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General Equilibrium without Utility Functions: How far to go?

  • Yves Balasko

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

  • Mich Tvede

    (Department of Economics, University of Copenhagen)

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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Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 09-17.

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Length: 26 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:kud:kuiedp:0917
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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. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  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. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
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  9. Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer, vol. 33(3), pages 413-435, December.
  10. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
  11. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  12. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
  13. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  14. Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-65, March.
  15. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October.
  16. Schecter, Stephen, 1979. "On the structure of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 1-5, March.
  17. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
  18. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
  19. 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.
  20. 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.
  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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