A nonsmooth, nonconvex model of optimal growth


This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to one, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches one, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.

Keywords: Nonconvex, nonsmooth, and discontinuous technology; optimal growth; unbounded growth; extinction; neighborhood turnpike.

JEL classification: C61; D90; O41

Research Institute for Economics and Business Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: (81) 78 803 7036
Fax: (81) 78 803 7059

Santanu ROY
Department of Economics
Southern Methodist University