Economic distributions, primitive distributions, and demand recovery in Monopolistic Competition

We link fundamental technological and taste distributions to endogenous economic distributions of prices and firm size (output, profit) generated under monopolistic competition with heterogeneous productivities as per recent Trade and IO models. We new derive properties for monopoly pricing and equivalence properties on demand curvature, profit functions, and marginal revenue, which we use to ensure distributions of cost, price, output, and profit can be matched under monopolistic competition. Demand and one distribution determine the rest. We provide constructive proofs to recover demand and all distributions from just two (e.g., price and cost distributions uncover demand form), and derive consistency conditions that distribution pairs must satisfy. We then extend to include mark-up distributions.