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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. 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.
    3. 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.
    4. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    5. 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.
    6. 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.
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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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