General Equilibrium without Utility Functions: How far to go?
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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- Debreu, Gerard, 1972.
Econometric Society, vol. 40(4), pages 603-15, July.
- 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.
- Yves Balasko, 2007. "Out-of-equilibrium price dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 413-435, December.
- Jean-Marc Bonnisseau, 2003.
"Regular economies with non-ordered preferences,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
- Schmeidler, David, 1969.
"Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences,"
Econometric Society, vol. 37(4), pages 578-85, October.
- 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).
- Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
- George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
- 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.
- 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.
- 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).
- Schecter, Stephen, 1979. "On the structure of the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 1-5, March.
- Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-69, May.
- 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.
- Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-65, 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.
- Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
- Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, vol. 109(2), pages 333-359, April.
- 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.
- M. I. Finley, 1958. "Note," Economic History Review, Economic History Society, vol. 11(1), pages 97-97, 08.
- Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
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