Moral hazard with bounded payments

We study the moral hazard problem with general constraints on how little or much the agent can be paid as a function of output. We provide a characterization and existence result using only very simple methods. In the dual problem of minimizing costs for a given effort level, a constraint that harms the principal will always result in a contract that pays according to the constraint on some range of outcomes. For the case of a simple fixed minimum feasible payment, the resultant contract will be option-like. We show how the “strike price” and intensity of incentives once the strike price is exceeded vary in the minimum payment and the outside option of the agent. When the principal can also choose the effort to induce, then, even if the constraint harms the principal, he may optimally choose a contract that never pays the minimum (or maximum). We show that this can only occur if the problem without the payment constraints fails a form of concavity.