Competitive equilibria in semi-algebraic economies

• 成果类型: Article
• 署名作者: Kubler, Felix; Schmedders, Karl
• 署名单位: University of Zurich; University of Zurich
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.10.004
• 发表日期: 2010
• 页码: 301-330
• 关键词: Semi-algebraic preferences; Equilibrium correspondence; Polynomial equations; Grobner bases; Equilibrium multiplicity

摘要

This paper develops a method to compute the equilibrium correspondence for exchange economics 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. (C) 2009 Elsevier Inc. All rights reserved.