∂Fi(Ci)∕∂ci has support Ct = [cf,cf]. As a matter of notation, we let c ==
(^⅛)i∈Λ C—» — = Xi∈∕⅞) 3*∏d C-» = Xj≠i,Cj∙
The farm output is processed and the processed product is sold at a mar-
ket. We assume that one unit of farm output leads to one unit of processed
product and that the market price of the processed product net of processing
costs is constant and equal to p. In the terminology from the economics of
cooperatives, p is the constant Net Average Revenue Product (NARP).
There are many possibilities to organize processing. Different owner-ship
structures are possible, price and quantity negotiations may be organized in
different ways, production rights may be allocated using different auction
mechanisms, and profits may be shared using a variety of sharing rules to
name just a few of the design variables available. Fortunately, by the rev-
elations principle, see e.g. Myerson(1979), we know that whatever can be
accomplished by a given organization can be accomplished also in a direct
revelation game in which the individual farmers have incentives to honestly
reveal their private costs and where production and compensation levels are
allowed to depend on the cost types reported. Therefore, letting
¾(.) : C —► [O,gf]
Sj(.) : C —> 3⅛o
be the production and compensation plan for farmer ii i ∈ ʃ, we can formu-
late the organizational design problem as one of designing production and
payment schemes ρ(.) = (¾(.))*∈/ and s(.) == (si(.))ie/ to solve (P)
max
g(c),*(c)
G(q, s)
s.t. ¾ (si(c) - Cj ∙ ¾(c)) ≥ 0 ∀cj,i
E?_, (s<(c) - cj ∙ qi(c)) ≥ (si(cj,c-j) — cj ∙ gj(cj,c-j)) ∀ci,cj,i
∑t=ι¾(c) ≤ ΣfajP∙¾(c) Vc
0<¾(c)≤⅛, Vc, i
where is the conditional expectation with respect to c_t given <⅛. The
objective function of the design program is arbitrary at this point. The first
set of constrains are the individual rationality (IR) constraints. They ensure
that all farmers get at least their reservation utility, arbitrarily normed
to be 0. The second set of constraint are the incentive compatibility (IC)
constraints. They ensure that all farmers will reveal their true types. The