A non-parametric approach to smoothing by aggregation over preferences

Abstract

A distributional dispersion condition on C 2 monotone preferences, defined by unit normals to indifference surfaces, yields a C 0 mean demand function when one integrates over such suitably diffuse consumers with convex preferences, regardless of the distribution of their initial endowments. For non-convex preferences, the dispersion condition implies that at any price vector, individual demands are finite sets for almost every agent. A stronger dispersion condition, involving both utility functions and unit normals, yields C 0 mean demand functions with monotone non-convex preferences.