General Equilibrium without Utility Functions: How far to go?
AbstractHow far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: 1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; 2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; 3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; 4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; 5) the pathconnectedness of the sets of stable equilibria.
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Bibliographic InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 09-17.
Length: 26 pages
Date of creation: Aug 2009
Date of revision:
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general equilibrium; equilibrium manifold; natural projection; demand functions;
Other versions of this item:
- Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer, vol. 45(1), pages 201-225, October.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-11 (All new papers)
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