Increasing Returns and Optimal Oscillating Labor Supply

Abstract

Models featuring increasing returns to scale in at least one factor of production have been used to study two separate phenomena: (1) multiplicity of self-fulfilling rational expectations equilibria (i.e. sunspots), and (2) production schedules that optimally feature bunching. We show in a continuous-time model with increasing returns to labor (IRL) that if the economy features multiple competitive equilibria, the optimal path of investment, employment and consumption cannot be constant, or even smoothly-varying. Any macroeconomic policies that shielded the economy from sunspot fluctuations would necessarily not be optimal. We then characterize the optimal allocation (the solution to the planner's problem) in a discrete time version of the model. We find that the optimal investment, employment and consumption policies under increasing returns can feature (1) discontinuous jumps, (2) endogenous cycles (with time-varying cycle limits) and (3) stochastic controls (lotteries). Our discrete-time model is very close to that studied by Christiano and Harrison (1999) they, however, find that fluctuations are not optimal. We show that this difference is driven by their assumption that production is linear in capital.

Keywords: Increasing returns, externalities, fluctuations, lotteries

JEL Classification: E3, C6, D6