Preference Conditions for Invertible Demand Functions

30 Pages Posted: 23 Feb 2017 Last revised: 27 Aug 2019

See all articles by Theodoros Diasakos

Theodoros Diasakos

University of Stirling - Department of Economics

Georgios Gerasimou

University of St. Andrews

Date Written: August 23, 2019

Abstract

It is frequently assumed in several domains of economics that demand functions are invertible in prices. At the primitive level of preferences, however, the characterization of such demand functions remains elusive. We identify conditions on a utility-maximizing consumer’s preferences that are necessary and sufficient for her demand function to be continuous and invertible in prices: strict convexity, strict monotonicity and differentiability in the sense of Rubinstein (2012). We show that preferences are Rubinstein-differentiable if and only if the corresponding indifference sets are smooth. As we demonstrate by example, these notions relax Debreu’s (1972) preference smoothness.

Keywords: demand function, invertibility, differentiable preferences

JEL Classification: C60, D01

Suggested Citation

Diasakos, Theodoros and Gerasimou, Georgios, Preference Conditions for Invertible Demand Functions (August 23, 2019). Available at SSRN: https://ssrn.com/abstract=2921099 or http://dx.doi.org/10.2139/ssrn.2921099

Theodoros Diasakos (Contact Author)

University of Stirling - Department of Economics ( email )

Stirling, FK9 4LA
United Kingdom

Georgios Gerasimou

University of St. Andrews ( email )

The Gateway
North Haugh
St Andrews, Fife KY16 9RJ
United Kingdom

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