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 consumersâ preferences. We show in this paper that if consumersâ 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 InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 45 (2010)
Issue (Month): 1 (October)
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Web page: http://link.springer.de/link/service/journals/00199/index.htm
Other versions of this item:
- Yves Balasko & Mich Tvede, 2009. "General Equilibrium without Utility Functions: How far to go?," Discussion Papers 09-17, University of Copenhagen. Department of Economics.
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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).
- 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.
- 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.
- 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.
- Wayne Shafer & Hugo Sonnenschein, 1974.
"Equilibrium in Abstract Economies Without Ordered Preferences,"
94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
- 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).
- 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.
- 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.
- 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.
- Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
- Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-69, May.
- Debreu, Gerard, 1972.
Econometric Society, vol. 40(4), pages 603-15, July.
- Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
- M. I. Finley, 1958. "Note," Economic History Review, Economic History Society, vol. 11(1), pages 97-97, 08.
- Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
- Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
- Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-65, March.
- Schecter, Stephen, 1979. "On the structure of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 1-5, March.
- Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer, vol. 33(3), pages 413-435, December.
- Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
- 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.
- Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, vol. 109(2), pages 333-359, April.
- Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer, vol. 54(3), pages 463-484, November.
- 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.
- A. Mantovi, 2014. "On luxury and equilibrium," Economics Department Working Papers 2014-EP02, Department of Economics, Parma University (Italy).
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