Abstract

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) ). 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 surroundingP*₂.

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