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Vladimir Danilov, Gleb Koshevoy, Frank Page and Myrna Wooders
''Existence of equilibrium with unbounded short sales: a new approach''
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
JEL: C3 - Multiple or Simultaneous Equation Models: General
D5 - General Equilibrium and Disequilibrium: General
Manuscript Received : Oct 10 2012 Manuscript Accepted : Oct 31 2012

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