From Ordients to Optimization: Substitution Effects without Differentiability

Ludovic Renou and Karl Schlag

No 09/6, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

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.

Keywords: Binary relation; ordient; maxima; envelope theorem; implicit function theorem (search for similar items in EconPapers)
JEL-codes: C6 D01 (search for similar items in EconPapers)
Date: 2009-02
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