Distributional comparative statics with heterogeneous agents

We propose a formal way to systematically study the differential effects of exogenous shocks in economic models with heterogeneous agents. Our setting applies to models that can be rephrased as "competition for market shares" in a broad sense. We show that even in presence of any number of arbitrarily heterogeneous agents, a single recursion relation characterizes the distributional pattern of equilibrium market shares and related measures. We identify the general conditions under which the market share function rotates, thereby either causing more or less equality among the agents. Our setting highlights the exceptional rule that power functions play for the distributional effects. We apply our method across economic models, including examples from monopolistic competition, discrete choice, partial and general equilibrium theory and contest theory.