School of Economics and Finance

No. 702: Preference Symmetries, Partial Differential Equations, and Functional Forms for Utility

Christopher J. Tyson , Queen Mary, University of London

April 1, 2013

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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.

J.E.L classification codes: C60, D01, D81

Keywords:Continuous symmetry, Separability, Smooth preferences, Utility representation