Markets with many more agents than commodities: Aumann's hidden assumption

• 成果类型: Article
• 署名作者: Tourky, R; Yannelis, NC
• 署名单位: University of Melbourne; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2000.2705
• 发表日期: 2001
• 页码: 189-221

摘要

We address a question posed by J.-F. Mertens and show that, indeed, R. J. Aumann's classical existence and equivalence theorems depend on there being many more agents than commodities. We show that for an arbitrary atomless measure space of agents there is a fixed non-separable infinite dimensional commodity space in which one can construct an economy that satisfies all the standard assumptions but which has no equilibrium, a core allocation that is not Walrasian, and a Pareto efficient allocation that is not a valuation equilibrium. We identify the source of the failure as the requirement that allocations be strongly measurable. Our main example is set in a commodity-measure space pair that displays an acute scarcity of strongly measurable allocations - where strong measurability necessitates that consumer choices be closely correlated no matter the prevailing prices, This makes the core large since there may not be any strongly measurable improvements even though there are many weakly measurable strict improvements. Moreover, at some prices the aggregate demand correspondence is empty since disaggregated demand has no strongly measurable selections, though it does have weakly measurable selections. We note that our example can be constructed in any vector space whose dimension is greater than the cardinality of the continuum-that is, whenever there are at least as many Commodities as agents. We also prove a positive core equivalence result for economics in non-separable commodity spaces. (C) 2001 Academic Press.