Homothetic preferences on star-shaped sets

Fabio Maccheroni

Decisions in Economics and Finance, 2001, vol. 24, issue 1, 47 pages

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. Copyright Springer-Verlag Italia 2001

Keywords: Mathematics Subject Classification (2000): 91B06; 91B16; 06A05; 06F99; Journal of Economic Literature Classification: D11; D81; C69 (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/s102030170008

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