A Unified Production and Matching Function: Implications for Factor Shares

This paper develops microfoundations for a unified aggregate production function. Labor market frictions are naturally built into the aggregate production function because matching and production are two aspects of a single process. Entrepreneurs with heterogeneous productivity levels hire capital and compete for workers. If no entrepreneurs approach a given worker he is unemployed, otherwise the entrepreneur with the highest productivity hires the worker. The model provides new insights into the behavior of factor shares. If the entrepreneurs' productivity distribution is Pareto, the aggregate production function is Cobb-Douglas only in the limit as frictional unemployment disappears. In this limiting case, factors are paid their marginal product and factor shares are constant. Outside this limit, factor shares are not generally constant, enabling us to examine their behavior. A key prediction of the model is that labor's share is counter-cyclical provided that workers' outside option is sufficiently high.