Calculus of Variations and Geometric Measure Theory

A. Lachapelle - F. Santambrogio

On the strategic use of risk and undesirable goods in multidimensional screening

created by santambro on 01 Jun 2010
modified on 21 Sep 2011


Accepted Paper

Inserted: 1 jun 2010
Last Updated: 21 sep 2011

Journal: J. Math. Economics
Year: 2010


A monopolist sells goods with possibly a characteristic consumers dislike (for instance, he sells random goods to risk averse agents), which does not affect the production costs. We investigate the question whether using undesirable goods is profitable to the seller. We prove that in general this may be the case, depending on the correlation between agents types and aversion. This is due to screening effects that outperform this aversion. We analyze, in a continuous framework, both 1D and multidimensional cases. The formalism for the continuous case is given by the calculus of variation formulation by Rochet and Choné, which amounts to the minimization of an integral functional in the cone of convex functions.

Keywords: principal-agent problem, adverse selection, convexity constraints