Edgeworth's Conjecture with Infinitely Many Commodities
AbstractEquivalence of the core and the set of Walrasian allocations has long been taken as one of the basic tests of perfect competition. The present paper examines this basic test of perfect competition in economies with an infinite dimensional space of commodities and a large finite number of agents. In this context we cannot expect equality of the core and the set of Walrasian allocations; rather, as in the finite dimensional context, we look for theorems establishing core convergence (that is, approximate decentralization of core allocations in economies with a large finite number of agents). Previous work in this area has established that core convergence for replica economies and core equivalence for economies with a continuum of agents continue to be valid under assumptions much the same as those usual in the finite dimensional context. For general large finite economies, however, we present here a sequence of examples of the failure of core convergence. These examples point to a serious disconnection between replica economies and continuum economies on the one hand an general large finite economies on the other hand. We identify the source of this disconnection as the measurability requirements that are implicit in the continuum model, and which correspond to compactness requirements that have especially serious economic content in the infinite dimensional context. We also obtain positive results. When the commodity space is a Riesz space, we show that familiar assumptions lead to a kind of local core convergence; strong assumptions lead to global core convergence. In the differentiated commodities context, we obtain core convergence results that are quite parallel to known equivalence results for continuum economies. Our positive results depend on infinite dimensional versions of the Shapley-Folkman theorem.
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Bibliographic InfoPaper provided by University of California at Berkeley in its series Economics Working Papers with number 95-235.
Date of creation: 01 May 1995
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Postal: University of California at Berkeley, Berkeley, CA USA
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- Anderson, Robert M. & Zame, William R., 1995. "Edgeworth's Conjecture with Infinitely Many Commodities," Department of Economics, Working Paper Series qt5kb2x3cd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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- Roberto Serrano & Rajiv Vohra & Oscar Volij, 2001.
"On the Failure of Core Convergence in Economies with Asymmetric Information,"
Econometric Society, vol. 69(6), pages 1685-1696, November.
- Roberto Serrano & Rajiv Vohra & Oscar Volij, 2000. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometric Society World Congress 2000 Contributed Papers 0141, Econometric Society.
- Roberto Serrano & Rajiv Vohra & Oscar Volij, 1999. "On the Failure of Core Convergence in Economies with Asymmetric Information," Economic theory and game theory 011, Oscar Volij.
- Roberto Serrano & Rajiv Vohra & Oscar Volij, 1999. "On the Failure of Core Convergence in Economies with Asymmetric Information," Working Papers 99-22, Brown University, Department of Economics.
- Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer, vol. 19(1), pages 113-185, March.
- M. Ali Khan & Kali P. Rath, 2011. "The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment," Economics Working Paper Archive 586, The Johns Hopkins University,Department of Economics.
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