Page Jr., Frank H., Wooders, Myrna H. and Monteiro, Paulo K (2000) Inconsequential arbitrage. In: 1998 Econometric-Society Winter Meeting, Chicago, Illinois, Jan 1998. Published in: Journal of Mathematical Economics, 34 (4). pp. 439-469. ISSN 0304-4068.

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Abstract

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, prove that inconsequential arbitrage is sufficient for existence of equilibrium. Moreover, with a slightly stronger condition of nonsatiation than that required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that inconsequential arbitrage, the existence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal - for example, when local nonsatiation holds - inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales.

Finally, we compare inconsequential arbitrage to the conditions limiting arbitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293-311], Werner [Werner, J., 1987. Econometrica 55, abs 1403-1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, E, 1999. J. Econ. Theory 87, 169-193] and Allouch [Allouch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de Paris I]. For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold. (C) 2000 Elsevier Science S.A. All rights reserved.

Item Type:	Conference Item (Paper)
Subjects:	H Social Sciences > HC Economic History and Conditions Q Science > QA Mathematics H Social Sciences
Divisions:	Faculty of Social Sciences > Economics
Journal or Publication Title:	Journal of Mathematical Economics
Publisher:	Elsevier
ISSN:	0304-4068
Official Date:	December 2000
Dates:	Date Event December 2000 UNSPECIFIED
Volume:	34
Number:	4
Number of Pages:	31
Page Range:	pp. 439-469
Status:	Peer Reviewed
Publication Status:	Published
Conference Paper Type:	Paper
Title of Event:	1998 Econometric-Society Winter Meeting
Type of Event:	Other
Location of Event:	Chicago, Illinois
Date(s) of Event:	Jan 1998

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