Linear And NonLinear Price Decentralization
The present paper provides compendious and thorough solutions to the price equilibrium existence problem, the second welfare theorem, and the limit theorem on the core of an economy for exchange economies whose commodity space is an arbitrary ordered Frechet space. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory commodity spaces that are not vector lattice ordered and whose positive cones have empty interior, a typical situation in models of portfolio trading with incomplete markets. Our assumptions are made on the primitive objects fo the economy. Remarkably, the assumptions that we make on the order structure of the commodity space are indispensable. For wproper economies, these assumptions are both sufficient and necessary for the existence of equilibrium, the second welfare theorem, and the EdgeworthWalras equivalence theorem. We take advantage of new developments in the theory of ordered vector spaces, in particular the possibility of embedding the price cone into a lattice cone called the superorder dual of the ordered vector space. Therefore, even though the commodity price duality has no lattice structure important lattice theoretic techniques can be applied outside this duality.
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Length:  22 pages 
Date of creation:  2003 
Date of revision:  
Handle:  RePEc:mlb:wpaper:867 
Contact details of provider:  Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia Phone: +61 3 8344 5355 Fax: +61 3 8344 6899 Web page: http://fbe.unimelb.edu.au/economics Email: More information through EDIRC

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