Preference Symmetries, Partial Differential Equations, and Functional Forms for Utility

Christopher Tyson

No 702, Working Papers from Queen Mary University of London, School of Economics and Finance

Abstract: A 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.

Keywords: Continuous symmetry; Separability; Smooth preferences; Utility representation (search for similar items in EconPapers)
JEL-codes: C60 D01 D81 (search for similar items in EconPapers)
Date: 2013-04-01
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Citations: View citations in EconPapers (4)

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Journal Article: Preference symmetries, partial differential equations, and functional forms for utility (2013)
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