Decoupling the CES Distribution Circle with Quality and Beyond: Equilibrium Distributions and the CES-Logit Nexus

Abstract

Abstract We show for CES demands with heterogeneous productivities that profit, revenue and output distributions lie in the same closed power family as the productivity distribution (e.g., the ‘Pareto circle’). The price distribution lies in the inverse power family. Equilibrium distribution shapes are linked by linear relations between their density elasticities. Introducing product quality decouples the CES circle, and reconciles Pareto price and Pareto sales revenue distributions. We use discrete choice underpinnings to find variable mark-ups for a more flexible demand formulation bridging CES to logit and beyond. For logit demand, exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions.