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 Industrial Organization models. We derive full equivalence properties for monopoly mark-ups, demand shape, marginal revenue, and profits to match distributions of cost, price, output, and profit 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 restrictions on distribution pairs. Finally, we extend to analyze mark-up distributions.