A utility representation theorem with weaker continuity condition
AbstractWe prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than theirs.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 401.
Length: 24 pages
Date of creation: Sep 2008
Date of revision:
linear continuity; utility representation;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
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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.
- 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.
- Inoue, Tomoki, 2010. "A utility representation theorem with weaker continuity condition," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 122-127, January.
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