A non-parametric approach to smoothing by aggregation over preferences

A distributional dispersion condition on C² monotone preferences, defined by unit normals to indifference surfaces, yields a C⁰ 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 C⁰ mean demand functions with monotone non-convex preferences.