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Local concavifiability of preferences and determinacy of equilibrium

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  • Pascoa, Mario Rui
  • Werlang, Sérgio Ribeiro da Costa

Abstract

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Suggested Citation

  • Pascoa, Mario Rui & Werlang, Sérgio Ribeiro da Costa, 1991. "Local concavifiability of preferences and determinacy of equilibrium," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 174, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    • Handle: RePEc:fgv:epgewp:174
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