Cores and Prices in an Exchange Economy with an Atomless Sector

The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: "big" traders, represented by atoms of the measure space, and "small" traders, represented by the atomless part of the measure space. The restriction of an allocation to the...

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Bibliographic Details
Published inEconometrica Vol. 40; no. 6; pp. 1091 - 1108
Main Authors Drèze, J., Gabszewicz, J. J., Schmeidler, D., Vind, K.
Format Journal Article
LanguageEnglish
Published Menasha, Wis The Econometric Society 01.11.1972
George Banta Pub. Co. for the Econometric Society
Blackwell Publishing Ltd
Subjects
Atoms
Budget allocation
Commodities
Competition
Economic competition
Economic policy
Economic theory
Equivalence relation
Hyperplanes
Mathematical functions
Mathematical models
Mathematical theorems
Preferences
Price vector
Prices
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Summary:The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: "big" traders, represented by atoms of the measure space, and "small" traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every "small" trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless, coalition, or by the complement of any atomless coalition, and call it the @?"2-core. The main results of the paper consist in defining sufficient conditions under which allocations in the @?"2-core have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.
ISSN:0012-9682
1468-0262
DOI:10.2307/1913857