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Ordients: Optimization and comparative statics without utility functions

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  • Renou, Ludovic
  • Schlag, Karl H.

Abstract

This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradient for functions (utilities). Ordients have a natural economic interpretation as marginal rates of substitution. Some examples of ordientable binary relations include the lexicographic order, binary relations resulting from the sequential applications of multiple rationales or binary relations with differentiable representations. We characterize the constrained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem.

Suggested Citation

  • Renou, Ludovic & Schlag, Karl H., 2014. "Ordients: Optimization and comparative statics without utility functions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 612-632.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:612-632
    DOI: 10.1016/j.jet.2014.09.013
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    References listed on IDEAS

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    Cited by:

    1. Theodoros Diasakos & Georgios Gerasimou, 2017. "Preference Conditions for Invertible Demand Functions," Discussion Paper Series, School of Economics and Finance 201708, School of Economics and Finance, University of St Andrews, revised 23 Aug 2019.
    2. Tomáš Langer, 2016. "Optimum spotřebitele a model ekonomické interpretace v mikroekonomii [Consumer Optimum and Model of Economic Interpretation in Microeconomics]," Politická ekonomie, Prague University of Economics and Business, vol. 2016(7), pages 789-803.
    3. Mark Whitmeyer, 2025. "Comparative Statics for the Subjective," Papers 2501.12926, arXiv.org, revised Feb 2025.

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    More about this item

    Keywords

    Binary relation; Ordient; Maxima; Envelope theorem; Implicit function theorem;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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