This paper combines elementary revealed preference principles and nonparametric estimation techniques to obtain nonparametric bounds on the distribution of the money metric utility over a population of heterogeneous households. Our approach is independent of any functional specification on the household utility functions, meaning that our results are robust against parametric specification errors. Our methodology can also be used to establish bounds on the distribution of the demand function in counterfactual price regimes. To demonstrate the relevance of our approach, we illustrate our findings using a repeated cross–sectional household consumption data set.