Determinancy of Equilibria in Nonsmooth Economies

Abstract

Concavifiable preferences are representable by a function which is twice differentiable almost everywhere, by Alexandroff's [1] theorem. We show that if the bordered hessian determinant of a concave utility representation vanishes only a null set of bundles, then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of CI manifolds. Given this property, equilibrium prices will be locally unique, for almost every endowment. We given an example of an economy satisfying these conditions but not the Katzner [6] - Debreu [2], [3] smoothness conditions.