Strictly monotonic preferences on continuum of goods commodity spaces
AbstractWe consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K is finite or countable. However, it is not easy for spaces like l[infinity]([0,1]), the space of bounded functions on the unit interval. In this note we investigate the roots of this difficulty. We show that strictly monotonic preferences always exist. However, if K is uncountable no such preference on l[infinity](K) is continuous and none of them have a utility representation.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 5 (September)
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Web page: http://www.elsevier.com/locate/jmateco
Utility representation Strictly monotonic preferences;
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