PROTECTING CONTRACT GROWERS OF BROILER CHICKEN INDUSTRY

schedule, the growers decide whether to accept or reject the offers. If the growers accept the
offers, then they exert effort and outcomes (feed use) are realized. The integrator observes
outcomes and makes the payment. If they reject the offers, each party receives his reservation
payoff.

As mentioned above, the output target for each grower is set to y . This is so because
the integrator treats all the growers homogeneously, ex ante, avoiding adverse selection
problem. Feed used by grower, χ^l, i ∈ N ={ 1,2,...,n} is in the interval [xl,x_h]. Let x ≡
(x¹,...,xⁿ) and _x~^l = (x¹,..., x^i-1, xi⁺¹,..., xⁿ) denote the feed levels obtained by all growers
including i and excluding i, respectively. To derive the optimal utility payments, we characterize
the incentive-efficient scheme assuming that there are only two types effort eL and eH. with where
eL < eH.

Let e =(e¹,..., eⁿ) and e^-i =( e¹,..., e^i-1, eⁱ⁺¹,..., eⁿ)denote the efforts exerted by all agents
including i and excluding i, respectively. In the presence of common shocks, the distributions of
feed are dependent. Let χ (x/e ) denote the joint density function of x given the actions of the
growers, h(xi/e) denote the marginal density obtained from χ (x/e ), and H(xⁱ /e) denote the
distribution function. The density h(x/e) has full support, that is h(xⁱ /e)>0 for all e and all x,_x^l .
It is assumed that H(xⁱ / e_L, e^-i) ≤ H(xⁱ / e_H, e^-i ) with eⁱ< eⁱ for every χ^l, with strict inequality
for a set of values of x^lwith positive probability, and for every e^-i and i. These are flrst-order
stochastlc domlnance conditions saying that the probability that the feed used by a grower
exceeds any given level decreases with his effort.

The grower is assumed to have a von Neumann-Morgenstern utility function of the form
U(rⁱ)-c(eⁱ), where rⁱ is the grower's remuneration and c(eⁱ) is his disutility of effort. The function
U(.) is twice continuously differentiable, with U'(^.)>0, U"(^.)<0. The disutility of effort shows c'(^.)
>0 and c^,,(.) >0. The principal is risk-neutral with respect to profit. The output market is assumed
to be competitive, the price of output p is deterministic and the price of feed is normalized to
one.

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