We present a new, information-theoretic approach for estimating a system of many demand equations where the unobserved reservation or choke prices vary across consumers. We illustrate this method by estimating a nonlinear, almost ideal demand system (AIDS) for four types of meat using cross-sectional data from Mexico, where most households did not buy at least one type of meat during the survey week. The system of de­mand curves vary across demo­graphic groups.