The Advantage of Cooperatives under Asymmetric Cost Information

Vi. This is a property shared by many standard distributions, including the
normal, the uniform, the chi-squared, the logistic and the exponential distri-
bution.

From the integrand of G^to(q, s), we see that the processor would like to
choose the maximal production level ¾(e_i) = g_j^σ when (p-c_i)∕_i(c_i)-F_i(c⅛) >
0 and the minimal production level q_i(c_i) ≡≡ 0 when (p—c_i)f_i(c_i) — F_i(c_i) < 0.
Since (p—c⅛) is decreasing in c_i and F_i(c_i)∕∕_i(c_i) is weakly increasing in c⅛, this
does not conflict with the monotonicity of ¾(.). Hence, letting c_i = sup{¾∣
(p — Ci)fi(ci) — F_i(c_i) ≥ 0}, the optimal contracts under an investor owned
monopsonist are

where c_i is defined as the unique solution to

except for the boundary case where (p — cf)∕i(c∣^,) — F,(⅛^f) > 0 in which case
we have ¾ = cf.

As previously, the conclusions can be sharpened a bit further. Since
the average production must be either minimal or maximal, so must all the
specific production levels, i.e. we have gf^o(c) = q_i^o(c_i) Vi, c.

Above, we have characterized the best possible outcome for the monop-
sonist. One interpretation of the revelation game is that the monopsonist
offers a menu of contracts from which the farmers’ choose. Another is that
he commits to a certain production and payment plan which depend on the
cost reported by the farmers. It is interesting to note however that the out-
come could also be implemented by a mechanism in which the processor
simply offers farmer i a price equal to c_i per unit.

The optimal solution is generally ex post inefficient. When c_i is an inner
solution, we have c_i=p- F_i(C_i) / f_i(c_t) < p. This means that attractive pro-
duction is forgone, namely when c_i ∈ (c_i,p). The monopsonist avoids trading
with the higher costs farmers, not because they are too costly per se but to
save on the information rents paid to low cost farmers. This loss of welfare is
the result of the asymmetric information. Such losses are common in models

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