Flexible Moral Hazard

This paper considers a moral hazard problem where the agent can choose any output distribution with a support in a given compact set. The agent's effort-cost is smooth and increasing in first-order stochastic dominance. To analyze this model, we develop a generalized notion of the first-order approach applicable to optimization problems over measures. We demonstrate that each output distribution can be implemented and characterize those contracts which implement that distribution. Contracts are shown to satisfy a simple first-order condition which equates the agent's marginal cost of changing the implemented distribution locally with its marginal benefit. Furthermore, the agent's wage turns out to be increasing in output. Finally, we consider the problem of a profit-maximizing principal and provide a first-order characterization of principal-optimal distributions.