TY - JOUR

T1 - Determinacy of equilibria in nonsmooth economies

AU - Páscoa, Mário

AU - Ribeiro Da Costa Werlang, Sérgio

N1 - Funding: Páscoa acknowledges support from FEDER and PRAXIS XXI (project 2/2.1 Eco 28/94).

PY - 1999/11

Y1 - 1999/11

N2 - Concavifiable preferences are representable by a function which is twice differentiable almost everywhere, by theorem of Alexandroff [Alexandroff, A.D., 1939. Almost Everywhere Existence of Second Differentials of Convex Functions and Some Related Properties of Convex Surfaces (Russian), Leningrad State University Annals, 3, Math. Series 6, 3-35]. We show that if the bordered hessian determinant of a concave utility representation vanishes only on a null set of bundles, then demand is approximately pointwise Lipschitzian outside of the preimage of a null set of bundles. Given this property, equilibrium prices will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the smoothness conditions of Katzner [Katzner, D., 1968. A note on the differentiability of consumer demand functions. Econometrica 36, 415-418], Debreu [Debreu, G., 1970. Economies with a finite set of equilibria. Econometrica 44, 387-392], and Debreu [Debreu, G., 1972. Smooth preferences. Econometrica 40, 603-615].

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

KW - Determinacy of equilibria

KW - Nonsmooth economies

UR - http://www.scopus.com/inward/record.url?scp=0042187939&partnerID=8YFLogxK

U2 - 10.1016/S0304-4068(98)00052-4

DO - 10.1016/S0304-4068(98)00052-4

M3 - Article

AN - SCOPUS:0042187939

VL - 32

SP - 289

EP - 302

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 3

ER -