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Production Equilibria in Vector Lattices

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  • Monique Florenzano

    (Universite Paris 1)

  • Valeri Marakulin

    (Russian Academy of Sciences)

Abstract

The general purpose of this paper is to prove quasiequilibrium existence theorems for production economies with general consumption sets in an infinite dimensional commodity space, without assuming any monotonicity of preferences or free-disposal in production. The commodity space is a vector lattice commodity space whose topological dual is a sublattice of its order dual. We formulate two kinds of properness concepts for agents' preferences and production sets, which reduce to more classical ones when the commodity space is locally convex and the consumption sets coincide with the positive cone. Assuming properness allows for extension theorems of quasiequilibrium prices obtained for the economy restricted to some order ideal of the commodity space. As an application, the existence of quasiequilibrium in the whole economy is proved without any assumption of monotonicity of preferences or free-disposal in production.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1396.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1396

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  1. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
  2. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  3. repec:ltr:wpaper:1997.01 is not listed on IDEAS
  4. Aliprantis, C.D. & R. & Tourky & Yannelis, N.C., 1998. "A Theory of Value With Auction Prices," Department of Economics - Working Papers Series 670, The University of Melbourne.
  5. repec:ltr:wpaper:1997.03 is not listed on IDEAS
  6. Larry E. Jones, 1982. "A Competitive Model of Commodity Differentiation," Discussion Papers 526, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer, vol. 14(2), pages 297-310.
  8. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
  9. Marakulin, Valeri M., 1998. "Production equilibria in vector lattices with unordered preferences : an approach using finite-dimensional approximations," CEPREMAP Working Papers (Couverture Orange) 9821, CEPREMAP.
  10. Darrell Duffie & William Zame, 1988. "The Consumption-Based Capital Asset Pricing Model," Discussion Papers 88-10, University of Copenhagen. Department of Economics.
  11. 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.
  12. Boyd, John H, III & McKenzie, Lionel W, 1993. "The Existence of Competitive Equilibrium over an Infinite Horizon with Production and General Consumption Sets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 1-20, February.
  13. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
  14. Aliprantis, Charalambos D. & Brown, D. J., 1982. "Equilibrium in Markets with a Riesz Space of Commodities," Working Papers 427, California Institute of Technology, Division of the Humanities and Social Sciences.
  15. Aliprantis, C. D. & Tourky, R. & Yannelis, N. C., 2000. "The Riesz-Kantorovich formula and general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 55-76, August.
  16. 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.
  17. Tourky, Rabee, 1999. "Production equilibria in locally proper economies with unbounded and unordered consumers," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 303-315, November.
  18. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  19. 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.
  20. 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.
  21. 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.
  22. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-53, September.
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Cited by:
  1. Allouch, N. & Florenzano, M., 2000. "Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy," Papiers d'Economie Mathématique et Applications 2000.119, Université Panthéon-Sorbonne (Paris 1).
  2. Marakulin, V., 2011. "Contracts and Domination in Competitive Economies," Journal of the New Economic Association, New Economic Association, issue 9, pages 10-32.
  3. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
  4. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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