The rise and fall of unions in the United States

Union membership in the United States displayed a ∩-shaped pattern over the 20th century, while income inequality sketched a ∪. A model of unions is developed to analyze these facts. There is a distribution of productivity across firms in the economy. Firms hire capital, plus skilled and unskilled labor. Unionization is a costly process. A union chooses how many firms to organize and the union wage. Simulation of the model establishes that skill-biased technological change, which affects the productivity of skilled labor relative to unskilled labor, can potentially explain the observed paths for union membership and income inequality.