Homothetic preferences on star-shaped sets
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.
Volume (Year): 24 (2001)
Issue (Month): 1 ()
|Note:||Received: 17 April 2000|
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