Over-exploitation of open-access natural resources and global indeterminacy in an economic growth model

In this paper we use global analysis techniques to investigate 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)). The dynamics of our model admits a locally attracting steady state which is, in fact, a poverty trap, coexisting with another steady state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the economy state variables are close enough to those of the attractive point, then there exists a continuum of equilibrium orbits approaching the poverty trap and one orbit approaching the saddle-point.