Afriat's theorem for indivisible goods

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for "discrete axiom of revealed preference") is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our results complement the main finding of Polisson and Quah, Am. Econ. J.: Micro. 5(1) p.28-34 (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.