout to its farmer members, PA + dA . Because all
A
profits are distributed to farmer members, PA + dA = F − K
. So in order to
QA
maximize the total payout to members, given PB and PC , the management
of the cooperative will seek to maximise the number of farmers who supply
the cooperative with produce. In other words, it will seek to maximise its
membership.
We assume that a cooperative cannot set a negative farm gate price. So
if processor A is a cooperative, its management will set the value of PA that
maximizes QA where:
(F − PA − dA )QA − KA = 0
and
PA ≥ 0, dA ≥ 0
(2)
Given farm gate prices and, if relevant, the expected cooperative dividend,
each farmer will decide which processor to supply.
Farmer cooperatives and competition
7
Farmers have a cost of ‘transporting’ their output to a processor. We
can think of this as a physical cost (for example, with raw milk transport)
or a cost related to differences between a farmer’s output specifications and
the optimal input specifications of the processor (for example, with fruit for
juicing or vegetables for canning). Denote the per unit cost of transport for
each farmer by t. Thus if a farmer i located at xi sells to a profit maximizing
processor j located at xj for a price Pj , the return to the farmer is given by
πj = (Pj − c) − |xi − xj |t. If a farmer i located at xi sells to a cooperative
processor j located at xj for a price Pj , and the expected dividend is d˜j , then
the expected return to the farmer is given by πj = (Pj + d˜j − c) − |xi − xj |t.
Each farmer will choose to sell to the processor that maximizes her individual
expected return πj , subject to her profit being positive. We assume that
c and t are both sufficiently low so that all farmers choose to produce in
equilibrium.
A profit maximizing processor will only choose to participate in the market if it expects to make a positive profit. This will depend on the ‘mix’ of
competing processors and the specific processor’s fixed cost, Kj . We assume
that each Kj is sufficiently low so that when there are three profit maximizing processors, all processors make non-negative profits in equilibrium. In
particular, we assume that Kj ≤ 9t .
Formally, the game played between the processors and the farmers is:
t=0: Nature chooses whether or not processor A will be a cooperative.
t=1: Each profit maximizing cooperative sequentially decides whether to
continue or to drop out of production. If a processor continues then it
pays its fixed cost, Kj .
t=2: Processors simultaneously set their farm gate prices.
t=3: Farmers choose which processors to supply.
t=4: All prices and dividends are paid.
If a profit maximizing cooperative chooses not to continue as an ‘active’
processor at t = 2 then it receives a payoff of zero.
Farmer cooperatives and competition
8
We consider the subgame perfect equilibria of this game. Note that this
implies that the expected and actual dividend payments by a cooperative
will coincide in equilibria. In other words, if processor A is a cooperative
then d˜A = dA in equilibrium.
For the subgame beginning at t = 2, we consider pure strategy equilibrium outcomes where any two processors ‘share’ the farmers located between
them. Let IA be an indicator function such that IA = 1 if processor A is
a cooperative and IA = 0 if processor A is a profit maximiser. If all three
processors participate then, given prices Pj , j ∈ {A, B, C}, a farmer located
at xi ∈ [0, 31 ] will sell to either processor A or processor B. The farmer will
sell to processor A (resp. B) if PA + IA d˜A − c − xi t is greater than (resp. less
˜
than) PB −c−( 31 −xi )t. The farmer will be indifferent if xi = PA +IA2tdA −PB + 61 .
Similarly, considering farmers at other locations, we can calculate the amount
of produce sold to each processor, given the prices set by each processor, as:
2(PA + IA d˜A ) − PB − PC 1
+
2t
3
2PB − (PA + IA d˜A ) − PC 1
+
=
2t
3
2PC − PB − PA 1
=
+
2t
3
QA =
QB
QC
If there are two active processors then, without loss of generality, assume
that they are processors A and B. Given prices Pj , j ∈ {A, B}, a farmer
located at xi ∈ [0, 13 ] will be indifferent between the two processors if xi =
(PA +IA d˜A )−PB
2t
+ 61 . A farmer located at xi ∈ [ 13 , 1) will be indifferent between
˜
the two processors if xi = (PA +IA2tdA )−PB + 31 . The amount of produce sold to
each processor, given the prices set by each processor, will be:
(PA + IA d˜A ) − PB 1
+
2t
2
˜
PB − (PA + IA dA ) 1
=
+
2t
2
QA =
QB
Finally, because there is a sequential choice at t = 1, all active processors
will make a profit in equilibrium. This avoids issues of mixed-strategies when
two processors are profitable but three are not all profitable. Without loss
Farmer cooperatives and competition
9
of generality, we assume that the order of choice is processor A, followed by
processor B and then processor C, so in any sub game perfect equilibrium
where only two processors are profitable, processor C will always be the
processor that is inactive.
3
Preliminaries: coordination and multiple
equilibria with a cooperative
If processor A is a cooperative then its management will seek to maximize
the membership of the cooperative when it sets the price PA . However, as
lemma 3.1 shows, the exact choice of PA in any subgame beginning at t = 2
when processor A is a cooperative, is irrelevant, in the sense that there is an
equilibrium with identical outcomes for any other value of PA ≥ 0.
The reason for this is simple. Because the farmers receive all residual
income of the processor as dividends, if there is an equilibrium with farm
gate price PA0 and dividend d0A then there will also be an equilibrium with
farm gate price PA1 = PA0 + ∆ and d1A = d0A − ∆, so long as the non-negativity
constraints are satisfied. In the new equilibrium, farmers simply adjust their
expectations about the dividend that they will receive and this expectation
is met in equilibrium.
Lemma 3.1 formalises this intuition.
Lemma 3.1 Consider an equilibrium of the subgame beginning at t = 2
where processor A is a cooperative. Denote the equilibrium prices and quantities in this equilibrium as (PA0 , PB0 , PC0 ) and (Q0A , Q0B , Q0C ) where Pj0 = Q0j = 0
for any profit maximizing processor j that does not participate. Let PA1 =
KA
≥ 0. Then there is an equilibrium
Q0A
1
0
0
(PA , PB , PC ) and quantities (Q0A , Q0B , Q0C ).
PA0 + ∆ where PA1 ≥ 0 and F − PA1 −
of the subgame with prices
Proof: First, note that in the original equilibrium, the expected and actual
dividend paid by the cooperative processor at t = 4 is F − PA0 −
A
Denote this by d0A . Note that F − PA1 − K
= d0A − ∆.
Q0
A
KA
Q0A
≥ 0.
Farmer cooperatives and competition
10
Second, if at t = 3, farmers observe farm gate prices (PA1 , PB0 , PC0 ) and
have dividend expectations d˜1 = d0 −∆, then all farmers will make the same
A
A
choice as in the original equilibrium. So sales to each processor will be given
by (Q0A , Q0B , Q0C ). Further, farmers’ dividend expectations will be met in
A
= d0A −∆ = d1A .
equilibrium as the new dividend payment will be F −PA1 − K
Q0
A
Thus, the farmers actions and expectations are a subgame perfect equilibrium
for the subgame beginning at t = 3 where prices are (PA1 , PB0 , PC0 ).
