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

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  • Antoci, Angelo
  • Galeotti, Marcello
  • Russu, Paolo

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) [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 .

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 2 (March)
Pages: 569-591

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:2:p:569-591

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Global and local indeterminacy Poverty trap Environmental externalities History versus expectations Open-access natural resources;

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Citations

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Cited by:
  1. Angelo Antoci & Marcello Galeotti & Paolo Russu, 2012. "Global Analysis and Indeterminacy in a Two-sector Growth Model with Human Capital," Working Papers - Economics wp2012_14.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  2. Luca Gori & Mauro Sodini, 2011. "Nonlinear Dynamics in an OLG Growth Model with Young and Old Age Labour Supply: The Role of Public Health Expenditure," Computational Economics, Society for Computational Economics, vol. 38(3), pages 261-275, October.
  3. Call, Isabel & Vosti, Stephen A. & Boucher, Stephen R. & Luedeling, Eike, 2012. "Technology Adoption and Climate-Related Policy Evaluation among East African Smallholders: A Bioeconomic Model of the Trade-offs between Trees and Subsistence," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 125015, Agricultural and Applied Economics Association.
  4. Golub, Alexander & Toman, Michael, 2014. "Climate change, industrial transformation, and"development traps"," Policy Research Working Paper Series 6951, The World Bank.
  5. OA. Carboni & P. Russu, 2012. "Global Indeterminacy in a Tourism Sector Model," Working Paper CRENoS 201230, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  6. Carboni, Oliviero A. & Russu, Paolo, 2013. "Linear production function, externalities and indeterminacy in a capital-resource growth model," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 422-428.
  7. Im, Fernando Gabriel & Rosenblatt, David, 2013. "Middle-income traps : a conceptual and empirical survey," Policy Research Working Paper Series 6594, The World Bank.

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