A theoretical analysis is proposed of segregation as an equilibrium phenomenon in a random-matching model of the marriage market. Otherwise identical partners possess a pay-off-irrelevant characteristic, colour. We derive the set of colour-blind equilibria and show that they are generically constrained inefficient. Equilibrium segregation strategies are strategies that condition actions on the type of match. It is shown that distributions of types exist such that segregation equilibrium pay-offs Pareto dominate colour-blind pay-offs. For other distributions, segregation also generates conflict, where the majority unambiguously gains, while the minority group may lose. Giving preferential treatment, that is, minority bias, can increase overall welfare.

This reply refutes the objection raised by Levy (2009) about the fit of the upper tail of the city size distribution in Eeckhout (2004). I show that the method on which his conclusion is based is unsubstantiated. The visual interpretation of the fit on log-log plots is misleading. In addition, the methodology used to estimate a truncated subsample of the distribution while testing its significance against a distribution with prespecified parameters is ill-founded. The main conclusion is that Gibrat's law holds: city sizes follow proportionate growth, thus giving rise to a lognormal size distribution, tail included.

Two empirical regularities concerning the size distribution of cities have repeatedly been established: Zipf's law holds (the upper tail is Pareto), and city growth is proportionate. Census 2000 data are used covering the entire size distribution, not just the upper tail. The nontruncated distribution is shown to be lognormal, rather than Pareto. This provides a simple justification for the coexistence of proportionate growth and the resulting lognormal distribution. An equilibrium theory of local externalities that can explain the empirical size distribution of cities is proposed. The driving force is a random productivity process of local economies and the perfect mobility of workers.

In many economic applications of matching, the teams that form compete later in market structures with strategic interactions or with knowledge spillovers. Such post-match competition introduces externalities at the matching stage: a team’s payoff depends not only on their members’ attributes but also on those of other matched teams. This article develops a large market model of matching with externalities, in which first teams form, and then they compete. We analyse the sorting patterns that ensue under competitive equilibrium as well as their efficiency properties. Our main results show that insights substantially differ from those of the standard model without externalities: there can be multiple competitive equilibria with different sorting patterns; both optimal and competitive equilibrium matching can involve randomization; and competitive equilibrium can be inefficient with a matching that can drastically deviate from the optimal one. We also shed light on the economic relevance of our matching model with externalities. We analyse two economic applications that illustrate how our model can rationalize the trend in within- and between-firm inequality, and also the evolution of markups of sectors where firms have market power.

We develop a dynamic model with knowledge spillovers in production. The model contains two opposing forces. Imitation of other firms helps followers catch up with leaders, but the prospect of doing so makes followers want to free ride. The second force dominates and creates permanent inequality. We show that the greater are the average spillovers and the easier they are to obtain, the greater is the free-riding and inequality. More directed copying raises inequality by raising the free-riding advantages of hanging back. Using Compustat and patent-citation data we find that copying is highly undirected.

Manager pay has increased considerably since 1980, and so has inequality in manager pay. Over the same period, there has been a sharp rise in market power. We start from the premise that the role of managers is to increase firm productivity. When markets are imperfectly competitive, productivity not only helps firm grow in size, productivity also affects market power. We model how imperfect competition in product markets affects manager pay, and break down the contributions of firm size and market power to compensation. We find that market power, on average, accounts for 45.2% of total manager pay. Notably, there is substantial variation across managers. Top managers are disproportionately employed by firms with market power, and they benefit from it: in 2019, 80.3% of top manager pay is attributable to market power. Our main conclusion is that rise of market power explains half of the increase in average manager pay, and nearly all of the increase in manager pay inequality.