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From Ordients to Optimization: Substitution Effects without Differentiability

Renou, Ludovic and Schlag, Karl H (2009) From Ordients to Optimization: Substitution Effects without Differentiability. Working Paper. University of Leicester Discussion Papers in Economics 09/6.

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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.

Item Type: Monograph (Working Paper)
Uncontrolled Keywords: Binary relation; ordient; maxima; envelope theorem; implicit function theorem
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Social Sciences > Economics, Department of
Depositing User: Jim Jamieson
Date Deposited: 14 Jan 2015 13:30
Last Modified: 14 Jan 2015 13:30
URI: http://repository.essex.ac.uk/id/eprint/12299

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