On the moral hazard problem without the first-order approach

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show how this expression can be used to perform comparative statics exercises in which we study (i) the effect of a change in the agentʼs wealth on the well-being of the principal; and (ii) the effects of the outside option and minimum payment on the effort level optimally implemented.