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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