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Production equilibria

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  • Aliprantis, Charalambos D.
  • Florenzano, Monique
  • Tourky, Rabee

Abstract

This paper studies production economies in a commodity space that is an ordered locally convex space. We establish a general theorem on the existence of equilibrium without requiring that the commodity space or its dual be a vector lattice. Such commodity spaces arise in models of portfolio trading where the absence of some option usually means the absence of a vector lattice structure. The conditions on preferences and production sets are at least as general as those imposed in the literature dealing with vector lattice commodity spaces. The main assumption on the order structure is that the Riesz-Kantorovich functionals satisfy a uniform properness condition that can be formulated in terms of a duality property that is readily checked. This condition is satisfied in a vector lattice commodity space but there are many examples of other commodity spaces that satisfy the condition, which are not vector lattices, have no order unit, and do not have either the decomposition property or its approximate versions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 42 (2006)
Issue (Month): 4-5 (August)
Pages: 406-421

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Handle: RePEc:eee:mateco:v:42:y:2006:i:4-5:p:406-421

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
  2. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer, Springer, vol. 23(2), pages 353-370, January.
  3. 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.
  4. 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.
  5. Charalambos Aliprantis & Monique Florenzano & Victor-Filipe Martins-Da-Rocha & Rabee Tourky, 2004. "Equilibrium analysis in financial markets with countably many securities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086810, HAL.
  6. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2005. "Linear and non-linear price decentralization," Journal of Economic Theory, Elsevier, vol. 121(1), pages 51-74, March.
  7. Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614, 9.
  8. Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "General equilibrium analysis in ordered topological vector spaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086791, HAL.
  9. 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.
  10. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
  11. Rabee Tourky, 1999. "The limit theorem on the core of a production economy in vector lattices with unordered preferences," Economic Theory, Springer, Springer, vol. 14(1), pages 219-226.
  12. Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 756R, Cowles Foundation for Research in Economics, Yale University.
  13. 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.
  14. repec:ltr:wpaper:1997.03 is not listed on IDEAS
  15. 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.
  16. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, Econometric Society, vol. 55(5), pages 1075-1108, September.
  17. 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.
  18. C. D. Aliprantis & D. Brown & J. Werner, 1999. "Minimum-Cost Portfolio Insurance," Discussion Paper Serie A 599, University of Bonn, Germany.
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Citations

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Cited by:
  1. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
  2. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  3. Khan, M. Ali Khan, 2007. "Perfect Competition," MPRA Paper 2202, University Library of Munich, Germany.
  4. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b04116, Université Panthéon-Sorbonne (Paris 1).

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