Optimal growth models with bounded or unbounded returns: A unifying approach

• 成果类型: Article
• 署名作者: Le Van, C; Morhaim, L
• 署名单位: heSam Universite; Universite Pantheon-Sorbonne; Centre National de la Recherche Scientifique (CNRS); Universite Catholique Louvain
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2001.2880
• 发表日期: 2002
• 页码: 158-187
• 关键词: Optimal growth; optimal path; value function; Bellman equation; unbounded from below utility functions

摘要

In this paper we propose a unifying approach to the study of optimal growth models with bounded or unbounded returns (above-below). Following our approach, we prove the existence of optimal solutions and show, without using the contraction method, that the value function is the unique solution to the Bellman equation for a particular class of functions. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. Moreover, following our approach we obtain the recent results of F. Alvarez and N. Stokey (1998, J. Econ. Theory 82, 167-189) as well as the well-known results. Journal of Economic Literature Classification numbers: C61, O41. (C) 2002 Elsevier Science (USA).