Convex Supply Curves

We provide evidence that industries' supply curves are convex. To guide our empirical analysis, we develop a putty-clay model in which capacity constraints at the plant level generate convex supply curves at the industry level. The model's key insight is that an industry's capacity utilization rate is a sufficient statistic for the slope of its supply curve. Using data on capacity utilization and three different instruments, we estimate the supply curve and find robust evidence for convexity. Supply curves are essentially flat at low levels of capacity utilization but increasing at higher levels. Further, industries with low initial capacity utilization rates expand production twice as much after demand shocks as industries that produce close to their capacity limit. The nonlinearity we identify has a number of macroeconomic implications, including that responses to shocks are state-dependent, that the Phillips curve is convex, and that the welfare costs of business cycles are larger than in Lucas (1987).