Determinacy of equilibria in nonsmooth economies

摘要: Abstract Concavifiable preferences are representable by a function which is twice differentiable almost everywhere, theorem of Alexandroff [Alexandroff, A.D., 1939. Almost Everywhere Existence Second Differentials Convex Functions and Some Related Properties Surfaces (Russian), Leningrad State University Annals, 3, Math. Series 6, 3–35]. We show that if the bordered hessian determinant concave utility representation vanishes only on null set bundles, then demand approximately pointwise Lipschitzian outside preimage bundles. Given this property, equilibrium prices will be locally unique, for every endowment. give an example economy satisfying these conditions but not smoothness Katzner [Katzner, D., 1968. A note differentiability consumer functions. Econometrica 36, 415–418], Debreu [Debreu, G., 1970. Economies with finite equilibria. 44, 387–392], 1972. Smooth preferences. 40, 603–615].