A nonsmooth, nonconvex model of optimal growth

• 成果类型: Article
• 署名作者: Kamihigashi, Takashi; Roy, Santanu
• 署名单位: Kobe University; Southern Methodist University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2005.06.007
• 发表日期: 2007
• 页码: 435-460
• 关键词: nonconvex; nonsmooth; and discontinuous technology; optimal growth; unbounded growth; extinction; neighborhood turnpike

摘要

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 1, 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 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock. (c) 2005 Elsevier Inc. All rights reserved.