Procurement with an Endogenous Type Distribution

We study a procurement problem where the distribution of types is determined by a productive, yet unobservable, prior effort of the agent. Productivity enhancing investments and learning are discussed as canonical examples. Our analysis explains unusually high levels of production for the most efficient firms, that is premia at the top. Distortions and overproduction at the top arise if the top is informative about investments. Distortions and premia at the top are the larger the more informative the top about unobserved investments. In the limiting case where the inference at the top is almost exact, optimal contracts can be approximated arbitrarily closely by standard procurement contracts adjusted by a reward for the top. In the context of learning we explain the emergence of extreme reward schemes when the principal is a quasi risk lover and the emergence of equalized incentive schemes when the principal is a quasi risk averter. These results are derived within a first order approach. Sufficient conditions validating the approach are derived and found less restrictive than those in pure moral hazard problems: contracts under asymmetric information ex post are necessarily monotonic while this has to be ensured in settings of pure moral hazard.