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The Existence of Maximal Elements: Generalized Lexicographic Relations

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  • Jens Leth Hougaard

    (Institute of Economics, University of Copenhagen)

  • Mich Tvede

    (Institute of Economics, University of Copenhagen)

Abstract

In the present paper, the existence of maximal elements for binary relations are studied. Generalized lexicographic relations are introduced, and some results on existence of maximal elements are provided. A simple example shows that economies with "lexicographic consumers" need not have equilibria even though demand functions associated with generalized lexicographic relations may be continuous for positive prices.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 01-05.

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Length: 9 pages
Date of creation: May 2001
Date of revision:
Handle: RePEc:kud:kuiedp:0105

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Keywords: Maximal Elements; Binary Relations; Lexicographic Relations;

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  1. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(3), pages 403-404, June.
  2. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
  3. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
  4. Juan Vicente Llinares Císcar, 1995. "Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1995-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Tian, Guoqiang, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 60(4), pages 949-58, October.
  6. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, Elsevier, vol. 16(2), pages 470-474, December.
  7. Colman, Andrew M. & Stirk, Jonathan A., 1999. "Singleton bias and lexicographic preferences among equally valued alternatives," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 40(4), pages 337-351, December.
  8. Michael Lockwood, 1999. "Preference Structures, Property Rights, and Paired Comparisons," Environmental & Resource Economics, European Association of Environmental and Resource Economists, European Association of Environmental and Resource Economists, vol. 13(1), pages 107-122, January.
  9. Fishburn, Peter C, 1975. "Axioms for Lexicographic Preferences," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(3), pages 415-19, July.
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Cited by:
  1. Knoblauch, Vicki, 2005. "Continuous lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 812-825, November.

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