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The geometry of arbitrage and the existence of competitive equilibrium

Nizar Allouch, Cuong Le van () and Frank Page

The Warwick Economics Research Paper Series (TWERPS) from University of Warwick, Department of Economics

Abstract: We present the basic geometry of arbitrage and use this basic geometry to shed new light on the relationships between various noarbitrage conditions found in the literature. For example, under very mild conditions of Hart (1974) and Werner (1987) are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents' sets of useless net trades are linearly independent, then the Hart-Werner conditions are equilivent to the stronger condition of no-unbounded-arbitrage due to Page (1987) - and, in turn, all are equilivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner's uniformity condition, the Hart-Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no half lines - a condition weaker than Werner's no-half lines condition - we show that the Hart-Werner conditions are both necessary and sufficient for existence.

Keywords: ARBITRAGE; COMPETITIVE EQUILIBRIUM; RECESSION CONES (search for similar items in EconPapers)
JEL-codes: C62 D50 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2001
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Journal Article: The geometry of arbitrage and the existence of competitive equilibrium (2002) Downloads
Working Paper: The Geometry of Arbitrage and the Existence of Competitive Equilibrium (2001) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:wrk:warwec:598

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