On the number of critical equilibria separating two equilibria

• 成果类型: Article
• 署名作者: Balasko, Yves
• 署名单位: University of York - UK
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1555-7561
• DOI: 10.3982/TE822
• 发表日期: 2012-01-01
• 页码: 163-181
• 关键词: Equilibrium prices; equilibrium manifold; equilibrium path; critical equilibrium; catastrophe; D41; D51

摘要

It is shown that two arbitrary equilibria in the general equilibrium model without sign restrictions on endowments can be joined by a continuous equilibrium path that contains at most two critical equilibria. This property is strengthened by showing that regular equilibria having an index equal to 1, a necessary condition for stability, can be joined by a path containing no critical equilibrium. These properties follow from the real-algebraic nature of the set of critical equilibria in any fiber of the equilibrium manifold.