Strictly monotonic preferences on continuum of goods commodity spaces
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.
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- Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.