Antoci, Angelo and Galeotti, Marcello and Russu, Paolo (2011) Poverty trap and global indeterminacy in a growth model with open-access natural resources. Journal of Economic Theory, Vol. 146 (2), p. 569-591. eISSN 1095-7235. Article.
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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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