Distributional Comparative Statics with Heterogeneous Agents

We propose a general approach to study the differential effects of exogenous shocks in economic models with heterogeneous agents. Our setting applies to models that can be stated as ``competition for market shares'' in a broad sense. Examples that fit our type of structure are ubiquitous in competition theory, monopolistic competition, political economics and applied game theory. We show that even in presence of any number of arbitrarily heterogeneous agents, a single recursive relation characterizes the distributional pattern of equilibrium market shares, and related measures. We identify conceptual conditions under which the market share function rotates, thereby either causing more or less equality among the agents, and study the distributional comparative statics in examples from various economic fields