Poverty trap and global indeterminacy in a growth model with open-access natural resources

• 成果类型: Article
• 署名作者: Antoci, Angelo; Galeotti, Marcello; Russu, Paolo
• 署名单位: University of Sassari; University of Florence
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2010.12.003
• 发表日期: 2011
• 页码: 569-591
• 关键词: Global and local indeterminacy; Poverty trap; Environmental externalities; History versus expectations; Open-access natural resources

摘要

In this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system (the framework is the one introduced by Wirl (1997) [53]). The dynamics of our model admits a locally attracting stationary state P-1*, which is, in fact, a poverty trap, coexisting with another stationary state P-2* possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the initial values of the state variables are close enough to the coordinates of P-1*, then there exists a continuum of equilibrium trajectories approaching P-1* and one trajectory approaching P-2*. Therefore, our model exhibits global indeterminacy, since either P-1* or P-2* can be selected according to agent expectations. Moreover, we prove that conditions guaranteeing the attractivity of P-1* also imply the saddle-point stability of P-2*. However, when P-1* is not attractive, numerical simulations show the possible existence of one or two limit cycles: an attractive one surrounding P-1* and one endowed with a two-dimensional stable manifold surrounding P-2*. (C) 2010 Elsevier Inc. All rights reserved.