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General Equilibrium without Utility Functions: How far to go?

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  • Yves Balasko

    (Department of Economics and Related Studies, University of York)

  • Mich Tvede

    (Department of Economics, University of Copenhagen)

Abstract

How 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.

Suggested Citation

  • Yves Balasko & Mich Tvede, 2009. "General Equilibrium without Utility Functions: How far to go?," Discussion Papers 09-17, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0917
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2009/0917.pdf/
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    References listed on IDEAS

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    11. Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-365, March.
    12. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-978, September.
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    Citations

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    Cited by:

    1. Lutz Arnold, 2013. "Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 237-270, January.
    2. Jacques Dreze, 2016. "Existence and multiplicity of temporary equilibria under nominal price rigidities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 279-298, June.
    3. Andrea Mantovi, 2014. "On Luxury and Equilibrium," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 6(2), pages 87-118, December.
    4. Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 463-484, November.

    More about this item

    Keywords

    general equilibrium; equilibrium manifold; natural projection; demand functions;

    JEL classification:

    • 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

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