Models of monopolistic competition with heterogeneous firms provide a fertile laboratory for studying a range of problems in many fields. Much of this work has assumed special functional forms, usually CES preferences and a Pareto distribution of firm productivity, though more recent contributions have explored the implications of relaxing these assumptions. In this paper, we present exact conditions under which particular assumptions about the distribution of firm productivity imply particular forms of the distribution of sales or output, and we use the Kullback-Leibler divergence to quantify the information loss when a predicted distribution fails to match the actual one. (Coauthors: Monika Mrázová and Mathieu Parenti.)