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Arbitrage and equilibrium in unbounded exchange economies with satiation

Nizar Allouch, Cuong Le Van () and Frank H. Page
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Cuong Le Van: CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Frank H. Page: UA - University of Alabama [Tuscaloosa]

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Abstract: In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations.Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents' preferences are satiated, the absence of arbitrage is suffcient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades - that is, as long as agents' preferences satisfy weaknonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation - a condition considerably weaker than local or global nonsatiation - that makes possible this transformation.

Keywords: Arbitrage; Asset Market Equilibrium; Nonsatiation; Recession Cones.; Recession Cones (search for similar items in EconPapers)
Date: 2006-09
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00096040
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Published in Journal of Mathematical Economics, Elsevier, 2006, 42 (06), pp.661-674. ⟨10.1016/j.jmateco.2006.03.001⟩

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Journal Article: Arbitrage and equilibrium in unbounded exchange economies with satiation (2006) Downloads
Working Paper: Arbitrage and equilibrium in unbounded exchange economies with satiation (2006) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00096040

DOI: 10.1016/j.jmateco.2006.03.001

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