depends on the aggregate production. However, the social planner’s solution
may be approximated better by an IO than by a CO processor in this case.
The assumption of a constant p is necessary to avoid the. overproduction
problem otherwise generated by a cooperative. In a cooperative, a member
takes into account the price reduction that his production inflict on himself,
but he does not internalize the loss imposed on the other members. This
makes him overproduce. An IO processor on the other hand internalizes
these losses. It follows that an IO processor may be socially superior as
the internalization of the price reduction effect may more than outweigh
cooperative when p decreases with production and costs are uncertain is the
lack of coordination of production levels. By the processor’s revenue function
being concave, the socially optimal production levels will be coordinated
such that producer i produces relatively more when farmer j has high costs
and therefore produces less. This coordination is necessary even though
costs types are independent - but it is not accomplished by a traditional
cooperative.
the rationing due to asy
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etric information.
An added drawback of the
The assumed irrelevance of the income distribution is obvious. The co-
operative solution generates one distribution - favoring the most efficient
farmers - and if this is not satisfactory, the ∞operative solution may not be
the optimal one.
In addition to the above qualitatively essential assumptions, we have in-
troduced a more technical assumption about the class of cost functions. We
have assumed that the fanners have linear costs and fixed capacity levels.
One can argue that this is a relatively narrow class of cost functions. This
is deliberate, however. Since we want to demonstrate that a cooperative
is necessary to ensure the socially optimal production levels, a small class
of function makes the result stronger. The other implication, i.e. that the
cooperative suffices to give optimal production levels, would favor working
with a large class. This way, however, is simpler and it holds for arbitrary
classes of cost functions: Whatever his cost function (∖(ρi), farmer i wi∏
choose the socially optimal production level, i.e. the ¾ maximizing p¾ — c⅛)
when processing is organized as a cooperative since in this case he is paid
P[∑j∈∕ ¾(cj)⅛∕[∑j∈/¾(cj)] ≡= PQi- We could have simplified the assump-
tions even further by using a discrete set of possible ci values. A drawback
of this however is that it require us to assume that p can take on the same
values - a somewhat awkward assumption. Furthermore, using these assump-
tions we would not get the simple hazard rate results from Section 5. We
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