Assortative Matching with Large Firms: Span of Control over More versus Better Workers∗

In large firms, management resolves a trade off between hiring more versus better workers. The span of control or size is therefore intimately intertwined with the sorting pattern. Span of control is at the center of many studies in macroeconomics, comparisons of factor productivity, trade, and labor. With heterogeneous workers, we analyze the worker assignment, firm size, and wages. The pattern of sorting between workers and firms is governed by an intuitive cross-margin-complementarity condition that captures the complementarities between qualities (of workers and firms), and quantities (of the work force and firm resources). A simple system of two differential equations determines the equilibrium allocation, firm size and wages. We can analyze the impact of technological change: skill-biased change affects wages and increases the skill premium; quantity-biased change affects firm size, especially of productive firms. We also introduce search frictions and investigate how unemployment varies across skills and how vacancies vary across firm size.