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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.

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Bibliographic Info

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

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  1. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  2. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, Econometric Society, vol. 42(5), pages 913-19, September.
  3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  4. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, Econometric Society, vol. 37(4), pages 578-85, October.
  6. 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.
  7. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(1), pages 1-8, October.
  8. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, Econometric Society, vol. 40(5), pages 951-53, September.
  9. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
  10. M. I. Finley, 1958. "Note," Economic History Review, Economic History Society, Economic History Society, vol. 11(1), pages 97-97, 08.
  11. Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 109(2), pages 333-359, April.
  12. 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.
  13. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, Econometric Society, vol. 46(3), pages 557-69, May.
  14. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 38(3), pages 387-92, May.
  15. Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 102(411), pages 357-65, March.
  16. Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer, Springer, vol. 33(3), pages 413-435, December.
  17. Schecter, Stephen, 1979. "On the structure of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 1-5, March.
  18. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, Econometric Society, vol. 44(5), pages 971-78, September.
  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. 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.
  21. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 107(2), pages 573-97, May.
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Citations

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

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