The Advantage of Cooperatives under Asymmetric Cost Information

Let us consider now the case where p ≤ cf Vi. This is the casé where the
informational asymmetry is non-trivial - it is not common knowledge a priori
what the socially optimal production levels are. We can say also that this
represents a not too profitable market condition - the net average revenue
product p is not make it optimal to have all farmer types produce. From (3),
we get sf^p(c_i) = ki + p ∙ q∙⁷ Vi. Using the budget balancing constraint, the
payment can be pined down even further. To fulfill BB, we need fc_i = 0 Vi.
This conclusion is summarized in Proposition 2.

Proposition 2 When p ≤ cf^r Vi the socially optimal (and first best) pro-
duction levels can be implemented if and only if the cost dependent payments
satisfy

SlcA = I ^p'^g* ^ifc^^p     Vi

ʌ ɪ 0     otherwise

The solution in Proposition 1 is strikingly simple. It effectively sends the
market signals directly to the farmers. One way to implement this market
oriented solution is to ignore the communication procedure of the revelation
game and offer the farmers to buy whatever they produce at the price p
per unit. As we shall emphasize below, this is also the cooperative solution.
Note that by the risk-neutrality of the farmers, the optimal payment schemes
can only be characterized in expected terms. The payment plan is defined
modula zero mean lotteries.

If p > c^ for one or more farmers, the above payment plan still works.
However, in this case, there are alternative arrangements, including some
which would result in a non-allocated surplus, e.g. a strictly positive profit
to a processor. The possible solutions in this case are all those with the
structure given in (3) and constants k_iti ∈ ʃ satisfying

The inequality (4) puts some constraint on the way the surplus can be al-
located to the farmers and the processor. It leaves a surplus ∑√∙_p>_c^u (P “
- ∑_ielk_i to the поп-farmers, e.g. the processor or the government.
We record this as a proposition as well.

Proposition 3 Whenp > , the socially optimal (and first best) production
levels can be implemented if and only if the expected cost dependent payments
satisfy (S) and (4)∙

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