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 Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number vuecon-sub-12-00002.
Date of creation: 03 Dec 2012
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arbitrage; unbounded short sales; asset market models; sum of weakly preferred sets; existence of equilibrium;
Other versions of this item:
- Danilov, Vladimir & Koshovoy, Gleb & Page, Frank & Wooders, Myrna, 2011. "Existence of equilibrium with unbounded short sales: A new approach," MPRA Paper 37778, University Library of Munich, Germany, revised Mar 2012.
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
- D5 - Microeconomics - - General Equilibrium and Disequilibrium
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-02-03 (All new papers)
- NEP-MIC-2013-02-03 (Microeconomics)
- NEP-UPT-2013-02-03 (Utility Models & Prospect Theory)
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