Economic distributions and primitive distributions in monopolistic competition

We link fundamental technological and taste distributions to endogenous economic distributions of firm size (output, profit) and prices in extensions of canonical IO and Trade models. We develop a continuous logit model of monopolistic competition to show that exponential or normal distributions respectively generate Pareto or log-normal economic size distributions. Two groups of distributions (output, profit, and quality-cost; and price and cost) are linked through the technological relation between cost and quality-cost. We formulate a general monopolistic competition model and recover the demand structure, mark-ups, and the quality-cost distribution from the output and profit distributions. Adding the price distribution recovers the cost distribution and the relation between quality-cost and cost. We also find long-run equilibrium distributions as a function of the primitives. On the Trade side, we provide a parallel analysis for the CES and break the Pareto circle by introducing quality.