Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces
AbstractIt is an easy task for most commodity spaces, to find examples of strictly monotonic preference relations. For example, in the space of bounded sequences of real numbers.. However, it is not easy for spaces like the space of bounded functions defined in the real interval [0, 1]. In this note we investigate the roots of this difficulty. We show that strictly monotonic preferences on the space of bounded function on any set K always exist. However, if K is uncountable no such preference is continuous and none of them have a utility representation.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15157.
Date of creation: 14 Mar 2009
Date of revision:
utility representation/ strictly monotonic preferences;
Find related papers by JEL classification:
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- B50 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - General
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