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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.

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Paper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 702.

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Date of creation: Apr 2013
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Handle: RePEc:qmw:qmwecw:wp702

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

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  1. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  3. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
  5. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Certainty Independence and the Separation of Utility and Beliefs," ICER Working Papers - Applied Mathematics Series 40-2002, ICER - International Centre for Economic Research.
  6. Mas-Colell, Andreu, 1977. "Regular, Nonconvex Economies," Econometrica, Econometric Society, vol. 45(6), pages 1387-1407, September.
  7. Peter C. Fishburn, 1968. "Utility Theory," Management Science, INFORMS, vol. 14(5), pages 335-378, January.
  8. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-32, July.
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Cited by:
  1. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).

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