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[μi — ε⅛,μi + εi] where ε; ∈ [0, μ] measures the
uncertainty about farmer i’s costs. Also, let the average net revenue product
be p > μi — εi 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
μi-εi
It is straightforward to show that an IO processor will choose
⅞ — mm{μt + ɛi, 2
If for example μi = I1 εi ≈ 1 and p == 2, the IO processor offers ci = 1, i.e. he
foregoes trading with half of the farmer types, the high costs types ci ∈ (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 μi + εi < ½(p + μi- ei), i.e. if and only if
P - Mi ≥ ɜɛi
Hence, the expected profit margin p-μi must exceed 3 times the uncertainty
measure εi. (Of course, in the case p < μi — 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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