A new approach to the uniqueness of equilibrium with CRRA preferences

• 成果类型: Article
• 署名作者: Won, Dong Chul
• 署名单位: Ajou University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2023.105607
• 发表日期: 2023
• 关键词: Unique equilibrium; Constant relative risk aversion; Higher-order price effect; Quasi-convex demand; Law of demand

摘要

This paper investigates the uniqueness of equilibrium in the economy where agents have preferences with possibly distinct levels of relative risk aversion. Equilibrium prices exist in a price range determined by micro and macroeconomic information. Macroeconomic information is inferred from two representativeagent economies, which provide lower and upper bounds on aggregate demand, respectively. Analysis of the first and second-order price effects shows that individual demand has a unique inflection point at which the income effect maximally dominates the substitution effect. In contrast, aggregate demand may have multiple inflection points, which creates multiple equilibria. Sufficient conditions for the uniqueness of equilibrium are characterized by the local behavior of individual demand at the inflection point. They require that aggregate demand must have no more than two inflection points in the equilibrium price range. The result of this paper sheds light on the Sonnenschein-Mantel-Debreu theory that has negative implications for the uniqueness of equilibrium. (c) 2023 Elsevier Inc. All rights reserved.