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

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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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  2. 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.
  3. Mas-Colell, Andreu, 1977. "Regular, Nonconvex Economies," Econometrica, Econometric Society, vol. 45(6), pages 1387-1407, September.
  4. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-32, July.
  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. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  7. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  8. Peter C. Fishburn, 1968. "Utility Theory," Management Science, INFORMS, vol. 14(5), pages 335-378, January.
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