Third, for the subgame beginning at t = 2, as farmers’ responses are the
same as in the original equilibrium, PB0 and PC0 remain best responses when
processor A sets a farm gate price of PA1 and farmers expect a dividend from
processor A of d˜1 . Thus, P 0 and P 0 remain equilibrium strategies for the
A
B
C
subgame beginning at t = 2. Also, given PB and PC are unchanged, and as
PA0 + d0A = PA1 + d1A , setting PA1 must continue to maximise the membership
of the processor and so remains an equilibrium strategy for the cooperative
processor A.
As the strategies form an equilibrium in each subgame from t = 2, there
is an equilibrium of the subgame at t = 2 where the cooperative sets a farm
gate price PA1 = PA0 + ∆, farmers who are members of the cooperative expect
to receive, and do receive, a dividend from the cooperative of d1A = d0A − ∆,
the private processors set prices PB0 and PC0 and quantities supplied to each
processor are (Q0A , Q0B , Q0C ).
Lemma 3.1 means that the management of a cooperative processor has
considerable discretion. The cooperative management can arbitrarily set one
of PA or dA . This discretion can help the cooperative deal with the potential
issue of multiple equilibria.
Multiple equilibria can arise for a farmers cooperative because farmers
face a coordination problem. The dividend paid by a cooperative to each
farmer member is F − PA −
KA
.
QA
But this dividend depends on the number
of farmers who actually supply the cooperative, with the realized dividend
falling if fewer farmers decide to sell their output to the cooperative. If
farmers are ‘optimistic’ believing that QA will be high, then this can be self
reinforcing and they will have a high expected dividend which is realized.
Farmer cooperatives and competition
11
Optimism can be an equilibrium. However, if farmers are pessimistic, expecting a small dividend, they will be less likely to supply the cooperative,
given PB and PC . The result will be a low QA and a low realised dividend.
So pessimism can also be an equilibrium.
To see this, suppose that at t = 2 processor A is a cooperative and prices
KA
are
Q0A
(0, PB0 , PC0 ),
(PA0 , PB0 , PC0 ), quantities (Q0A , Q0B , Q0C ) and dividend d0A = F − PA0 −
an equilibrium of the subgame. Then from lemma 3.1, prices
quantities (Q0A , Q0B , Q0C ) and dividend dA = d0A + PA0 is also an equilibrium of
the subgame. However, given the zero price set by processor A there will also
be an outcome where no farmers decide to supply the cooperative. Of course,
this would not be an equilibrium because the profit maximizing processors
would then seek to raise their prices. However, in possibility of a ‘no supply’
equilibrium for the cooperative cannot be avoided if the management of the
cooperative set a ‘too low’ price.
While such multiple equilibrate are possible, the management of the cooperative seeks to maximise the amount of produce sold to the cooperative
processor. They can do this and avoid the low price’ equilibria by using
lemma 3.1. For example, suppose prices (PA0 , PB0 , PC0 ) are associated with
two potential equilibrium outcomes, one with a high dividend d0h
A and one
with a low dividend d0l
A . The management of the cooperative can eliminate
the ‘undesirable’ low dividend equilibrium simply by raising the price to
0l
PA1 = PA0 + ∆ such that d0h
A − ∆ ≥ 0 but dA − ∆ < 0. By lemma 3.1, the new
prices (PA1 , PB0 , PC0 ) will form an equilibrium with the high dividend and the
low dividend equilibrium is no longer feasible.
One particular value of ∆ that achieves this outcome is ∆ = d0h
A . Thus,
management of the cooperative can always avoid the problem of multiple
equilibria, and maximize the value of PA + dA by following a simple decision
rule: given PB and PC the management of the cooperative will set the highest farm gate price that is consistent with an equilibrium where dA = 0. By
lemma 3.1 such a rule will not restrict the cooperative from maximizing its
objective. But, by limited liability, it means that given the prices, all equilibria will involve dA = 0 and each farmer can make her supply decision without
concern about the number of other farmers that supply the cooperative.
Farmer cooperatives and competition
12
In our analysis below we assume that the management of a cooperative
achieves its objective in this way and simply consider outcomes where, given
PB and PC , the cooperative sets PA such that dA = 0 in equilibrium.
4
Competition between processors
We begin by considering the alternative outcomes that can arise in the subgame beginning at t = 2 depending on the number and configuration of
processors. These outcomes will allow us to consider when different equilibria arise depending on both the types of processors and the level of fixed
costs for processors.
4.1
Competition between three profit maximizing processors
When all processors are profit maximizers, there will be a pure strategy
equilibrium where the processors all set the same price to farmers and share
the market equally. While processors may have different fixed costs, these
do not alter the processors’ decisions so long as each processor’s profits is
non-negative. There is an ‘efficient’ allocation of farmers to processors in the
sense that each farmer will sell her produce to the closest processor.
Lemma 4.1 summarizes the outcome with three profit maximising processors.
Lemma 4.1 With three profit maximizing processors, the symmetric equilibrium will involve each processor setting a price to farmers of Pj = F − 3t . The
processors will share the market equally and will make profits of Πj = 9t − Kj .
Proof: Note that, given PB and PC , processor A will set PA to maximise (F −
PA )QA − KA . Substituting in for QA , processor
2PA − PB − PC
(F − PA )
+
2t
A will set PA to maximize:
1
− KA
3
Farmer cooperatives and competition
13
The first order condition is:
1
2t
2F − 4PA + PB + PC −
=0
2t
3
But in a symmetric equilibrium, PA = PB = PC = F −
t
3
with QA = QB =
1
.
3
QC =
Substituting back into the profit function, each processor makes
profit Πj = 9t − Kj .
By assumption, Kj ≤
t
9
for each processor, so each processor will make
non-negative profits in this subgame.
4.2
Competition between a farmers cooperative and
two profit maximizing processors
Now suppose that one of the three processors is a farmers cooperative. Without loss of generality, we assume that processor A is the cooperative. The
cooperative will maximize the return to its farmer members subject to covering all costs, including capital costs.
As noted above, by lemma 3.1, without loss of generality, we can consider
outcomes where the dividend payments for the members of the cooperative
are zero and farmer members are simply remunerated through the price paid
by the cooperative. From (2), the cooperative processor will set the highest
PA so that, (F − PA )QA − KA = 0.
The outcome of the industry with a single cooperative processor is summarised by lemma 4.2.
Lemma 4.2 Suppose there are two profit maximising processors and one
cooperative processor. In the equilibrium, the price received by all farmers
will be at least F −
t
3
and is decreasing in the fixed costs of the cooperative
processor KA . The cooperative processor will have more than one-third of
farmers as members, while the profit-maximising processors will each receive
produce from less than one-third of the farmers. However, the cooperative
processor’s market share is decreasing in KA . The profit of each of the profitmaximizing processors is increasing in KA but will be lower than the situation
where all processors were profit maximizing.
