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

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  • Christopher J. Tyson

    (Queen Mary, University of London)

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.

Suggested Citation

  • Christopher J. Tyson, 2013. "Preference Symmetries, Partial Differential Equations, and Functional Forms for Utility," Working Papers 702, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:702
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    References listed on IDEAS

    as
    1. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
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    5. Mas-Colell, Andreu, 1977. "Regular, Nonconvex Economies," Econometrica, Econometric Society, vol. 45(6), pages 1387-1407, September.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Peter C. Fishburn, 1968. "Utility Theory," Management Science, INFORMS, vol. 14(5), pages 335-378, January.
    8. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Giacomo Corneo & Sergio Vergalli, 2016. "Taxes, subsidies, regulation in dynamic models," Journal of Economics, Springer, vol. 119(2), pages 97-99, October.
    2. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).
    3. Andrea Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Journal of Economics, Springer, vol. 119(2), pages 147-169, October.

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    More about this item

    Keywords

    Continuous symmetry; Separability; Smooth preferences; Utility representation;
    All these keywords.

    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

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