Covarrubias, Enrique (2008): Determinacy of equilibria of smooth infinite economies.

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Abstract
This paper deals with generic determinacy of equilibria for infinite dimensional consumption spaces. Our work could be seen as an infinitedimensional analogue of Dierker and Dierker (1972), by characterising equilibria of an economy as a zero of the aggregate excess demand, and studying its transversality. In this case, we can use extensions of the transversality density theorem. Assuming separable utilities, we give a new proof of generic determinacy of equilibria. We define regular price systems in this setting and show that an economy is regular if and only if its associated excess demand function only has regular equilibrium prices. We also define the infinite equilibrium manifold and show that it has the structure of a Banach manifold.
Item Type:  MPRA Paper 

Original Title:  Determinacy of equilibria of smooth infinite economies 
Language:  English 
Keywords:  Determinacy, equilibria, infinite economies, Fredholm maps, equilibrium manifold, Banach manifolds 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium > D50  General D  Microeconomics > D5  General Equilibrium and Disequilibrium > D51  Exchange and Production Economies 
Item ID:  9437 
Depositing User:  Enrique Covarrubias 
Date Deposited:  04 Jul 2008 04:35 
Last Modified:  28 Sep 2019 04:34 
References:  Abraham, R. and Robbin, J. Transversal Maps and Flows. Benjamin, New York, 1967. Araujo, A. The NonExistence of Smooth Demand in General Banach Spaces. Journal of Mathematical Economics 17 (1988) 309319. Balasko, Y. Foundations of the Theory of General Equilibrium Academic Press Inc., 1988. Balasko, Y. The natual projection approach to the infinite horizon model. Journal of Mathematical Economics 27 (1997) 251265. Chichilnisky, G. and Zhou, Y. Nonlinear functional analysis and market theory. Working paper (1995) Columbia University. December. Chichilnisky, G. and Zhou, Y. Smooth Infinite Economies. Journal of Mathematical Economics 29 (1998) 2742. Dierker, E. and Dierker, H. The Local Uniqueness of Equilibria Econometrica 40 (1972) 867881. Dierker, E. Regular Economies. Handbook of Mathematical Economics, vol.2, edited by K.J. Arrow and M.D. Intriligator. NorthHolland Publihing Company, 1982. Kehoe, T.J., Levine, D.K., MasColell, A. and Zame, W.R. Determinacy of Equilibrium in LargeScale Economies. Journal of Mathematical Economics 18 (1989) 231262. Quinn, F. Transversal Approximation on Banach Manifolds. 1970 Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) pp. 213–222 Amer. Math. Soc., Providence, R.I. Shannon, C. Determinacy of competitive equilibria in economies with many commodities. Economic Theory 14 (1999) 2987. Shannon, C. and Zame, W.R. Quadratic Concavity and Determinacy of Equilibrium. Econometrica 70 (2002) 631662. Smale, S. An Infinite Dimensional Version of Sard’s Theorem. American Journal of Mathematics 87 (1965) 861866. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/9437 