Farmer cooperatives and competition
14
Proof: Given PB and PC , the cooperative processor A will set PA such that:
2PA − PB − PC 1
(F − PA )
+
− KA = 0
2t
3
From the first order condition for the profit maximising processors we know
that:
2F − 4PB + PA + PC −
2t
2t
= 0 and 2F − 4PC + PA + PB −
=0
3
3
By symmetry PB = PC . Simultaneously solving the equations gives two potential solutions for PA . However, from the cooperative processor’s objective
function we have KA = 0, PA = F , leaving the solution:
p
1 PA = F −
5t − t(−216Ka + 25t)
12
and
p
1 13t − t(−216Ka + 25t)
36
It immediately follows that the equilibrium price offered by each of the proPB = PC = F −
cessors to farmers is decreasing in KA . By substitution:
p
1 −t + t(−216Ka + 25t)
)
QA = +
3
18t
p
1 t − t(−216Ka + 25t)
QB = QC = +
)
3
36t
Note that QA is decreasing in KA while QB and QC are increasing in KA .
By construction, the profits of the cooperative processor are always zero.
The profits of the profit maximising processors are given by (F − Pj )Qj − Kj .
Noting that Pj is falling in KA and Qj is increasing in KA for j = B, C, it
immediately follows that ΠB and ΠC are increasing in KA .
Finally, to show that farmers receive a price of at least F − 3t , QB =
QC ≤
1
3
while QA ≥
1
3
and Πj ≤
t
9
− Kj , j = B, C, note that KA ≤ 9t .
By substitution, when KA = 9t , the outcome is identical to the equilibrium
with three profit maximising processors so that PA = PB = PC = F − 3t ,
with each processor buying one-third of farmers’ produce and Πj =
t
9
− Kj ,
j = B, C. The inequalities follow directly from the changes to prices, profits
and markets shares as KA decreases.
Farmer cooperatives and competition
15
If processor A is a farmers cooperative while processors B and C maximize
profits, then the profits of processors B and C are minimized when KA = 0.
When KA = 0, the cooperative processor will set a price of F and πj =
4t
−Kj
81
∂π
for each of the profit maximizing processors. As ∂KjA > 0 for j ∈ {B, C}, this
means that all processors will make non-negative profits whenever KA ∈ [0, 9t ]
4t
and Kj ∈ [0, 81
], j ∈ {B, C}.
However, if either KB or KC are greater than
4t
,
81
either one or both of
the private processors may not make positive profits in the subgame perfect
equilibrium at t = 2 with three processors.
4.3
Competition between a farmers cooperative and
one profit maximizing processor
Suppose that processor C chooses not to participate in the market when
processor A is a farmers cooperative. Processors A and B will compete for
farmers. The outcome of this competition is summarised in lemma 4.3.
Lemma 4.3 FINISH USING MATHEMATICA
4.4
When is only a single profit maximizing processor
viable?
As noted in section 4.1, three profit maximizing processors are always profitable given our assumption that Kj ≤
t
9
for j ∈ {A, B, C}. Similarly, from
4t
],
81
j ∈ {B, C} then profit maximizing processors B
section 4.2, if Kj ∈ [0,
and C can profitably operate even if processor A is a farmers cooperative.
However, if either KB and/or KC is higher than
4t
81
then, depending on KA ,
one or both profit maximizing processors may be unprofitable.
The interactions between the profitability of the different processors will
depend on the exact value of the fixed costs. As the profits of processors
B andC are increasing in KA then higher levels of KA can help the profit
maximizing processors. For example, if KA is close to
t
9
then the private
processors will also be profitable for high values of fixed costs, close to 9t . But
Farmer cooperatives and competition
16
as KA falls, the set of fixed costs that allow a profit maximizing processor
to be profitable will be reduced. This is because a lower fixed cost KA is
associated with higher, more competitive, pricing by the farmers cooperative.
One situation of particular interest is where the processors are equally efficient. As discussed in the introduction, there is no a priori reason to expect
that a farmers cooperative will have either higher or lower costs than a profit
maximizing cooperative. Both institutions face principal-agent problems between the shareholders and the management, and it is not clear that farmer
shareholders will be more or less able to hold management to account when
compared to other shareholders. Lemma 4.4 considers the case when Kj is
identical for all processors and considers when only a single profit maximizing
processor is viable.
Lemma 4.4 Suppose KA = KB = KC = K. Then if processor A is a
4t t
farmers cooperative and K ∈ ( 49
, 9 ), processors B and C will make negative
profits in the sub game with three processors starting at t = 2.
Proof TO CHECK: From the proof of lemma 4.2, the private processors
profits are given by:
p
1 πB = πC =
−108KA + 97t − 13 t(−216KA + 25t) −Kj j ∈ {B, C}
648
Setting KA = KB = KC = K, πB = 0 and solving for K gives K =
and K = 9t . Noting that
∂πB
∂K
< 0 when K =
4t
,
49
4t
49
it follows that profits are
4t t
, 9) negative for both private processors when KA = KB = KC , Kj ∈ ( 49
The presence of a cooperative processor can make a profit-maximising
processor unprofitable. As lemma 4.4 shows, this can arise even when processors have identical costs. That is, even if the processors are equally efficient and three profit maximizing processors can co-exist in the absence of
a farmers cooperative, the presence of a cooperative may make the industry
structure unviable.
If only one of the private processors is unviable, then we assume it is
processor C. Regardless, at t = 2, if two profit maximizing processors are
unviable but one is viable in the presence of a farmers cooperative then
Farmer cooperatives and competition
17
processor B will continue, while processor C will decide not to be active in
the subgame perfect equilibrium.11
4.5
Can a farmers cooperative make both profit maximizing processors unprofitable?
FILL IN
5
Who wins and who loses from a farmers
cooperative?
Section 4 considered the alternative outcomes that could arise in the sub
game perfect equilibria from t = 2. However, as discussed in section 4.2, in
some of these equilibria, one of the profit maximising processors may make
negative profits. In such a situation we assume that processor C will make
negative profits. Thus, this processor will choose not to be active at t = 1
and will ‘drop out’ of production.
The effects of a cooperative on market participants will depend on the
viability of the profit maximizing processors. If both processors B and C
remain viable in equilibrium then the farmers cooperative intensifies competition. Compared to a situation with three profit maximising processors,
this intensified competition benefits all farmers, including those that do not
supply the cooperative. This result is formalized in proposition 5.1.
Proposition 5.1 Suppose that at t = 0 nature chooses processor A to be a
farmers cooperative and in the subgame starting at t = 2 both profit maxi11
When the fixed costs of profit maximizing processors differ, then it may be argued
that the ‘more efficient’ private processor should continue to operate. We do not address
this issue here, and allow for the possibility that a ‘high cost’ processor may continue
to operate while a ‘low cost’ processor that is unprofitable when there are two other
processors, chooses to exit.
