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Partially upper continuous preferences: Representation and maximal elements

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  • Nosratabadi, Hassan

Abstract

This paper generalizes two theorems in Campbell and Walker (1990), which is based on weak upper continuity. A new property, called partial upper continuity, is shown to be sufficient for representation and existence of a maximal element. Noting that transfer weak upper continuity (Tian and Zhou, 1995) characterizes the existence of a maximal element, we show it is not strong enough to guarantee representation.

Suggested Citation

  • Nosratabadi, Hassan, 2014. "Partially upper continuous preferences: Representation and maximal elements," Economics Letters, Elsevier, vol. 125(3), pages 408-410.
    • Handle: RePEc:eee:ecolet:v:125:y:2014:i:3:p:408-410
    DOI: 10.1016/j.econlet.2014.10.025
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    References listed on IDEAS

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    1. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    2. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    3. Tian, Guoqiang & Zhou, Jianxin, 1992. "Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets," MPRA Paper 41227, University Library of Munich, Germany.
    4. Jaffray, Jean-Yves, 1975. "Existence of a Continuous Utility Function: An Elementary Proof," Econometrica, Econometric Society, vol. 43(5-6), pages 981-983, Sept.-Nov.
    5. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    6. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
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    Cited by:

    1. Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    2. Gianni Bosi & Magalì E. Zuanon, 2017. "Maximal elements of quasi upper semicontinuous preorders on compact spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-117, April.
    3. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.

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    More about this item

    Keywords

    Representation; Maximal elements; Weak upper continuity; Transfer continuity; Preference relation;
    All these keywords.

    JEL classification:

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

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