Poverty trap and global indeterminacy in a growth model with open-access natural resources
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 , which is, in fact, a poverty trap, coexisting with another stationary state 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 , then there exists a continuum of equilibrium trajectories approaching and one trajectory approaching . Therefore, our model exhibits global indeterminacy, since either or can be selected according to agent expectations. Moreover, we prove that conditions guaranteeing the attractivity of also imply the saddle-point stability of . However, when is not attractive, numerical simulations show the possible existence of one or two limit cycles: an attractive one surrounding and one endowed with a two-dimensional stable manifold surrounding .
Year of publication: |
2011
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Authors: | Antoci, Angelo ; Galeotti, Marcello ; Russu, Paolo |
Published in: |
Journal of Economic Theory. - Elsevier, ISSN 0022-0531. - Vol. 146.2011, 2, p. 569-591
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Publisher: |
Elsevier |
Keywords: | Global and local indeterminacy Poverty trap Environmental externalities History versus expectations Open-access natural resources |
Saved in:
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