Farmer cooperatives and competition
18
mizing processors, B and C, make non-negative profits if they are active in
the market. Then in equilibrium:
1. There will be three active processors, including a farmers cooperative;
2. Compared to the equilibrium where all three processors are profit maximizers, all farmers receive a higher price in the equilibrium where processor A is a farmers cooperative; and
3. The distribution of the farmers between processors will be inefficient in
the sense that some farmers will not supply their closest processor.
Proof: Part (1) of the proposition immediately follows from subgame perfection. If processor A is a farmers cooperative but, in the subgame starting
at t = 2, both B and C make non-negative profits, then both B and C will
be at least as well off by continuing to be active as if they dropped out. As
such, each of processors B and C will choose to continue at t = 1 and there
will be three active processors in the market.
For part (2) of the proposition, let Pjn be the equilibrium price set by
processor j when all competing processors are profit maximizers, while Pjc
is the equilibrium price of processor j when processors B and C are profit
maximisers but processor A is a farmers cooperative. Using the prices derived
in lemma 4.1 and 4.2 we can find ∆Pj = Pjc − Pjn f orj ∈ {A, B, C}:
p
1 −t + t(−216Ka + 25t)
12
p
1 ∆PB = ∆PC =
−t + t(−216Ka + 25t)
36
As ∆PA = ∆PB = ∆PC = 0 when KA = 9t (which is the maximum value by
∆PA =
A
B
C
assumption); ∂∆P
< 0; and ∂∆P
= ∂∆P
< 0, it immediately follows that
∂KA
∂KA
∂KA
prices are higher for all farmers when one processor is a co-operative.
Part (3) of the proposition follows directly from lemma 4.2, noting that
processor A is supplied by more than one third of farmers in equilibrium. Proposition 5.1 shows how the presence of a farmers cooperative can
benefit all farmers, including those farmers whose produce is better suited to
Farmer cooperatives and competition
19
either of the profit maximizing processors, B and C. The result is driven by
the competition provided by the farmers cooperative, which spills-over into
the pricing offered by the profit maximizing processors.
To see this, consider the extreme case where KA = 0. In this situation the
cooperative does not have to cover any fixed costs and can set the maximum
mix of price and dividend to its members, so PA = F . Clearly this price is
higher than the price that processor A would have offered if it had been a
profit maximizer for t > 0.
With the price of a competitor increasing, the best response of a profit
maximizing processor is also to increase price. In this case, the price set by
the profit-maximising processors rises to F − 2t9 compared to a price of F − 3t
that is set when all processors are profit-maximizers. These higher prices
benefit all farmers who sell to processors B or C, including those who are
located between processors B and C.
The presence of a cooperative will also change the distribution of farmers
between processors. From the proof of proposition 4.2, when processor A is a
cooperative, it will serve all farmers located between [0, 16 + γ) and [ 56 − γ, 1)
where
p
1 −t + t(−216Ka + 25t) )
36t
Note that γ > 0 for KA ∈ [0, 9t ) The asymmetric distribution of farmers
γ=
between processors when A is a cooperative represents a social loss in the
sense that farmers who are located relatively close to either processor B or
C may choose to incur extra expense to sell to the cooperative processor A.
Of course, the farmer is compensated for the extra cost through the higher
price set by the cooperative.
The farmers’ gain is a loss to the profit-maximizing processors. For example, consider the case where KA = 0. When all processors are profit maximizers, lemma 4.1 shows that each processor makes a profit of Πj = 9t − Kj .
In contrast, it follows from lemma 4.2, that when processor A is a cooperative with no fixed costs, the profit of the two remaining profit-maximising
processors falls to Πj =
4t
81
− Kj , j = B, C.
As noted in section 4.3, because the profits of the profit maximizing processors fall when processor A is a farmers cooperative, this may lead to exit
Farmer cooperatives and competition
20
by one (or both) of processors B and C. Such an outcome will lead to different pricing and change the mix of beneficiaries from the presence of a farmers
cooperative.
FILL IN NEW PROPOSITION
6
Stability of market structures
The analysis in subsection 4 took the market structure as given. However,
market structure can change endogenously. In particular:
• A profit maximizing processor may be bought by an entrepreneur and
turned into a farmers cooperative; or
• A farmers cooperative may be bought by an entrepreneur and turned
into a profit maximizing processor.
In this section we consider both of these possibilities. In section 6.1 we
consider whether it is possible to create a farmers cooperative from a profit
maximizing incumbent processor. Clearly, the profit maximizing processor
will need to be purchased in order for it to be transformed into a cooperative.
However, given the potential benefits to farmers from a cooperative, it may
be possible for an entrepreneur to mediate such a change by buying a private
processor and then operating it as a farmers cooperative. If this was the case
then a market structure with three profit maximizing processors would be
unstable in the sense that there would be market incentives to convert one
processor to a cooperative.
Alternatively, a farmers cooperative might be converted into a profit
maximizing business by the farmer members selling their shares to an entrepreneur. There are a range of examples of such transitions occurring
(EXAMPLES). We consider this case in section 6.2.
A farmer cooperative will require a voting rule for farmer members (i.e.
those farmers who supply the cooperative) if it is to change structure. As
farmers are differentiated, different farmer members will have different preferences. We consider a simple voting procedure: at least 50 per cent of
Farmer cooperatives and competition
21
farmer members must support the conversion for it to occur.12 If a majority of farmer members would be willing to support the conversion of their
cooperative into a profit maximizing business by selling the cooperative to
a private entrepreneur, then a market structure with two profit maximizing
processors and a cooperative could be viewed as unstable.
Our results show that both market structures are stable. If there is no
efficiency gain, then it will not be profitable for an entrepreneur to buy a
profit maximizing processor and turn it into a cooperative. Similarly, if there
is no efficiency gain, a majority of farmer members will not support selling
their processor to an entrepreneur who will operate it as a profit maximizing
business.
As a corollary, our analysis suggests that where cooperatives have been
transformed into profit maximizing processors (or vice versa) then this is due
to cost savings associated with the change of ownership.
6.1
Will farmers turn a profit maximizing processor
into a cooperative?
Suppose we have a market structure with three profit maximizing processors.
As shown in section 4, farmers can gain if there is a single cooperative processor. Indeed, proposition 5.1 showed that all farmers can gain if there is
a single cooperative competing against two profit maximizing cooperatives.
In such a situation, there would appear to be strong incentives for an entrepreneur to buy one of the profit maximizing processors and turn it into a
cooperative.
In this section, we consider whether an entrepreneur can moderate such a
deal without making a loss. We consider the situation analyzed in section 4.2
where two profit maximizing processors can profitably co-exist with a farmers
cooperative.
12
This voting rule will tend to favour transforming the cooperative in that structural
changes for actual cooperatives may require require the support of a super-majority of
members (e.g. two-thirds) to proceed.
