The geometry of arbitrage and the existence of competitive equilibrium
UNSPECIFIED (2002) The geometry of arbitrage and the existence of competitive equilibrium. In: European Workshop on General Equilibrium Theory, UNIV MAASTRICHT, MAASTRICHT, NETHERLANDS, MAY 17-19, 2001. Published in: JOURNAL OF MATHEMATICAL ECONOMICS, 38 (4). pp. 373-391.Full text not available from this repository.
We present the basic geometry of arbitrage, and use this basic geometry to shed new light on the relationships between various no-arbitrage conditions found in the literature. For example, under very mild conditions, we show that the no-arbitrage conditions of Hart [Journal of Economic Theory 9 (1974) 293] and Werner [Econometrica 55 (1987) 1403] 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 equivalent to the stronger condition of no-unbounded-arbitrage due to Page [Journal of Economic theory 41 (1987) 392]-and, in turn, all are equivalent 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. (C) 2002 Published by Elsevier Science B.V.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||H Social Sciences > HC Economic History and Conditions
Q Science > QA Mathematics
H Social Sciences
|Journal or Publication Title:||JOURNAL OF MATHEMATICAL ECONOMICS|
|Publisher:||ELSEVIER SCIENCE SA|
|Number of Pages:||19|
|Page Range:||pp. 373-391|
|Title of Event:||European Workshop on General Equilibrium Theory|
|Location of Event:||UNIV MAASTRICHT, MAASTRICHT, NETHERLANDS|
|Date(s) of Event:||MAY 17-19, 2001|
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