Now, if we set ω=0,then the problem will be the one for the integrator instead of the
regulator. Then the condition (5) boils down to
1
(5’)
U'(r (X) =--------------------:-----:-------------:------------------:-----: :-------------:----------- VX, i
h , „ri h(x / e = eL, e~i = eH )g(x~i /xi , e = eL ,e~i = eH )1
A + Ll [1]
h(xl / e = eH )g(x i /xl, e = eH )
Now, if we compare equation (5) and (5’) it is obvious that ri(x) is larger in case of
regulator’s scheme for any feed realization, since U(.) is concave
and (A + OJ)> A. For the
same effort eH, ri(x) is larger for the regulator’s problem. Hence, if the regulator impose this pay
structure on the integrator, the grower’s welfare will be larger because of larger payment for any
feed realization.. But the reverse is true for the integrator.
Integrator’s case
Since the distributions of feed are not independent because of the presence of common
uncertainty, individual feed utilization is not a sufficient statistic for xi with respect to individual
effort; the density g(x -iI xi, e) depends on ei. Hence, the feed levels obtained by the rest of the
group convey information about common production uncertainty and, as a result, the effort
choice of any given grower. In this case, condition (5,) implies that the optimum compensation
rule for grower i must depend not only on xi,but also on the feed levels obtained by all other
growers, x -i.
To solve this problem, it requires the precise knowledge of distributional forms.
However, as shown by Tsoulouhas and Vukina and Tsoulouhas, rule (5,) can be simplified
without distorting the incentives. For sufficiently large the number of growers, the average feed
-i
used by all growers except i, x can convey information about the common production
uncertainty, which suggests that the payment to each grower can depend only on the feed he