Disentangling Moral Hazard and Adverse Selection

This paper analyzes a canonical principal-agent problem with moral hazard and adverse selection. The agent is risk averse and has private information about his disutility of taking an unobservable action. The principal is risk neutral and designs a menu of contracts consisting of a compensation scheme and a recommended action for each type of agent to maximize expected profit. We first derive a set of sufficient conditions for menus to be feasible (i.e., satisfy participation and incentive compatibility). Then we provide a method of solution, decoupling, consisting of first solving a cost minimization problem for a pure moral hazard problem for each type, action, and utility level of the agent, and then using the resulting cost function to solve a suitable adverse selection problem. This relaxed problem is both tractable and delivers a candidate solution for the original problem. We show several classes of primitives under which this candidate solution is in fact feasible and hence optimal. We also describe several properties that optimal menus exhibit when decoupling is valid.