Strictly monotonic preferences on continuum of goods commodity spaces

Carlos Hervés-Beloso and Paulo Monteiro

Journal of Mathematical Economics, 2010, vol. 46, issue 5, 725-727

Abstract: We 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.

Keywords: Utility; representation; Strictly; monotonic; preferences (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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