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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 Nizar Allouch & Monique Florenzano, 2004.
"Edgeworth and Walras equilibria of an arbitragefree exchange economy,"
Economic Theory,
Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353370, January.
 Allouch, N. & Florenzano, M., 2000. "Edgeworth and Walras Equilibria of an ArbitrageFree Exchange Economy," Papiers d'Economie MathÃ©matique et Applications 2000.119, UniversitÃ© PanthÃ©onSorbonne (Paris 1).
 Nizar Allouch, 2000. "Edgeworth and Walras Equilibria of an ArbitrageFree Exchange Economy," Econometric Society World Congress 2000 Contributed Papers 1901, Econometric Society.
 Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitragefree exchange economy," Université Paris1 PanthéonSorbonne (PostPrint and Working Papers) halshs00086096, HAL.
 Stephen Clark, 2004. "A tangent cone analysis of smooth preferences on a topological vector space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 337352, January.
 Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85110, April.
 Robert A. Jarrow & Xing Jin & Dilip B. Madan, 1999. "The Second Fundamental Theorem of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 255273.
 Aliprantis, Charalombos & Burkinshaw, Owen, 1991. "When Is the Core Equivalence Theorem Valid?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 16982, April.
 Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987.
"Edgeworth Equilibria,"
Econometrica,
Econometric Society, vol. 55(5), pages 110937, September.
 Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
 Messaoud Deghdak & Monique Florenzano, 1999.
"Decentralizing Edgeworth equilibria in economies with many commodities,"
Economic Theory,
Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 297310.
 Florenzano, Monique & Deghdak, Messaoud, 1997. "Decentralizing edgeworth equilibria in economies with many commodities," CEPREMAP Working Papers (Couverture Orange) 9721, CEPREMAP.
 Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96121, May.
 Aliprantis, C. D. & D. J. Brown & I. A. Polyrakis & J. Werner, 1996.
"Portfolio Dominance and Optimality in Infinite Security Markets,"
Discussion Paper Serie B
383, University of Bonn, Germany.
 Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347366, October.
 Rabee Tourky, 1997.
"A New Approach to the Lmit Theorem on the Core of an Economy in Vector Lattices,"
Working Papers
1997.03, School of Economics, La Trobe University.
 Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, vol. 78(2), pages 321328, February.
 Valeri M. Marakulin, 2001. "Equilibria in infinite dimensional commodity spaces revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 621633.
 Zame, William R, 1987. "Competitive Equilibria in Production Economies with an InfiniteDimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 10751108, September.
 Back, Kerry, 1988.
"Structure of consumption sets and existence of equilibria in infinitedimensional spaces,"
Journal of Mathematical Economics,
Elsevier, vol. 17(1), pages 8999, February.
 Kerry Back, 1986. "Structure of Consumption Sets and Existence of Equilibria in Infinite Dimensional Spaces," Discussion Papers 633, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
 Rabee Tourky, 1999. "The limit theorem on the core of a production economy in vector lattices with unordered preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 219226.
 Charalambos D. Aliprantis & Rabee Tourky, 2002.
"Markets That Don'T Replicate Any Option,"
Department of Economics  Working Papers Series
832, The University of Melbourne.
 Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443447, August.
 Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Nonmarketed options, nonexistence of equilibria, and nonlinear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345357, February.
 Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465485.
 MasColell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 111, February.
 Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416427, August.
 Richard, Scott F., 1989. "A new approach to production equilibria in vector lattices," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 4156, February.
 Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 7589.
 Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252291, December.
 Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
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