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General equilibrium without utility functions: how far to go?

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  • Yves Balasko

    ()

  • Mich Tvede

    ()

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.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 45 (2010)
Issue (Month): 1 (October)
Pages: 201-225

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Handle: RePEc:spr:joecth:v:45:y:2010:i:1:p:201-225

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Related research

Keywords: General equilibrium; Non-ordered preferences; Equilibrium manifold; Natural projection; Demand functions; C62; D11; D51;

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References

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  1. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP -67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  3. Balasko, Yves, 1975. "Some results on uniqueness and on stability of equilibrium in general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 95-118.
  4. Smale, S., 1974. "Global analysis and economics III : Pareto Optima and price equilibria," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 107-117, August.
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  6. SCHMEIDLER, David, . "Competitive equilibria in markets with a continuum of traders and incomplete preferences," CORE Discussion Papers RP -62, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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 971-78, September.
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  12. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  13. M. I. Finley, 1958. "Note," Economic History Review, Economic History Society, vol. 11(1), pages 97-97, 08.
  14. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
  15. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
  16. Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-65, March.
  17. Schecter, Stephen, 1979. "On the structure of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 1-5, March.
  18. Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer, vol. 33(3), pages 413-435, December.
  19. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
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  21. Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, vol. 109(2), pages 333-359, April.
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Citations

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Cited by:
  1. Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer, vol. 54(3), pages 463-484, November.
  2. Lutz Arnold, 2013. "Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition," Economic Theory, Springer, vol. 52(1), pages 237-270, January.
  3. A. Mantovi, 2014. "On luxury and equilibrium," Economics Department Working Papers 2014-EP02, Department of Economics, Parma University (Italy).

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