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Pareto Optimality and Existence of Quasi-Equilibrium in Exchange Economies with an Indefinite Future

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JournalJournal of Mathematical Economics
DateAccepted/In press - 16 Sep 2016
DateE-pub ahead of print - 11 Oct 2016
DatePublished (current) - 1 Dec 2016
Volume67
Number of pages15
Pages (from-to)138-152
Early online date11/10/16
Original languageEnglish

Abstract

We study the attainability of Pareto optimal allocations and existence of quasi-equilibrium in exchange economies where agents have utility functions that value consumption in an indefinite future. These utility functions allow for fairly general discounting of consumption over finite time horizons, but add a utility weight to the bulk of the consumption sequence, which we identify with the indefinite future. As our commodity space we use the space of all convergent sequences with the limit of the sequence representing consumption in the indefinite future. We derive a necessary and sufficient condition for the attainability of the Pareto optimal allocations. This condition implies that efficiency can only be attained if consumers’ valuations of time are very similar. Our proof relies on the existence of an interior solution to certain infinite dimensional optimization problems. If the condition is not met, no interior quasi-equilibria exist. We extend the model to include consumers with Rawlsian-like maximin utility.

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© 2016 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

    Research areas

  • Infinite horizon exchange economy, Non-discounting preferences, Pareto optimality

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