Sorting and Factor Intensity: Production and Unemployment across Skills

When firms choose the allocation of workers, they can adjust not only the type of worker, the extensive margin, but also the intensive margin, how many of those worker to employ. We propose a tractable matching model with such factor intensity. Positive sorting arises under cross-margin-complementarity: within-complementarities in extensive and intensive margin exceed the between-complementarities across intensive and extensive margin. We characterize the equilibrium allocation, wages and factor intensities. Extended to frictional hiring, the presence of unemployment across types is analyzed. Unemployment is decreasing in skills, and we find conditions under which firm size is increasing in skill.