Farmer cooperatives and competition
22
In order to buy processor A, the entrepreneur will need to compensate
the profit maximizing processor for its foregone profits. So a first step is to
check if the total gains to all farmers from having a cooperative in the presence of two profit maximizing processors (as opposed to having three profit
maximizing processors and no cooperative) exceed the profit of processor A
when it maximizes profits. Lemma 6.1 shows that this is the case, so there
are potential overall gains from trade by transforming processor A into a
cooperative.
4t
Lemma 6.1 Let Kj ∈ [0, 81
] for j ∈ {A, B, C}. The total gain to farmers by
having one cooperative and two profit maximizing processors is greater than
the equilibrium profit of a profit maximizing processor when all processors are
profit maximizers.
Proof: When there are three profit maximising processors, each processor
serves exactly one-third of farmers. When processor A is a cooperative, it
will serve all farmers located between [0, 16 + γ) and [ 56 − γ, 1). As KA < 9t ,
γ > 0.
From lemma 4.1, in the absence of a cooperative processor, PA = PB =
PC = F −
t
3
with profit Πj =
t
9
− Kj , j ∈ {A, B, C}.
We need to show that, if A is a cooperative, then the total gain to farmers
exceeds
t
9
− KA . To do this we divided the farmers into two sets:
• Farmers who sell to processor A when it is profit maximizing.
• Other farmers.
First, consider the farmers who sell to processor A when it is profit maximizing. They continue to sell to processor A when it is a cooperative. When
the processor is profit maximizing, these farmers in total received a benefit
(after the costs of producing their crop) of
1
3
Z 1
Z 1
6
t
F − −c −
xtdx −
(1 − x)tdx
5
3
0
6
(3)
Farmer cooperatives and competition
23
When processor A is a cooperative, and noting that the fixed cost KA is
shared by cooperative members which are at least
1
3
of farmers, these farmers
receive at least a benefit of:
1
(F − 3KA − c) −
3
Z
1
6
1
Z
xtdx −
0
(1 − x)tdx
(4)
5
6
The difference between (3) and (4) is at least
t
9
− KA . But, this is just
ΠA . So the total gain to farmers who always sell to processor A is at least
the private processor’s profit. It just remains to show that other farmers are
bester off in total when processor A is a cooperative compared to when it is
profit maximizing. But this follows directly from the proof of proposition 5.1
noting that KA < 9t .
Lemma 6.1 flows from the increase in competition when there is a cooperative processor and the increased market share of the cooperative. The
increased competition ensures that all farmers, including those who only supply a profit maximizing processor, receive a higher price and benefit from the
presence of the cooperative. The increased market share of the cooperative
ensures that more than one third of farmers ‘share’ the fixed costs of operating the cooperative.
Given the overall gains to farmers from having a cooperative processor,
it might be thought that an entrepreneur could moderate this structural
change. Proposition 6.2 shows that, so long as the entrepreneur has to buy
the processor and then simply operate it as a cooperative, without any transfers from farmers who do not sell produce to the cooperative, then this is not
the case. In other words, the overall gain to farmers from turing processor
A into a cooperative cannot be realized.
Proposition 6.2 Suppose that all processors, including processor A, are
profit maximizing processors. If processor A is purchased by an entrepreneur
that turns it into a farmers cooperative with no loss of efficiency, and the cost
of the purchase must be funded by the cooperative (so the entrepreneur makes
no loss), then the equilibrium outcome is identical to the market outcome
when all processors operate to maximize profits.
Farmer cooperatives and competition
24
Proof: Suppose the entrepreneur pays the private owner of processor A a
price k to purchase the processor and turn it into a cooperative. In order
to buy the processor from its private owner, the owner must at least be
compensated for any lost profit ΠA = 9t − KA . Thus k ≥ 9t − KA .
The price k will be part of the capital costs of the processor. Thus, we
can define an augmented capital cost to the cooperative as KA∗ = k + KA .
Note that KA∗ ≥ 9t .
There are two cases that follow from lemmas 4.1 and 4.2:
• If KA∗ >
t
9
the cooperative will never be able to recover its capital costs
in equilibrium. Thus if k > 9t − KA the entrepreneur will make a loss,
violating the condition of the proposition.
• If KA∗ =
t
9
the equilibrium with the cooperative processor is identical
to the equilibrium when all processors are profit maximizers.
Thus an entrepreneur can only purchase the private processor A and
convert it to a cooperative processor with no loss if the outcome with the
cooperative is identical to the situation with three profit maximizing processors.
Proposition 6.2 reflects that, in order to buy out a private processor with
monopsony power, farmers must compensate the owner with the profits that
he would have made from the exercise of monopsony power. But, if the
purchase price must be funded through the revenues of the cooperative, the
cooperative is only able to raise the relevant funds if it equally exercises
monopsony power. In that situation, there is no gain to farmers.
Together, proposition 6.1 and lemma 6.2 highlight a problem for farmers.
Overall, farmers gain from a cooperative and the size of this gain is more
than enough to compensate the private owner of processor A. However,
some farmers gain through a higher price and lower profits for processors
B and C. These farmers are not members of the cooperative and do not
sell their produce to the cooperative. They do not contribute to the cost of
buying the processor and creating the cooperative. In effect, they free-ride
Farmer cooperatives and competition
25
on the farmers who supply and fund the cooperative. Because only a subset
of farmers pay the cost of making processor A a cooperative, the gains to
those farmers are insufficient to create a cooperative from a private processor,
despite there being overall gains for farmers.
This free riding problem could be solved if farmers who never sell to the
cooperative processor could be convinced to make a payment to encourage
the creation of the cooperative. However, they have no individual incentive
to do this as each farmer would prefer to free ride on the contributions of
other farmers.
6.2
Can an entrepreneur turn a cooperative into a
profit maximizing processor?
The gains to farmers of a cooperative are dispersed and unevenly distributed
between farmers. Could an entrepreneur use these differences to convince a
majority of farmer members of the cooperative to sell the cooperative so it
can be operated as a profit maximizing business? While this harms farmers
overall, only those farmers who are members of the cooperative will get to
‘vote’ on the future of the cooperative. Could an entrepreneur gain the
support of enough farmer-members to privatise the cooperative even though
overall farmers lose?
4t
We will focus on the situation where Kj ∈ [0, 81
] for j ∈ {A, B, C} so
that there is an equilibrium with two profit maximizing processors and a
cooperative. We assume that processor A is the cooperative. The farmer
members will be those farmers who supply the cooperative in equilibrium
if there is a cooperative processor. So the farmer members for cooperative
processor A are those farmers located between [0, 16 + γ) and [ 56 − γ, 1). Note
by our restriction on KA , γ > 0.
Each farmer member has shares equal to the amount that the farmer
supplies the cooperative. In our model, this means that each farmer member
has one share in the cooperative so that all farmers have an equal vote.
