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Homothetic preferences on star-shaped sets

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  • Fabio Maccheroni

Abstract

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.

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Bibliographic Info

Article provided by Springer in its journal Decisions in Economics and Finance.

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

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Handle: RePEc:spr:decfin:v:24:y:2001:i:1:p:41-47

Note: Received: 17 April 2000
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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. Osterdal, Lars Peter, 2005. "Axioms for health care resource allocation," Journal of Health Economics, Elsevier, vol. 24(4), pages 679-702, July.
  3. 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.

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