Some remarks about uniqueness of equilibrium for infinite dimensional economies

  • Elvio Accinelli Instituto de Matemática y Estadística
Keywords: general equilibrium theory, Mitjushim-Polterovich condition

Abstract

For economies with infinitely many goods, with two different approaches we obtain sufficient conditions for uniqueness of competitive equilibrium. In the second approach we prove that the Mitjushim-Polterovich condition is a sufficient condition for uniqueness of equilibrium when the consumption space is a positive cone included in a Banach space. We do not suppose separability of the utility function.

References

Araujo, A. (1987). "The Non-Existence of Smooth Demand in General Banach Spaces", Journal of Mathematical Economics, vol. 17, pp. 1-11.

Araujo, A., and P. K. Monteiro (1989). "Equilibrium without Uniform Conditions", Journal of Economic Theory, vol. 48, pp. 416-427.

Becker, G. S. (1971). Economic Theory, Alfred A. Knopf, New York.

Dana, R. A. (1993). "Existence, Uniqueness and Determinacy of Arrow-Debreu Equilibria in Finance Models".

Karatzas, I., and S. E. Sreve (1988). Brownian Motion and Stochastic Calculus, Springer Verlag.

Kehoe, T. J. (1991). "Computation and Multiplicity of Equilibria", in W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, vol. IV, New York, North Holland.

Kolmogorov, A. N., and S. V. Fomin (1972). Elementos de la teoría de funciones y del análisis funcional, Moscú, Mir.

McKenzie, L. (1960). "Matrices with Dominant Diagonal on Economic Theory", in K. Arrow, S. Karlin, and P. Suppes (eds.), Mathematical Methods in the Social Sciences, pp. 47-62.

Mas-Colell, A. (1985). The Theory of General Equilibrium, a Differentiable Approach, Cambridge University Press.

Mas-Colell, A. (1986). "The Price Equilibrium Existence Problem in Topological Vector Latices", Econometrica, vol. 54, pp. 1039-1053.

Mas-Colell, A. (1988). "On the Uniqueness Equilibrium Once Again", (preprint).

Mas-Colell, A. (1991). "Indeterminacy in Incomplete Market Economies", Economic Theory, vol. 1, pp. 45-62.

Mitjushim, L. G., and V. W. Polterovich (1978). "Criteria for Monotonicity of Demand Functions", Ekonomika i Matematicheskie Methody, vol. 14, pp. 122-128.

Zsiáhv, E. (1990). Nonlinear Functional Analysis and its Applications, Sprínger-Verlag.

Published
01-01-1996
How to Cite
AccinelliE. (1996). Some remarks about uniqueness of equilibrium for infinite dimensional economies. Estudios Económicos, 11(1), 3-32. https://doi.org/10.24201/ee.v11i1.263
  • Abstract viewed - 372 times
  • PDF downloaded: 105 times