Competitive equilibria in semi-algebraic economies
This paper develops a method to compute the equilibrium correspondence for exchange economies with semi-algebraic preferences. Given a class of semi-algebraic exchange economies parameterized by individual endowments and possibly other exogenous variables such as preference parameters or asset payoffs, there exists a semi-algebraic correspondence that maps parameters to positive numbers such that for generic parameters each competitive equilibrium can be associated with an element of the correspondence and each endogenous variable (i.e. prices and consumptions) is a rational function of that value of the correspondence and the parameters. This correspondence can be characterized as zeros of a univariate polynomial equation that satisfy additional polynomial inequalities. This polynomial as well as the rational functions that determine equilibrium can be computed using versions of Buchberger's algorithm which is part of most computer algebra systems. The computation is exact whenever the input data (i.e. preference parameters etc.) are rational. Therefore, the result provides theoretical foundations for a systematic analysis of multiplicity in applied general equilibrium.
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- Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 1-27.
- Kubler, Felix & Schmedders, Karl, 2000. "Computing Equilibria in Stochastic Finance Economies," Computational Economics, Springer;Society for Computational Economics, vol. 15(1-2), pages 145-172, April.
- Brown, Donald J & Matzkin, Rosa L, 1996.
"Testable Restrictions on the Equilibrium Manifold,"
Econometric Society, vol. 64(6), pages 1249-1262, November.
- Mas-Colell,Andreu, 1990.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521388702, May.
- Herings P. Jean-Jacques & Kubler Felix, 2000.
"Computing Equilibria in Finance Economies,"
010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- P.J.J. Herings & F. Kubler, 2001. "Computing Equilibria in Finance Economies," GE, Growth, Math methods 0205003, EconWPA.
- Herings P. Jean-Jacques & Kubler Felix, 2002. "Computing Equilibria in Finance Economies," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Lawrence E. Blume & William R. Zame, 1993.
"The Algebraic Geometry of Perfect and Sequential Equilibrium,"
Game Theory and Information
- Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
- David Cass, 2006.
"Musings on the Cass Trick,"
PIER Working Paper Archive
06-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Felix Kubler, 2007. "Approximate Generalizations and Computational Experiments," Econometrica, Econometric Society, vol. 75(4), pages 967-992, 07.
- Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
- Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
- Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
- Gjerstad, S., 1996. "Multiple Equilibria in Exchange Economies with Homothetic, Nearly Identical Preferences," Papers 288, Minnesota - Center for Economic Research.
- Anderson, Robert M. & Raimondo, Roberto C., 2007. "Incomplete markets with no Hart points," Theoretical Economics, Econometric Society, vol. 2(2), June.
- Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
- Balasko, Yves, 1979. "Economies with a finite but large number of equilibria," Journal of Mathematical Economics, Elsevier, vol. 6(2), pages 145-147, July.
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