Rank, separability, and conditional demands

Rank demand systems that are either conditioned on some good (such as durables) or are separable from that good, are shown to be identical to unconditional demand systems having rank or + 1. More generally, the rank of a conditional demand system or a separable subsystem is a lower bound on the rank of the corresponding demand system over all goods. This relationship is applied to reinterpret some existing empirical results regarding rank, conditioning goods, and separability.