Revealed preference and differentiable demand

We prove that, for finitely many demand observations, the Strong Axiom of Revealed Preference tests not only the existence of a strictly concave, strictly monotone and continuous utility generator, but also one that generates an infinitely differentiable demand function. Our results extend those of previous related results (Matzkin and Richter, 1991; Chiappori and Rochet, 1987), yielding differentiable demand functions but without requiring differentiable utility functions.