We investigate the role of complementarities in production and skill mobility across cities. We propose a general equilibrium model of location choice by heterogeneously skilled workers, and consider different degrees of complementarities between the skills of workers. The nature of the complementarities determines the equilibrium skill distribution across cities. We prove that with extreme-skill complementarity, the skill distribution has fatter tails in large cities; with top-skill complementarity, there is first-order stochastic dominance. Using the model to back out skills from wage and housing price data, we find robust evidence of fat tails in large cities. Big cities have big inequality. This pattern of spatial sorting is consistent with extreme-skill complementarity: the productivity of high skilled workers and of the providers of low skilled services is mutually enhanced.
complementarity cities sorting price-theoretic measure of skills population mobility city size matching theory general equilibrium skill distribution