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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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    1. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    2. Kfir Eliaz & Ran Spiegler, 2011. "Consideration Sets and Competitive Marketing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 235-262.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. , & ,, 2013. "Choice by iterative search," Theoretical Economics, Econometric Society, vol. 8(3), September.
    5. Houy, Nicolas & Tadenuma, Koichi, 2009. "Lexicographic compositions of multiple criteria for decision making," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1770-1782, July.
    6. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
    7. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    8. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    9. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    10. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    11. Clausen, Andrew & Strub, Carlo, 2013. "A General and Intuitive Envelope Theorem," SIRE Discussion Papers 2015-43, Scottish Institute for Research in Economics (SIRE).
    12. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
    13. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
    14. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
    15. Al-Najjar Nabil, 1993. "Non-transitive Smooth Preferences," Journal of Economic Theory, Elsevier, vol. 60(1), pages 14-41, June.
    16. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
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    Cited by:

    1. Mark Whitmeyer, 2025. "Comparative Statics for the Subjective," Papers 2501.12926, arXiv.org, revised Feb 2025.
    2. 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.
    3. 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.

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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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