Assortative Matching with Large Firms∗

Technological progress allows firms to scale production processes over an increasingly large number of workers. This affects the size of the firm as well as the skill level of its workforce. 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. We illustrate the theory using German matched employer data, and apply it to analyze quantity-biased technological change in conjunction with skill-biased technological change. We find that quantity-biased technological change is sizable and important. Moreover, it partially dampens the skill-premium, which would have increased even more. Skill-biased technological change is therefore even larger than the increase in the skill premium indicates.