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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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  • Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:2:p:569-591
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    Cited by:

    1. Yasuhiro Nakamoto & Koichi Futagami, 2016. "Dynamic Analysis of a Renewable Resource in a Small Open Economy: The Role of Environmental Policies for the Environment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(3), pages 373-399, July.
    2. Alexander Golub & Michael Toman, 2016. "Climate Change, Industrial Transformation, and “Environmental Growth Traps”," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(2), pages 249-263, February.
    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. repec:wsi:jicepx:v:06:y:2015:i:03:n:s1793993315500131 is not listed on IDEAS
    5. Potrafke, Niklas, 2010. "The growth of public health expenditures in OECD countries: Do government ideology and electoral motives matter?," Journal of Health Economics, Elsevier, vol. 29(6), pages 797-810, December.
    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. Angelo Antoci & Marcello Galeotti & Paolo Russu, 2014. "Global analysis and indeterminacy in a two-sector growth model with human capital," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(4), pages 313-338, December.
    8. 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, Springer;Society for Computational Economics, vol. 38(3), pages 261-275, October.
    9. Golub, Alexander & Toman, Michael, 2014. "Climate change, industrial transformation, and"development traps"," Policy Research Working Paper Series 6951, The World Bank.
    10. Fernando Gabriel Im & David Rosenblatt, 2015. "Middle-Income Traps: A Conceptual and Empirical Survey," Journal of International Commerce, Economics and Policy (JICEP), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 1-39.
    11. Chaudhry, Azam & Tanveer, Hafsa & Naz, R., 2017. "Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability," Economic Modelling, Elsevier, vol. 63(C), pages 206-214.
    12. Antoci, Angelo & Russu, Paolo & Ticci, Elisa, 2012. "Environmental externalities and immiserizing structural changes in an economy with heterogeneous agents," Ecological Economics, Elsevier, vol. 81(C), pages 80-91.
    13. Argentiero, Amedeo & Cerqueti, Roy & Sabatini, Fabio, 2018. "Does social capital explain the Solow residual? A DSGE approach," MPRA Paper 87100, University Library of Munich, Germany.
    14. 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.

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