Preference Symmetries, Partial Differential Equations, and Functional Forms for Utility
AbstractA discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose trajectories generate a continuous symmetry. Any continuous symmetry of a preference relation implies that its representations satisfy a system of PDEs. Conversely the system implies the continuous symmetry if the latter is generated by a field. Moreover, solving the PDEs yields the functional form for utility equivalent to the symmetry. This framework is shown to encompass a variety of representation theorems related to univariate separability, multivariate separability, and homogeneity, including the cases of Cobb-Douglas and CES utility.
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Bibliographic InfoPaper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 702.
Date of creation: Apr 2013
Date of revision:
Continuous symmetry; Separability; Smooth preferences; Utility representation;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-27 (All new papers)
- NEP-MIC-2013-04-27 (Microeconomics)
- NEP-UPT-2013-04-27 (Utility Models & Prospect Theory)
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- Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004.
"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,"
Carlo Alberto Notebooks
12, Collegio Carlo Alberto, revised 2006.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
- Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-32, July.
- Peter C. Fishburn, 1968. "Utility Theory," Management Science, INFORMS, vol. 14(5), pages 335-378, January.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005.
"Certainty Independence and the Separation of Utility and Beliefs,"
Journal of Economic Theory,
Elsevier, vol. 120(1), pages 129-136, January.
- Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Certainty Independence and the Separation of Utility and Beliefs," ICER Working Papers - Applied Mathematics Series 40-2002, ICER - International Centre for Economic Research.
- Mas-Colell, Andreu, 1977. "Regular, Nonconvex Economies," Econometrica, Econometric Society, vol. 45(6), pages 1387-1407, September.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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