Preference Conditions for Invertible Demand Functions

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 corresponding characterization has remained elusive. We identify necessary and sufficient conditions on a utility-maximizing consumer's preferences for her demand function to be continuous and invertible: strict convexity, strict mono-tonicity and differentiability in the sense of Rubinstein (2006). We further show that Rubinstein differ-entiability is equivalent to the indifference sets being smooth, which is weaker than Debreu's (1972) notion of preference smoothness. We finally discuss implications of our analysis for demand functions that satisfy the "strict law of demand". * We are grateful to Hugo Sonnenschein, Phil Reny and the anonymous referees for very useful comments. Any errors are our own.