Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production technologies

• 成果类型: Article
• 署名作者: van der Laan, G; Talman, D; Yang, ZF
• 署名单位: Vrije Universiteit Amsterdam; Vrije Universiteit Amsterdam; Tinbergen Institute; Tilburg University; Yokohama National University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2000.2758
• 发表日期: 2002
• 页码: 411-428
• 关键词: indivisible commodities; divisible commodities; linear production; competitive equilibrium; equilibrium theorem; welfare theorem

摘要

In this paper we consider a class of economies with a Finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a no production without input -like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the First theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. (C) 2001 Elsevier Science (USA).