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Homothetic preferences on star-shaped sets


  • Fabio Maccheroni


This paper describes properties of homothetic preferences on a subset X of a vector space which is star-shaped with respect to 0 (e.g., a cone). We prove that a preference relation on X is homothetic, greedy and calibrated if and only if there exists a positively homogeneous function that represents it. This function is unique up to a strictly increasing and positively homogeneous transformation. As a corollary, we find that, if X is contained in a topological vector space, then ≽ is homothetic and continuous if and only if there exists a positively homogeneous and continuous function that represents it. Copyright Springer-Verlag Italia 2001

Suggested Citation

  • Fabio Maccheroni, 2001. "Homothetic preferences on star-shaped sets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(1), pages 41-47, May.
  • Handle: RePEc:spr:decfin:v:24:y:2001:i:1:p:41-47 DOI: 10.1007/s102030170008

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    References listed on IDEAS

    1. Gatti, D. Delli & Gallegati, M. & Gardini, L., 1993. "Investment confidence, corporate debt and income fluctuations," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 161-187, October.
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    Cited by:

    1. J. C. R. Alcantud & G. Bosi & C. Rodríguez-Palmero & M. Zuanon, 2003. "The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour," Microeconomics 0308002, EconWPA.
    2. Bosi, Gianni & Zuanon, Magali E., 2003. "Continuous representability of homothetic preorders by means of sublinear order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 333-341, July.
    3. Osterdal, Lars Peter, 2005. "Axioms for health care resource allocation," Journal of Health Economics, Elsevier, vol. 24(4), pages 679-702, July.

    More about this item


    Mathematics Subject Classification (2000): 91B06; 91B16; 06A05; 06F99; Journal of Economic Literature Classification: D11; D81; C69;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other


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