Existence of equilibrium with unbounded short sales: a new approach

Vladimir Danilov (), Gleb Frank (), Frank Page and Myrna Wooders
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Gleb Frank: Central Economics and Mathematics Institute, Russian Academy of Sciences

No 12-00002, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

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: C3 D5 (search for similar items in EconPapers)
Date: 2012-12-03
New Economics Papers: this item is included in nep-mic and nep-upt
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Working Paper: Existence of equilibrium with unbounded short sales: A new approach (2012)
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