A short note on the definable Debreu map in regular O-minimal equilibrium manifolds

Arias-R., Omar Fdo. (2014): A short note on the definable Debreu map in regular O-minimal equilibrium manifolds.

Abstract

The main purpose of this paper is to outline that the definable Debreu map is a local definable diffeomorphism. It implies the equilibrium is locally determined in each connected component partitioning a regular O-minimal equilibrium manifold. It complements the result in Theorem 5 of Arias-R. (2013) and converges to the local determinacy result of definable competitive equilibrium of Blume and Zame (1992).

• Item Type: MPRA Paper
• Language: English
• Keywords: O-minimal manifold, cell decomposition, Debreu map, local determinacy
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Arias-R., Omar Fdo. (2013). A remark on definable paths in regular O-minimal equilibrium manifolds. Munich Personal Repec Archive, 51820.

Balasko, Y. (1988). Foundations of the theory of general equilibrium. Academic press, Boston.

Blume, L. and Zame, W. (1992). The algebraic geometry of competitive equilibrium. Economic theory and international trade; essays in memoriam J. Trout Rader, ed. por W. Neuefeind y R. Reizman, Springer-Verlag, Berlin.

Bochnak, J., Coste, M. and Roy, M. (1991). Real Algebraic Geometry. Springer Verlag-Berlin.

Debreu, G. (1970). Economies with a finite set of equilibria. Econometrica, Vol. 38, No.3, pp. 387-392.

Nagata, R. (2004). Theory of regular economies. World scientific.

Van den Dries, L. (1998). Tame topology and O-minimal structures. Cambridge university press.