Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces
Abstract
It 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.Download Info
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15157.Length:
Date of creation: 14 Mar 2009
Date of revision:
Handle: RePEc:pra:mprapa:15157
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Related research
Keywords: 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-05-16 (All new papers)
- NEP-UPT-2009-05-16 (Utility Models & Prospect Theory)
References
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- Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
- Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Covarrubias, Enrique, 2008.
"The number of equilibria of smooth infinite economies with separable utilities,"
MPRA Paper
11099, University Library of Munich, Germany.
- Enrique Covarrubias, 2011. "The Number of Equilibria of Smooth Infinite Economies," Working Papers 2011-02, Banco de México.
- Covarrubias, Enrique, 2011.
"The equilibrium set of economies with a continuous consumption space,"
Journal of Mathematical Economics,
Elsevier, vol. 47(2), pages 137-142, March.
- Enrique Covarrubias, 2010. "The Equilibrium Set of Economies with a Continuous Consumption Space," Working Papers 2010-10, Banco de México.
- Enrique Covarrubias, 2007.
"Regular Infinite Economies,"
Levine's Working Paper Archive
843644000000000034, David K. Levine.
- Enrique Covarrubias, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 29.
- Enrique Covarrubias, 2010. "Regular Infinite Economies," Working Papers 2010-03, Banco de México.
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