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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.

Suggested Citation

  • Jens Leth Hougaard & Mich Tvede, 2001. "The Existence of Maximal Elements: Generalized Lexicographic Relations," Discussion Papers 01-05, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:0105
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2001/0105.pdf/
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    References listed on IDEAS

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    1. 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.
    2. Colman, Andrew M. & Stirk, Jonathan A., 1999. "Singleton bias and lexicographic preferences among equally valued alternatives," Journal of Economic Behavior & Organization, Elsevier, vol. 40(4), pages 337-351, December.
    3. Peter C. Fishburn, 1975. "Axioms for Lexicographic Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 415-419.
    4. Nicholas Georgescu-Roegen, 1954. "Choice, Expectations and Measurability," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 68(4), pages 503-534.
    5. Michael Lockwood, 1999. "Preference Structures, Property Rights, and Paired Comparisons," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 13(1), pages 107-122, January.
    6. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    7. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
    8. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    9. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
    10. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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    Cited by:

    1. Nikolai Hoberg & Stefan Baumgärtner, 2014. "Value pluralism, trade-offs and efficiencies," Working Paper Series in Economics 311, University of Lüneburg, Institute of Economics.
    2. Knoblauch, Vicki, 2005. "Continuous lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 812-825, November.
    3. Mitra, Manipushpak & Sen, Debapriya, 2014. "An alternative proof of Fishburn’s axiomatization of lexicographic preferences," Economics Letters, Elsevier, vol. 124(2), pages 168-170.

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    More about this item

    Keywords

    Maximal Elements; Binary Relations; Lexicographic Relations;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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