This paper proposes a framework to model welfare effects that are associated with a price change in a population of heterogeneous consumers. The framework is similar to that of Hausman and Newey (Econometrica, 1995, 63, 1445-1476), but allows for more general forms of heterogeneity. Individual demands are characterized by a general model that is nonparametric in the regressors, as well as monotonic in unobserved heterogeneity, allowing us to identify the distribution of welfare effects. We first argue why a decision maker should care about this distribution. Then we establish constructive identification, propose a sample counterparts estimator, and analyze its large-sample properties. Finally, we apply all concepts to measuring the heterogeneous effect of a change of gasoline price using US consumer data and find very substantial differences in individual effects across quantiles.