In order for the cooperative processor to be sold to an entrepreneur, we
Farmer cooperatives and competition
26
require that a clear majority of farmers must vote in favour of the sale. If
the cooperative is sold, the sale proceeds are divided between the farmer
members in proportion to their individual shareholdings. In our model, this
means that each farmer member receives an equal share of the sale price.
We assume that each farmer only votes in favour of the sale if she is at
least as well off with the sale proceeding as she is if processor A remains a
cooperative.
We assume that the sale of the processor cannot involve a future price
commitment by the entrepreneur or a supply commitment by any farmer
members. We also assume that an entrepreneur will only purchase a cooperative processor if the purchase leaves the entrepreneur no worse off than if
the sale doesn’t proceed.
Proposition 6.3 considers whether or not the cooperative processor will
be sold in this situation. It shows that it is not possible for the entrepreneur
to gain the support of a majority of farmers to sell the cooperative processor.
4t
Proposition 6.3 Suppose Kj ∈ [0, 81
] for j ∈ {A, B, C}, processor A is
a cooperative processor with fixed cost KA and each farmer located between
[0, 16 +γ) and [ 65 −γ, 1) is a member of the cooperative and holds a single voting
share in the cooperative. It is impossible for an independent entrepreneur to
gain the support of a majority of farmer members to sell the cooperative for
any price that does not make the entrepreneur worse off than if the sale does
not proceed.
Proof: Consider the farmer members located between [0, 61 ] and [ 56 , 1). Note
that these farmers will sell to processor A regardless of whether it is a cooperative or a profit maximizing processor. As such, these farmers will get
identical gains from the sale of the cooperative. Further, these farmers make
up more than 50 per cent of the members of the cooperative. It follows that
these farmers will always vote the same way, and if these farmers favour a
sale, then the sale will occur but if these farmers oppose a sale, the cooperative will not be sold.
When processor A is a cooperative and net of transport costs (which do
not vary whether the processor is a cooperative or a profit maximizer), these
Farmer cooperatives and competition
27
farmers receive a return on their produce of:
GC = F −
where
1
3
1
3
KA
+ 2γ
+ 2γ is the total number of farmer members in the cooperative.
If the cooperative is sold, the maximum price that an entrepreneur can
pay and be no worse off is the profit that a profit maximizing processor will
earn in equilibrium when there are three competing profit maximizing processors. Thus, the maximum payment that the farmer members can receive
from a sale is ΠA = 9t − KA .
Suppose this payment is made for the processor. It remains to show that
the farmers located between [0, 61 ] and [ 56 , 1) are worse off if this sale proceeds.
Noting: (1) that the payment for the cooperative is shared equally by all
farmer members; and (2) that the relevant farmers will continue to supply
processor A in equilibrium after the sale and will receive a price of F −
t
3
for their produce, if the sale proceeds each farmer member located between
[0, 16 ] and [ 56 , 1) receives:
t
t
1
− KA 1
GN = F − +
3
9
+ 2γ
3
Simplifying,
GC = F − KA
and
GN = F − KA
3
1 + 6γ
3
1 + 6γ
t
−
3
6γ
1 + 6γ
It immediately follows that the return to each farmer located between [0, 16 ]
and [ 56 , 1) is negative. Thus these farmers will always oppose the sale and
the sale can never receive majority support for any price that does not make
the entrepreneur worse off than if the sale does not proceed.
The sale fails because, even if the entrepreneur ‘passes back’ all profits
to the farmers as part of the sale price, post-sale, a minority of farmers will
switch to supplying a different processor. These farmers receive a share of
processor A’s profits through the sale price but do not contribute to those
Farmer cooperatives and competition
28
profits by selling their produce to profit maximizing processor A. Thus the
majority of the farmers do not receive back the full profits that they generate
for the profit maximizing processor A and so those farmers are made strictly
worse off by the sale.
This problem may be avoided, for example, if existing farmer members
were contractually ‘tied’ to sell to processor A, even after it had been sold, as
part of the sale agreement. Of course, if this was the case, the entrepreneur
would need to set the price that it would pay to the farmer members for
their produce as part of the sale. Otherwise, tied farmers could receive a
zero, or even a negative, price for their produce. But in this case, depending
on the exact nature of pricing, the competitive interaction between the profit
maximizing processors would change.
For example, if a profit maximizing processor A had to set the same price
to all farmers as it had agreed in the contract of sale (say due to some legal
constraint) then the sale contract could be used to create a first mover pricing
advantage for processor A. Alternatively, if processor A could set any price
for produce that it buys from non-contracted farmers, it would face a different
profit maximisation problem to the problem analyzed in section 4.1. In either
case, it may be possible for the entrepreneur and the farmer members to use
the contract of sale as a strategic device to alter post-sale competition and
create mutually profitable opportunities. While the strategic use of contract
conditions as part of a sale for a cooperative processor is interesting, it is
beyond the scope of this paper.
7
Extensions
In this section we consider two extensions to the model.
In our analysis in section 5 we assumed that each processor could only set
a single price. However, in the case of three processors, only one of which is
a farmer cooperative, it may be possible for profit maximizing processors to
price discriminate between those farmers for whom the cooperative is a viable
alternative and those farmers who are ‘captured’ by the profit maximizing
Farmer cooperatives and competition
29
cooperatives. We consider the effects of price discrimination in section 7.1.
Second, the cooperatives that we have considered so far have only a single class of shareholder. The shareholders are the farmers who supply the
cooperative and each farmers shareholdings are proportional to that farmers
share of sales to the cooperative.
However, cooperatives may have ‘dual’ classes of shares. While farmers
may hold voting shares in the cooperative, there may be non-voting shares
held by other parties who have financed the cooperative. We consider the
implications of two classes of shareholders in section 7.2.
7.1
Allowing processors to price discriminate
If there are two profit maximizing processors, B and C, that compete against
a cooperative processor A, then it may be possible for the profit maximizing
cooperatives to set different prices for different farmers. In particular, if the
profit maximizing cooperatives can identify a farmer’s location by the ‘third’
of the circle, then they can establish different prices for farmers located at
x ∈ ( 31 , 23 ] (i.e. between the two profit maximizing processors) compared to
farmers located either x ∈ [0, 31 ] (for processor B) or x ∈ ( 32 , 0) (for processor
C).
The possibility of price discrimination changes the outcomes compared to
the situation without price discrimination. Proposition 7.1 summarizes these
differences.
