Existence of equilibrium with unbounded short sales: A new approach
AbstractWe 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).
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 37778.
Date of creation: 2011
Date of revision: Mar 2012
arbitrage; unbounded short sales; asset market models; sum of weakly preferred sets; existence of equilibrium;
Other versions of this item:
- Vladimir Danilov & Gleb Koshevoy & Frank Page & Myrna Wooders, 2012. "Existence of equilibrium with unbounded short sales: a new approach," Vanderbilt University Department of Economics Working Papers vuecon-sub-12-00002, Vanderbilt University Department of Economics.
- D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
- D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
- D40 - Microeconomics - - Market Structure and Pricing - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-10 (All new papers)
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