Theorems on correspondences and stability of the core |
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Authors: | Farhad Hüsseinov |
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Institution: | (1) Department of Economics, Bilkent University, 06533 Bilkent, Ankara, TURKEY (e-mail: farhad@bilkent.edu.tr) , TR |
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Abstract: | In this note two theorems strengthening Grodal's (1971) Theorem on correspondences are proved. The first drops the convexity
assumption. The second strengthens that theorem further for the case when the range is the positive orthant. In this case,
the conclusion of Grodal's Theorem - the intersection of the integral with the interior of the range being open- is modified
to read as the integral being a relative open subset of the positive orthant. An example is provided to show that, such a
strengthening is not valid in general. This allows us to dispense with the requirment of convexity of preferences in Grodal's
(1971) theorems on the closedness of the set of Pareto optimal allocations, the core, and the continuity of the core correspondence
for pure exchange economies. We apply this result to show that blocking coalitions in a large economy are stable.
Received: September 30, 1998; revised version: September 18, 2001
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ID="*" The author is grateful to an anonymous referee for helpful comments. The usual disclaimer applies. |
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Keywords: | and Phrases: Correpondence Large economy Core Pareto set |
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