Proposition 7.1 Suppose that in the subgame at t = 2 there are two profit
maximizing cooperatives and one farmers cooperative. If the profit maximizing cooperatives can set different prices depending on whether a farmer is
located at x ∈ [0, 13 ], x ∈ ( 13 , 23 ] or x ∈ ( 23 , 0), then, compared to the situation
without price discrimination:
1. Farmers who are located between a profit maximizing processor and the
cooperative (i.e. each farmer i where xi ∈ [0, 31 ] or xi ∈ ( 23 , 0)) and, who,
in the absence of price discrimination, would sell to a profit maximizing
processor, are made better off by the possibility of price discrimination;
Farmer cooperatives and competition
30
2. Farmers who are located between the profit maximizing processors (i.e
each farmer i where xi ∈ ( 13 , 23 ]) are made worse off by the possibility
of price discrimination;
3. Farmers who are located between a profit maximizing processor and the
cooperative (i.e. each farmer i where xi ∈ [0, 13 ] or xi ∈ ( 32 , 0)) and,
who would sell to the cooperative processor both in the absence of price
discrimination and in the presence of price discrimination, are made
worse off by the possibility of price discrimination; and
4. Farmers who are located between a profit maximizing processor and the
cooperative (i.e. each farmer i where xi ∈ [0, 13 ] or xi ∈ ( 32 , 0)) and, who
would sell to the cooperative processor in the absence of price discrimination but who sell to a profit maximizing processor in the presence
of price discrimination, may be better or worse off depending on their
exact location.
Proof: With price discrimination, the profit maximizing processors can set
different prices to different farmers depending on whether the farmer is located to the ‘left’ or ‘right’ of the processor. Using L and R to denote left
and right we have demands for each processor:
QA =
2PA − PBR − PCL
+ 1/3
2t
PBR − PA
+ 1/6
2t
P L − PCR
QLB = B
+ 1/6
2t
PCR − PBL
QR
+ 1/6
C =
2t
P L − PA
QLC = C
+ 1/6
2t
As before, the cooperative sets its price, PA , such that (F −PA )QA −KA =
QR
B =
0. Each private processor j solves:
L
L
max (F − PjR )QR
j + (F − Pj )Qj − Kj
PjR ,PjL
Farmer cooperatives and competition
31
The first order conditions for profit maximization for the private processors
are:
3F + 3PA − 6PBR + t
3F + 3PCR − 6PBL + t
= 0,
=0
6t
6t
3F + 3PA − 6PCL + t
3F + 3PBL − 6PCR + t
= 0,
=0
6t
6t
Solving simultaneously we find prices to be:
p
1
PA = (2F − t + −8KA t + t2 )
2
1
PBL = PCR = (3F − t)
3
1
5t
3p
PBR = PCL = (6F − +
−8KA t + t2 )
6
2
2
By symmetry we can simply consider the farmers selling to processors A
and B.
For the first part of the proposition, consider the farmers located at
x ∈ [0, 31 ] (i.e. to the right of processor B) who would sell to processor
B in the absence of price discrimination. With price discrimination these
farmers could still choose to sell to processor B and receive price PBR . The
difference between PBR with price discrimination and PB in the absence of
price discrimination is given by:
∆PBR =
But, as
R
∂∆PB
∂KA
p
p
1 −2t + 9 t(−8KA + t) − t(−216KA + 25t)
36
< 0 for KA ∈ [0, 9t ] and ∆PBR = 0 when KA = 9t , ∆PBR ≥
0. Thus as these farmers each have the option of counting to selling to
processor B at a higher price with price discrimination than in the absence
of discrimination, they must be better off with [rice discrimination regardless
of the actual processor they choose to supply.
For the second part of the proposition, consider farmers located to the
left of processor B at x ∈ ( 13 , 12 ]. As processors B and C always price symmetrically, these farmers will supply processor B with and without price
discrimination. The price each of these farmers receives in equilibrium with
price discrimination less the price each of these farmers receives in equilibrium without price discrimination, is given by:
Farmer cooperatives and competition
∆PBL =
As
L
∂∆PB
∂KA
32
p
1
(t − t(−216KA + 25t))
36
> 0 for KA ∈ [0, 9t ] and ∆PBL = 0 when KA = 9t , ∆PBL ≤ 0 and
these farmers are always worse off under price discrimination.
For the third part of the proposition, consider farmers who sell to the
cooperative processor in equilibrium both with and without price discrimination. The price each of these farmers receives in equilibrium with price
discrimination less the price each of these farmers receives in equilibrium
without price discrimination, is given by:
∆PA =
As
∂∆PA
∂KA
p
p
1
(−11t + 6 t(−8KA + t) + t(−216KA + 25t))
12
< 0 for KA ∈ [0, 9t ] and ∆PA = 0 when KA = 0, ∆PA ≤ 0. The
price farmers receive when they sell to the cooperative is higher when there
is no price discrimination, so farmers shoo always supply the cooperative are
worse off in equilibrium with price discrimination.
For the final part of the proposition, note that the number of farmers
in [0, 13 ] who supply the cooperative processor will fall when there is price
discrimination compared to the situation without price discrimination. This
follows immediately from the fall in PA . So there are no farmers who would
sell to a profit maximizing processor in the absence of price discrimination,
who choose to supply the cooperative processor with price discrimination.
Consider those farmers who would chose to supply the cooperative in the
absence of price discrimination but who choose to supply a private processor
with price discrimination. In particular:
• Consider a farmer who was just indifferent between selling to a profit
maximizing processor and selling to the cooperative in the absence of
price discrimination. This farmer must be better off with price discrimination as the price paid by the profit maximizing processor rises with
price discrimination. By continuity, other farmers located close to this
farmer (but close to the cooperative) must also be better off with price
discrimination.
Farmer cooperatives and competition
33
• Consider a farmer who is just indifferent between selling to a profit
maximizing processor and selling to the cooperative in the presence
of price discrimination. This farmer must be worse off with price discrimination as the price paid by the cooperative processor falls with
price discrimination. By continuity, other farmers located close to this
farmer (but further from the cooperative) must also be worse off with
price discrimination.
By these two examples, farmers who are located between a profit maximizing
processor and the cooperative (i.e. each farmer i where xi ∈ [0, 31 ] or xi ∈
( 23 , 0)) and, who would sell to the cooperative processor in the absence of
price discrimination but who sell to a profit maximizing processor in the
presence of price discrimination, may be better or worse off depending on
their exact location, proving the fourth part of the proposition.
In the absence of price discrimination, each profit maximizing processor
must set a price to farmers based on the average level of competition. In
contrast, when price discrimination is possible, a profit maximizing processor
can alter its price depending on the competitive pressures that it faces for a
particular group of farmers.
From the perspective of a profit maximizing processor, a farmers cooperative behaves in a highly competitive fashion. Thus, when price discrimination
is possible, each profit maximizing processor will choose to price more aggressively to those farmers who are located between it and the cooperative
processor.
In contrast, each profit maximizing processor is less of a competitive
threat to the other profit maximizing processor. The ability to price discriminate removes the competitive influence of the cooperative processor when
setting prices for farmers located between the profit maximizing processors.
As a result, the equilibrium prices to farmers located in ( 13 , 32 ] fall with price
discrimination.
The farmers who supply the cooperative, however, also lose by the ability
of the profit maximizing processors to price discriminate. Despite pricing by
Farmer cooperatives and competition
34
these processors being higher for the relevant farmers, the price paid by the
cooperative processor is lower. This reflects the nature of the cooperative.
