The Advantage of Cooperatives under Asymmetric Cost Information

involving negotiations under asymmetric information, cf e.g. Akerlof( 1970),
Vickrey(1961) and Chatterjee and Samuelson(1983). A model with much the
same structure of the optimal solution as above is Antle and Eppen(1985).

An advantage of the formulations above is that they not only support the
qualitative conclusion that investor owned processing leads to a welfare loss
in many cases where the cooperative organization would solve the central
planner’s problem. They also allow us to measure the extent of the welfare
loss and to identify circumstances where this is particularly important. The
next section gives some examples.

6 Some Examples

To illustrate our results, let us assume that costs are independent and uni-
formly distributed, eɪ ~ U[μ_i — ε⅛,μ_i + ε_i] where ε; ∈ [0, μ] measures the
uncertainty about farmer i’s costs. Also, let the average net revenue product
be p > μ_i — ε_i Vi. The potential social value from having farmer i produce -
which is also the social value realized by the cooperative - is therefore

min{μ,¼,p}        ɪ

ʃ (P-Ci)X-Ifci
μ_i-ε_i

It is straightforward to show that an IO processor will choose

⅞ — mm{μ_t + ɛi, 2

If for example μ_i = I₁ ε_i ≈ 1 and p == 2, the IO processor offers c_i = 1, i.e. he
foregoes trading with half of the farmer types, the high costs types c_i ∈ (1,2],
to reduce his payment to the low cost types <⅛ ∈ [0,1] .

It follows that there will be no social loss from having a IO processor if
and only if μ_i + ε_i < ½(p + μ_i- e_i), i.e. if and only if

P - M_i ≥ ɜɛi

Hence, the expected profit margin p-μ_i must exceed 3 times the uncertainty
measure ε_i. (Of course, in the case p < μ_i — eɪ which we have excluded, there
will also not be a loss since in this case production is not even attractive
under the cooperative regime). Figure 2 below illustrates this.

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