Necessary and sufficient conditions for global uniqueness of equilibria

Covarrubias, Enrique (2008): Necessary and sufficient conditions for global uniqueness of equilibria.

Abstract

We study the problem of finding necessary and sufficient conditions that guarantee global uniqueness of equilibria in a pure exchange economy. We show that for every economy to have a unique equilibrium it is necessary and sufficient that (i) there are no critical economies and (ii) a compact set of economies has a compact set of equilibria.

• Item Type: MPRA Paper
• Language: English
• Keywords: general equilibrium, invertibility, global uniqueness, critical economy, regular economy, equilibrium manifold, natural projection, diffeomorphism, Jacobian
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Arrow K. and Hahn, F. \emph{General competitive equilibrium} North-Holland, Amsterdam, New York, and Tokyo, 1986.

Balasko, Y. \emph{Foundations of the theory of general equilibrium.} Academic Press Inc., 1988.

Chichilnisky, G. \emph{Topology and invertible maps.} Adv in Appl Math 21 (1998) 113-123.

Debreu, G. \emph{Economies with a finite set of equilibria} Econometrica 38 (1970) 387-392.

Debreu, G. \emph{Economic theory in mathematical mode.} Nobel Memorial Lecture, 1983.

Dierker, E. \emph{Two remarks on the number of equilibria of an economy.} Econometrica 40 (1972) 951-953.

Dierker, E. \emph{Regular Economies.} Handbook of Mathematical Economics, vol.2, edited by K.J. Arrow and M.D. Intrilligator. North-Holland Publishing Company, 1982.

Gordon, W.B. \emph{On the diffeomorphisms of Euclidean space.} The American Mathematical Monthly 79 (1972) 755-759.

Gordon, W.B. \emph{Addendum to ``On the Diffeomorphisms of Euclidean space''} The American Mathematical Monthly 80 (1973) 674-675.

Hadamard, J. \emph{Sur les transformations planes.} C.R. Acad. Sci. Paris 142 (1906) 74.

Hadamard, J. \emph{Sur les transformations ponctuelles.} Bull. Soc. Math. France 34 (1906) 71-84.

Hadamard, J. \emph{Sur les correspondances ponctuelles.} Oeuvres (1968) 383-384.

Hatcher, A. \emph{Algebraic Topology.} Cambridge University Press, Cambridge, 2002.

Ho, C.W. \emph{A note on proper maps.} Proc. Amer. Math. Soc. 51 (1975) 237-241.

Palais, R. S. \emph{Natural operations on differential forms.} Trans. Amer. Math. Soc. 92 (1959) 125-141.

Palais, R.S. \emph{When proper maps are closed.} Proc. Amer. Math. Soc. 24 (1970) 835-836.

Varian, H.R. \emph{A third remark on the number of equilibria of an economy.} Econometrica 43 (1975) 985-986.