We show that an agent maximizing some utility function on a discrete
(as opposed to continuous) consumption space will obey the generalized
axiom of revealed preference (GARP), so long as the agent
obeys cost efficiency. Cost efficiency will hold if there is some good,
outside the set of goods being studied by the modeler, that can be
consumed by the agent in continuous quantities. An application of
Afriat's Theorem then guarantees that there is a strictly increasing
utility function on the discrete consumption space that rationalizes
price and demand observations. (JEL D11)
Polisson, Matthew, and John K.-H. Quah.
"Revealed Preference in a Discrete Consumption Space."
American Economic Journal: Microeconomics,
Consumer Economics: Theory