Multi-Plant Firms, Variable Capacity Utilization, and the Aggregate Hours Elasticity

We develop a business cycle model with perfectly competitive product and labor markets in which production requires a minimum labor input, generating endogenous capacity utilization. The aggregate production function is kinked, featuring constant returns to scale below capacity—typically in recessions—and decreasing returns at capacity in expansions. Motivated by new empirical evidence that narratively identified labor tax shocks have significantly larger effects on hours and output when capacity utilization is below trend, we calibrate the model to U.S. data and show that the aggregate hours elasticity is higher in recessions, differing markedly from the micro elasticity implied by preferences.