Preference symmetries, partial differential equations, and functional forms for utility

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Paper ; No. 702

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General ; Microeconomic Behavior: Underlying Principles ; Criteria for Decision-Making under Risk and Uncertainty
• Subject: Continuous symmetry ; Separability ; Smooth preferences ; Utility representation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Tyson, Christopher J.
• Event: Veröffentlichung
• (who): Queen Mary University of London, School of Economics and Finance
• (where): London
• (when): 2013

Further information

• Handle: http://hdl.handle.net/10419/97346
• Last update: 10.03.2025, 11:41 AM CET