Center for Economic Research, Department of Economics, University of Minnesota
Two agents are involved in our model. The first agent is to announce
a schedule of rewards (or, equivalently, charges) which is a function of
the amount produced by the second agent. Then the second agent will decide,
using utility maximization, how much to produce. Knowing only the formof
the second agent's utility and production functions--not the exact values
of their parameters--the first agent seeks to choose a schedule which
maximizes the minimum (over all possible utility and productivity parameter
values) of a quantity related to his residual gain (residual gain being
that part of output remaining after rewards have been paid out). We show
that in a broad class of cases the only such maximum is a schedule which
takes one-half of production. It should be noted that this result is
valid even when schedules are allowed to have certain kinks and/or discontinuities,
so that such discontinuities and kinks do not yield any
special incentive properties in our model.
This problem is motivated by situations in which the first agent
may be thought of as the government and the residual gain (revenue from
taxation) is to be used for a paramount national or social objective,
e.g., defense to ensure national survival; in this case the second agent
represents the country's labor force to be rewarded so as to stimulate
a degree of effort maximizing the residual available for national defense.
Another possible interpretation is with first agent as a landlord, the
second as sharecropper, with value added as the "product" and the problem,
seen from the landlord's point of view, being that of maximizing his share
of value added.
Hurwicz, L. and Shapiro, L., (1977), "Incentive Structures Maximizing Residual Gain Under Incomplete Information", Discussion Paper No. 83, Center for Economic Research, Department of Economics, University of Minnesota.
Hurwicz, Leonid; Shapiro, Leonard.
Incentive Structures Maximizing Residual Gain Under Incomplete Information.
Center for Economic Research, Department of Economics, University of Minnesota.
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