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Equilibria for Pure Exchange Infinite Economies in the Sense of Incomplete Preference

Author

Listed:
  • Jinqing Zhang

    (Institute for Financial Studies, Fudan University
    Department of Applied Mathematics, Shandong Finance Institute)

Abstract

In this paper, we introduce a new concept of incomplete preference and cover the known ordering relations such preferences as in economics and semiorder in mathematics. In the sense of the incomplete preference, we obtain a principle of maximal consumption allocations, by which, for a pure exchange economy with infinitely many commodities and infinitely countable agents, we first prove the existence of a quasi-equilibrium, and then conclude that such a quasi-equilibrium can be extended to a general equilibrium of this economy if incomplete preferences are proper in a suitable way.

Suggested Citation

  • Jinqing Zhang, 2003. "Equilibria for Pure Exchange Infinite Economies in the Sense of Incomplete Preference," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 359-373, November.
  • Handle: RePEc:cuf:journl:y:2003:v:4:i:2:p:359-373
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    References listed on IDEAS

    as
    1. Monteiro, Paulo Klinger, 1996. "A new proof of the existence of equilibrium in incomplete market economies," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 85-101.
    2. Jones, Larry E., 1983. "Existence of equilibria with infinitely many consumers and infinitely many commodities : A theorem based on models of commodity differentiation," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 119-138, October.
    3. Richard, Scott F. & Zame, William R., 1986. "Proper preferences and quasi-concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 231-247, June.
    4. 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.
    5. Richard, Scott F. & Srivastava, Sanjay, 1988. "Equilibrium in economies with infinitely many consumers and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 9-21, February.
    6. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
    7. 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.
    8. Fishburn, Peter C, 1991. "Decision Theory: The Next 100 Years?," Economic Journal, Royal Economic Society, vol. 101(404), pages 27-32, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Incomplete preferences; Infinite economies; Maximal consumption allocations; Equilibria;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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