Complexity results for the weak axiom of revealed preference for collective consumption models

The purpose of this paper is to establish the complexity of alternative versions of the weak axiom of revealed preference (warp) for collective consumption models. In contrast to the unitary consumption model, these collective models explicitly take the multi-member nature of the household into account. We consider the three collective settings that are most often considered in the literature. We start with the private setting in which all goods are privately consumed by the household members. Next, we consider the public setting in which all goods are publicly consumed inside the household. Finally, we also consider the general setting where no information on the (private or public) nature of goods consumed in the household is available. We prove that the collective version of warp is np-hard to test for both the private and public settings. Surprisingly, we also find for the general setting that the collective version of warp is easy to test for two-member households.