Two cornerstones of empirical and policy analysis of firms, in macro, labor and industrial organization, are the determinants of the firm size distribution and the determinants of sorting between workers and firms. We propose a unifying theory of production where management resolves a tradeoff between hiring more versus better workers. The span of control or size is therefore intimately intertwined with the sorting pattern. We provide a condition for sorting that captures this tradeoff between the quantity and quality of workers and that generalizes Becker's sorting condition. A system of differential equations determines the equilibrium allocation, the firm size, and wages, and allows us to characterize the allocation of the quality and quantity of labor to firms of different productivity. We show that our model nests a large number of widely used existing models. We also augment the model to incorporate labor market frictions in the presence of sorting with large firms.

We investigate the role of search frictions in markets with price competition and how it leads to sorting of heterogeneous agents. There are two aspects of value creation: the match value when two agents actually trade and the probability of trading governed by the search technology. We show that positive assortative matching obtains when complementarities in the former outweigh complementarities in the latter. This happens if and only if the match-value function is root-supermodular, that is, its nth root is supermodular, where n reflects the elasticity of substitution of the search technology. This condition is weaker than the condition required for positive assortative matching in markets with random search.

We propose a theory of how market power affects wage inequality. We ask how goods and labor market power jointly determine the level of wages, the skill premium, and wage inequality. We then use detailed microdata from the U.S. Census Bureau between 1997 and 2016 to estimate the parameters of labor supply, technology, and the market structure. We find that a less competitive market structure lowers the average wage of high‐skilled workers by 11.3%, and of low‐skilled workers by 12.2%, contributes 8.1% to the rise in the skill premium, and accounts for 54.8% of the increase in between‐establishment wage variance.