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Homothetic preferences on star-shaped sets

Listed author(s):
  • Fabio Maccheroni
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    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

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    Article provided by Springer & Associazione per la Matematica in its journal Decisions in Economics and Finance.

    Volume (Year): 24 (2001)
    Issue (Month): 1 (05)
    Pages: 41-47

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    Handle: RePEc:spr:decfin:v:24:y:2001:i:1:p:41-47
    DOI: 10.1007/s102030170008
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