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From Ordients to Optimization: Substitution Effects without Differentiability

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  • Ludovic Renou

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  • Karl H. Schlag

Abstract

This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradients for functions (utilities). The lexicographic order, albeit not representable, has an ordient. Not only binary relations representable by differentiable functions have an ordient, but also preferences representable by non-differentiable functions might. We characterize the constrained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem. Ordients have a natural economic interpretation as marginal rates of substitution. We apply our results to the classic problem of maximizing preferences over budget sets.

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Bibliographic Info

Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 09/6.

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Date of creation: Feb 2009
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Handle: RePEc:lec:leecon:09/6

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Postal: Department of Economics University of Leicester, University Road. Leicester. LE1 7RH. UK
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Keywords: Binary relation; ordient; maxima; envelope theorem; implicit function theorem;

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References

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  1. Jose Apesteguia & Miguel A. Ballester, 2012. "Choice by sequential procedures," Economics Working Papers 1309, Department of Economics and Business, Universitat Pompeu Fabra.
  2. 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.
  3. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, 09.
  4. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  5. Driffill, John & Rotondi, Zeno, 2004. "Monetary Policy and Lexicographic Preference Ordering," CEPR Discussion Papers 4247, C.E.P.R. Discussion Papers.
  6. Tadenuma, Koichi, 1998. "Efficiency First or Equity First?: Two Principles and Rationality of Social Choice," Discussion Papers 1998-01, Graduate School of Economics, Hitotsubashi University.
  7. Tadenuma, Koichi, 2002. "Egalitarian-Equivalence and the Pareto Principle for Social Preferences," Discussion Paper 128, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  8. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
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