Ordients: Optimization and Comparative Statics without Utility Functions

46 Pages Posted: 25 Feb 2009 Last revised: 27 Jun 2012

See all articles by Ludovic Renou

Ludovic Renou

Queen Mary University of London

Karl H. Schlag

University of Vienna - Department of Economics

Date Written: Septembre 27, 2011

Abstract

This paper introduces the concept of ordient for binary relations (prefer- ences), a relative of the concept of gradient for functions (utilities). The main motivation for this study is to replace the binary relation at the center stage of economic analysis, rather than its representation (whenever it exists). Ordi- ents 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 con- strained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem.

Keywords: Binary relation, ordient, maxima, envelope theorem, implicit function theorem

JEL Classification: C6, D01

Suggested Citation

Renou, Ludovic and Schlag, Karl H., Ordients: Optimization and Comparative Statics without Utility Functions (Septembre 27, 2011). Available at SSRN: https://ssrn.com/abstract=1349092 or http://dx.doi.org/10.2139/ssrn.1349092

Ludovic Renou (Contact Author)

Queen Mary University of London ( email )

Mile End Road
London, London E1 4NS
United Kingdom

Karl H. Schlag

University of Vienna - Department of Economics ( email )

Oskar-Morgenstern-Platz 1
Vienna, A-1090
Austria