Competitive equilibria in semi-algebraic economies

Felix Kubler, Karl H Schmedders*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)301-330
Number of pages30
JournalJournal of Economic Theory
Volume145
Issue number1
DOIs
StatePublished - Jan 2010

Keywords

  • Equilibrium correspondence
  • Equilibrium multiplicity
  • Gröbner bases
  • Polynomial equations
  • Semi-algebraic preferences

ASJC Scopus subject areas

  • Economics and Econometrics

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