Competitive Equilibria in Semi-Algebraic Economies

Felix Kuber (kubler@sas.upenn.edu) and Karl Schmedders
Additional contact information
Felix Kuber: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: This paper examines the equilibrium correspondence in Arrow-Debreu exchange economies with semi-algebraic preferences. We show that a generic semi-algebraic exchange economy gives rise to a square system of polynomial equations with finitely many solutions. The competitive equilibria form a subset of the solution set and can be identified by verifying finitely many polynomial inequalities. We apply methods from computational algebraic geometry to obtain an equivalent polynomial system of equations that essentially reduces the computation of all equilibria to finding all roots of a univariate polynomial. This polynomial can be used to determine an upper bound on the number of equilibria and to approximate all equilibria numerically. We illustrate our results and computational method with several examples. In particular, we show that in economies with two commodities and two agents with CES utility, the number of competitive equilibria is never larger than three and that multiplicity of equilibria is rare in that it only occurs for a very small fraction of individual endowments and preference parameters.

Keywords: computable general equilibrium; semi-algebraic economy; Groebner bases (search for similar items in EconPapers)
JEL-codes: C63 D50 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2007-03-22
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://economics.sas.upenn.edu/sites/default/file ... ng-papers/07-013.pdf (application/pdf)

Related works:
Journal Article: Competitive equilibria in semi-algebraic economies (2010)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pen:papers:07-013

Access Statistics for this paper

More papers in PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 133 South 36th Street, Philadelphia, PA 19104. Contact information at EDIRC.
Bibliographic data for series maintained by Administrator (pier@econ.upenn.edu).