It sets the highest possible price subject to covering its fixed costs. But this
means that there is a positive externality between farmers who supply the
cooperative. When the price set by the profit maximizing processor rises,
some ‘marginal’ farmers move their business from the cooperative to the
profit maximizing processor. But this raises the average cost of operating
the cooperative for the farmers who remain with the cooperative. Farmers
who are ‘loyal’ to the cooperative are made worse off by price discrimination
despite the fact that they are offered a higher price by the profit maximizing
processors.
7.2
Cooperatives with two classes of shareholders
Cooperatives may have multiple classes of shareholders. In this section we
consider the implications of such a structure. In particular, we assume that
at t = 1, in order to continue to operate, a cooperative processor A needs to
raise funds KA by issuing non-voting shares. The cooperative will issue s non
voting shares at a price of $ KsA per share to raise KA and fund its capital
costs. The dividend paid will not depend on the type of share. So the total
number of shares will be s + QA and the management of the cooperative will
pay a dividend by dividing the total revenues of the cooperative, (F − PA )QA
by the number of shares QA + s. In other words, dA =
(F −PA )QA
.
QA +s
To be willing to fund the cooperative, investors who purchase the nonvoting shares must expect to receive at least KA in total in dividend payments. Let deA be the expected dividend from the perspective of the investors.
Thus, to be willing to invest sdeA ≥ KA .
However, because the investors buy shares before PA is set, the expected
dividend for the investors will depend on both the expected price that the cooperative will set and the expected equilibrium quantities. This raises issues
about the objective to be pursued by the management of the cooperative.
We analyse this issue in two steps. First, define a consistent outcome
of the game where the cooperative processor issues s non-voting shares and
Farmer cooperatives and competition
35
raises KA at t = 1, sets a price PA , a dividend dA and a level of sales QA such
that, if investors expect PA and dA at t = 1, and if the cooperative actually
sets PA at t = 2 then there is a subgame perfect equilibrium at t = 2, given
PA , that leads to dividend dA . Note that consistency does not change the
decision making of the farmers or of the profit maximizing processors, but it
does remove the discretion of the management of the cooperative processor
to set the price PA . In that sense, a consistent outcome need not be an
equilibrium of the entire game as it ignores the incentives of the management
of a farmers cooperative.
Lemma 7.2 mirrors lemma 3.1. It shows that if there is an equilibrium
without non-voting shareholders with farm gate price PA0 ≥ 0 and dividend
d0A ≥ 0 then there will also be a consistent outcome when the cooperative
raises KA by issuing non-voting shares at t = 1 with farm gate price PA1 =
PA0 + ∆ ≥ 0 and d1A = d0A − ∆ > 0, so long as the cooperative issues the
appropriate number of shares, s
Lemma 7.2 Consider an equilibrium of the subgame beginning at t = 2
where processor A is a cooperative. Denote the equilibrium prices and quantities in this equilibrium as (PA0 , PB0 , PC0 ) and (Q0A , Q0B , Q0C ) where Pj0 = Q0j = 0
for any profit maximizing processor j that does not participate. Let PA1 =
PA0 − ∆ where PA1 ≥ 0 and (F − PA1 )Q0A > 0. Then, if the cooperative issues
s = K∆A non-voting shares to investors at t = 1 at a price of (KA /s) per share,
then there is a consistent outcome of the game with prices (PA1 , PB0 , PC0 ) and
(Q0A , Q0B , Q0C ).
Proof: First, without loss of generality, from lemma 3.1, we only need to
consider initial equilibria (PA0 , PB0 , PC0 ) and (Q0A , Q0B , Q0C ) where (F −PA0 )Q0A −
KA = 0 so the initial dividend is zero.
Second, note that if prices (PA1 , PB0 , PC0 ) are set leading to quantities
(Q0A , Q0B , Q0C ) then the total funds available for the cooperative to distribute
as dividends is (F − PA1 )Q0A . But this is equal to (F − PA0 + ∆)Q0A . Noting
K +∆Q0
that (F − PA0 )Q0A = KA , each farmer will receive As+Q0 A in dividends. But
A
s = K∆A so the dividend received by each farmer shoe sells to the cooperative
processor will be
KA +∆Q0A
KA
+Q0A
∆
which equals ∆.
Farmer cooperatives and competition
36
Thus, given prices (PA1 , PB0 , PC0 ), if each farmer expects to receive a dividend of d˜A = ∆, then if farmers in total sell Q0 units to processor A each
A
farmer will receive
PA1 + ∆
=
PA0 .
But this means that there is an equilibrium
in the subgame at t = 3 where farmers sell quantities (Q0A , Q0B , Q0C ) to each
of processors A, B and C respectively.
Third, note that given the farmers behaviour, it remains an equilibrium
at t = 2 for processors B and C to set prices PB0 and PC0 respectively given
that processor A sets price PA1 .
Finally, we need to confirm that the investors receive KA in total. This
follows as investors receive s∆ in total dividend payments. Substituting in
for s this means that investors with non-voting shares will receive KA .
Thus, if the cooperative issues s = K∆A non-voting shares to investors at
t = 1 at a price of (KA /s) per share, then there is a consistent outcome of
the game with prices (PA1 , PB0 , PC0 ) and (Q0A , Q0B , Q0C ), as required.
Lemma 7.2 shows that the cooperative has a great deal of discretion when
setting a consistent price and share structure in that it can mimic any desired
equilibrium outcome with an alternative price and dividend by issuing the
correct number of non-voting shares. The sale of these shares will raise
exactly KA in funds and the investors with the non-voting shares will be
perfectly compensated through dividend payments.
The cooperative, however, faces a problem of consistency. The cooperative will set the farm gate price after it issues equity to investors. if the
cooperative sought to maximise farmers return it could do so by then setting
a high farm gate price with a low dividend. This would benefit the farmers but harm the non-voting shareholders. Knowing this, the non-voting
shareholders would not invest and there would not be an equilibrium.
To avoid this problem, a cooperative would like to have a policy that
allows it to commit in advance to set a ‘reasonable’ farm gate price. This
might occur through reputation. If a cooperative is growing and needs future
capital injections, it may appropriately remunerate non-voting shareholders
today knowing that if it didn’t it would not receive future funds.
Alternatively, legal rules requiring the cooperative to maximize profits if
Farmer cooperatives and competition
37
it issues (non-voting) equity may overcome the problem. In our framework,
if the cooperative management sought to maximise (F − PA )QA it could do
so by setting a zero price (subject to farmers having an optimistic view about
the dividend). Of course, as discussed in section 3, this can lead to multiple
equilibria.
In summary, if a cooperative processor needs to raise funds by issuing
non-voting shares at t = 1 to cover its capital costs, it can do so, but it faces
an issue of credibility. This may be solved, for example, by laws requiring
profit maximization. However, such a solution may make the cooperative
‘fragile’ in the sense that by setting a lower farm gate price, the cooperative
can face a coordination issue due to multiple equilibria.
8
conclusion
To be done.
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