On the Phelps-Koopmans theorem

• 成果类型: Article
• 署名作者: Mitra, Tapan; Ray, Debraj
• 署名单位: Cornell University; New York University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.08.004
• 发表日期: 2012
• 页码: 833-849
• 关键词: Capital overaccumulation; INEFFICIENCY; Phelps-Koopmans theorem; Nonconvex production set

摘要

We examine whether the Phelps-Koopmans theorem is valid in models with nonconvex production technologies. We argue that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that capital overaccumulation need not always imply inefficiency. Under mild regularity and smoothness assumptions, we provide an almost-complete characterization of situations in which every path with limit in excess of the smallest golden rule must be inefficient, so that a version of the Phelps-Koopmans theorem can be recovered. Finally, we establish that a nonconvergent path with limiting capital stocks above (and bounded away from) the smallest golden rule can be efficient, even if the model admits a unique golden rule. Thus the Phelps Koopmans theorem in its general form fails to be valid, and we argue that this failure is robust across nonconvex models of growth. (C) 2009 Elsevier Inc. All rights reserved.