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Smooth preferences, symmetries and expansion vector fields

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  • A. Mantovi

Abstract

Tyson (2013) introduces the notion of symmetry vector field for a smooth preference relation, and establishes necessary and sufficient conditions for a vector field on consumption space to be a symmetry vector field. The structure of a such a condition is discussed on both geometric and economic grounds. It is established that symmetry vector fields do commute (i.e. have vanishing Lie bracket) for additive and joint separability. The marginal utility of money is employed as a normalization of the expansion vector field (Mantovi (2013) which results in the fundamental (expansion-) symmetry vector field. Finally, a characterization of symmetry vector fields is given in terms of their action on the distance function, and a pattern of complete response is discussed for additive preferences. Examples of such constructions are explicitly worked out. Potential implications of the results are discussed.

Suggested Citation

  • A. Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Economics Department Working Papers 2016-EP01, Department of Economics, Parma University (Italy).
    • Handle: RePEc:par:dipeco:2016-ep01
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    1. A. Mantovi, 2021. "Bitcoin selection rule and foundational game theoretic representation of mining competition," Economics Department Working Papers 2021-EP02, Department of Economics, Parma University (Italy).
    2. Giacomo Corneo & Sergio Vergalli, 2016. "Taxes, subsidies, regulation in dynamic models," Journal of Economics, Springer, vol. 119(2), pages 97-99, October.

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    More about this item

    Keywords

    Utility Function; Symmetry; Separability; Vector Field; Expansion Path; Distance Function;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D04 - Microeconomics - - General - - - Microeconomic Policy: Formulation; Implementation; Evaluation
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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