Preference Conditions for Invertible Demand Functions
30 Pages Posted: 23 Feb 2017 Last revised: 27 Aug 2019
Date Written: August 23, 2019
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: Suggested Citation