This paper combines revealed preference and nonparametric estimation techniques to obtain nonparametric bounds on the distribution of the money metric utility and demand functions over a population of heterogeneous households. Our approach is independent of any functional specification on the household utility functions. Our method applies the weak axiom of revealed preference to a population of heterogeneous households. Although this does not produce the sharpest bounds, we show that it is computationally attractive and provides narrow bounds. We demonstrate the usefulness of our results by applying it to the Consumer Expenditure Survey, a U.S. cross–sectional consumption data set.