We consider the invertibility of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identiﬁcation of demand, estimation of demand, testing of revealed preference, and economic theory requiring uniqueness of market clearing prices. We introduce the notion of “connected substitutes” and show that this structure is suﬀicient for invertibility. The connected substitutes conditions require weak substitution between all goods and suﬀicient strict substitution to necessitate treating them in a single demand system. These conditions are satisﬁed in many standard models, have transparent economic interpretation, and allow us to show invertibility without functional form restrictions, smoothness assumptions, or strong domain restrictions.
Berry, Steven T.; Gandhi, Amit; and Haile, Philip A., "Connected Substitutes and Invertibility of Demand" (2011). Cowles Foundation Discussion Papers. 2150.