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

In large firms, management resolves a trade o¤ between hiring more versus better workers. Thespan of control or size is therefore intimately intertwined with the sorting pattern. This is importantfor macro and cross-country comparisons of productivity, for applications in international trade, andfor labor markets. We analyze the worker assignment, firm size, and wages. The sorting assignmentbetween workers and firms is governed by an intutitive cross-margin-complementarity condition thatcaptures the complementarities between qualities (of workers and firms), and quantities (of the workforce and firm resources). A simple system of two di¤erential equations determines the equilibrium firm size and wages. More productive firms are larger if their advantage to increase the span ofcontrol (the firm type-workforce size complementarity) outweighs the workers’relative advantage ofthe use of firm resources (the worker type-firm resource complementarity).