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Linear And Non-Linear Price Decentralization

  • CHARALAMBOS D. APLIPRANTIS
  • MONIQUE FLORENZANO
  • RABEE TOURKY

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 w-proper economies, these assumptions are both sufficient and necessary for the existence of equilibrium, the second welfare theorem, and the Edgeworth-Walras 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 super-order 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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Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 867.

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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
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  1. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer, vol. 23(2), pages 353-370, January.
  2. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
  3. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
  4. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
  5. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  6. 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 321-328, February.
  7. Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
    • Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  8. Richard, Scott F., 1989. "A new approach to production equilibria in vector lattices," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 41-56, February.
  9. Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443-447, August.
  10. Rabee Tourky, 1999. "The limit theorem on the core of a production economy in vector lattices with unordered preferences," Economic Theory, Springer, vol. 14(1), pages 219-226.
  11. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
  12. 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.
  13. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer, vol. 14(2), pages 297-310.
  14. Mas-Colell, 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 1-11, February.
  15. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96-121, May.
  16. Robert A. Jarrow & Xing Jin & Dilip B. Madan, 1999. "The Second Fundamental Theorem of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 255-273.
  17. Aliprantis, Charalombos & Burkinshaw, Owen, 1991. "When Is the Core Equivalence Theorem Valid?," Economic Theory, Springer, vol. 1(2), pages 169-82, April.
  18. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
  19. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
  20. Stephen Clark, 2004. "A tangent cone analysis of smooth preferences on a topological vector space," Economic Theory, Springer, vol. 23(2), pages 337-352, January.
  21. Valeri M. Marakulin, 2001. "Equilibria in infinite dimensional commodity spaces revisited," Economic Theory, Springer, vol. 18(3), pages 621-633.
  22. Back, Kerry, 1988. "Structure of consumption sets and existence of equilibria in infinite-dimensional spaces," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 89-99, February.
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