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Dealing with Monotonicity Constraints in Screening Problems: The Principal-Agent Model

This paper contains two parts clearly differentiated: a survey study about the use of monotonicity constraints in screening problems, and a research work extending the space of solutions in agency theory to non-smooth or even discontinuous action profiles. Specifically, we first systematize and compare, under a wide variety of assumptions on the endogenous variables of the model, existing approaches used for the derivation of necessary conditions in screening problems containing monotonicity constraints. Then, after identifying the most robust methods to generalize previous results, the paper derives a complete characterization of optimum contracts in the model of Jullien (2000), without resort to the usual continuity and smoothness assumptions on allocation functions. In this way, we conclude that most results in Jullien (2000) continue holding if, instead of the mentioned assumptions, the endogenous variables of the problem satisfy some weak regularity condition. Moreover, when the reservation utility fails to be type-dependent, as happens for instance in Guesnerie and Laffont (1978), the characterization of optimal contracts still holds without the need of imposing the referred regularity condition.