Econometrica: Mar 1985, Volume 53, Issue 2
Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience
A. AraujoThe existence of equilibrium and Pareto optimal allocations in economies with an infinite number of commodities is studied. It is shown that any topology stronger than the Mackey topology might lead to the nonexistence of nontrivial Pareto optimal allocations. I.e., there exists a well behaved economy with preferences that are continuous in this topology and without individually rational Pareto optimal allocations. A converse of this theorem, a slight modification of Bewley's  existence of equilibrium theorem, is also proved. Using a characterization of the Mackey topology in terms of impatience of consumers, due to Brown and Lewis , an interpretation of the theorem above is given: a topology is such that continuity with respect to it implies existence of nontrivial Pareto optimal allocations if and only if it also implies impatience on the part of the consumers.
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