Moral Hazard with Bounded Payments

We study the moral hazard problem when there are general constaints (mod-elled as continuous nondecreasing functions) 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. We show that 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 pay-ment 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 underlying problem fails a form of concavity.