On Revealed Preference and Indivisibilities

We consider a practical market model in which all commodities are inherently indivisible and thus are traded in integer quantities, or consumption choices are available only in discrete quantities. We ask whether a finite set of price-quantity observations satisfying the Generalized Axiom of Revealed Preference (GARP) is consistent with utility maximization. Due to the absence of perfect divisibility and continuity, the existing argument and also familiar assumptions such as non-satiation cannot be used in the current discrete model. We develop a new approach to deal with this problem and establish a discrete analogue of Afrita’s celebrated theorem. We also introduce a new concept called tight budget demand set which is a natural refinement of the standard notion of demand set and plays a crucial role in the current analysis. Exploring network structure and a new and easy-to-use variant of GARP, we propose an elementary, simple, combinatorial and constructive proof for our result.