Preference Conditions for Invertible Demand Functions

It is frequently assumed in several domains of economics that demand functions are invertible prices. At the primitive level preferences, however, corresponding characterization has remained elusive. We identify necessary and sufficient conditions on a utility-maximizing consumer’s preferences for her function to be continuous invertible: strict convexity, monotonicity, differentiability sense Rubinstein (2006). further show equivalent indifference sets being smooth, which weaker than Debreu’s (1972) notion preference smoothness. finally discuss implications our analysis satisfy “strict law demand.” (JEL DO1, D11)