Existence of equilibrium with unbounded short sales: A new approach

Vladimir Danilov (), Gleb Koshovoy, Frank Page and Myrna Wooders

MPRA Paper from University Library of Munich, Germany

Abstract: We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange economies, all papers known to us stating conditions for existence of equilibrium with unbounded short sales place conditions on recession cones of agents' preferred sets or, more recently, require compactness of the utility possibilities set.. In contrast, in this paper, we place conditions on the preferred sets themselves. Roughly, our condition is that the sum of the weakly preferred sets is a closed set. We demonstrate that our condition implies existence of equilibrium. In addition to our main theorem, we present two theorems showing cases to which our main theorem can we applied. We also relate our condition to the classic condition of Hart (1974).

Keywords: arbitrage; unbounded short sales; asset market models; sum of weakly preferred sets; existence of equilibrium (search for similar items in EconPapers)
JEL-codes: D40 D50 D53 (search for similar items in EconPapers)
Date: 2011, Revised 2012-03
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Related works:
Working Paper: Existence of equilibrium with unbounded short sales: a new approach (2012)
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