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 document the evolution of market power based on firm-level data for the U.S. economy since 1955. We measure both markups and profitability. In 1980, aggregate markups start to rise from 21% above marginal cost to 61% now. The increase is driven mainly by the upper tail of the markup distribution: the upper percentiles have increased sharply. Quite strikingly, the median is unchanged. In addition to the fattening upper tail of the markup distribution, there is reallocation of market share from low- to high-markup firms. This rise occurs mostly within industry. We also find an increase in the average profit rate from 1% to 8%. Although there is also an increase in overhead costs, the markup increase is in excess of overhead. We discuss the macroeconomic implications of an increase in average market power, which can account for a number of secular trends in the past four decades, most notably the declining labor and capital shares as well as the decrease in labor market dynamism.