Flexible moral hazard problems

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 each output distribution can be implemented and identify those contracts that implement that distribution. These contracts are characterized by a simple first-order condition for each output that equates the agent's marginal cost of changing the implemented distribution around that output with its marginal benefit. Furthermore, the agent's wage is shown 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.