Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/97346
Authors: 
Tyson, Christopher J.
Year of Publication: 
2013
Series/Report no.: 
Working Paper, School of Economics and Finance, Queen Mary, University of London 702
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.
Subjects: 
Continuous symmetry
Separability
Smooth preferences
Utility representation
JEL: 
C60
D01
D81
Document Type: 
Working Paper

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