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|
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/10203/index.htm |
|Order Information:||Web: http://link.springer.de/orders.htm|
When requesting a correction, please mention this item's handle: RePEc:spr:decfin:v:24:y:2001:i:1:p:41-47. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.