Flexible Moral Hazard Problems with Adverse Selection

We study a moral hazard problem with adverse selection: a risk-neutral agent can directly control the output distribution and possess private information about the production environment. The principal designs a menu of contracts satisfying limited liability. Deviating from classical models, not only can the principal motivate the agent to exert certain levels of aggregate efforts by designing the "power" of the contracts, but she can also regulate the support of the chosen output distributions by designing the "range" of the contract. We show that it is either optimal for the principal to provide a single full-range contract, or the optimal low-type contract range excludes some high outputs, or the optimal high-type contract range excludes some low outputs. We provide sufficient and necessary conditions on when a single full-range contract is optimal under convex effort functions, and show that this condition is also sufficient with general effort functions.