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

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Rafaela Pérez Sánchez & Jesús Ruiz, 2004. "Global and local indeterminacy and optimal environmental public policies in an economy with public abatement activities," Economic Working Papers at Centro de Estudios Andaluces E2004/79, Centro de Estudios Andaluces.
  2. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2009. "Homoclinic bifurcation and global indeterminacy of equilibrium in a two-sector endogenous growth model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 25-47.
  3. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
  4. Benhabib, Jess & Farmer, Roger E.A., 1991. "Indeterminacy and Increasing Returns," Working Papers 91-59, C.V. Starr Center for Applied Economics, New York University.
  5. Caulkins, J.P. & Hartl, R.F. & Kort, P.M. & Feichtinger, G., 2007. "Explaining fashion cycles : Imitators chasing innovators in product space," Other publications TiSEM dde09384-56b5-4b80-a718-5, Tilburg University, School of Economics and Management.
  6. McWhinnie, Stephanie F., 2009. "The tragedy of the commons in international fisheries: An empirical examination," Journal of Environmental Economics and Management, Elsevier, vol. 57(3), pages 321-333, May.
  7. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
  8. Benhabib, Jess & Eusepi, Stefano, 2005. "The design of monetary and fiscal policy: A global perspective," Journal of Economic Theory, Elsevier, vol. 123(1), pages 40-73, July.
  9. P. Pintus & D. Sands & R. de Vilder, 1998. "On the transition from local regular to global irregular fluctuations," THEMA Working Papers 98-18, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  10. Karp, Larry & Paul, Thierry, 2007. "Indeterminacy with environmental and labor dynamics," Structural Change and Economic Dynamics, Elsevier, vol. 18(1), pages 100-119, March.
  11. Eliasson, Ludvik & Turnovsky, Stephen J., 2004. "Renewable resources in an endogenously growing economy: balanced growth and transitional dynamics," Journal of Environmental Economics and Management, Elsevier, vol. 48(3), pages 1018-1049, November.
  12. Jess Benhabib & Kazuo Nishimura, 1999. "Indeterminacy Arising in Multi-sector Economies," The Japanese Economic Review, Japanese Economic Association, vol. 50(4), pages 485-506, December.
  13. Chen, Been-Lon & Lee, Shun-Fa, 2008. "Corrigendum to "Congestible public goods and local indeterminacy: A two-sector endogenous growth model": [Journal of Economic Dynamics & Control 31 (7) (2007) 2486-2518]," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1356-1356, April.
  14. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  15. Gardner M. Brown, 2000. "Renewable Natural Resource Management and Use without Markets," Journal of Economic Literature, American Economic Association, vol. 38(4), pages 875-914, December.
  16. Bischi, Gian Italo & Lamantia, Fabio, 2007. "Harvesting dynamics in protected and unprotected areas," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 348-370, March.
  17. Mino, Kazuo, 1999. "Non-separable utility function and indeterminacy of equilibrium in a model with human capital," Economics Letters, Elsevier, vol. 62(3), pages 311-317, March.
  18. Wagener, F.O.O., 2004. "Skiba points for small discount rates," CeNDEF Working Papers 04-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  19. Nishimura, Kazuo & Shimomura, Koji, 2002. "Indeterminacy in a dynamic small open economy," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 271-281, December.
  20. Berck, Peter & Perloff, Jeffrey M, 1982. "An Open-Access Fishery with Rational Expectations," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt876499mq, Department of Agricultural & Resource Economics, UC Berkeley.
  21. Meng, Qinglai & Yip, Chong Kee, 2008. "On indeterminacy in one-sector models of the business cycle with factor-generated externalities," Journal of Macroeconomics, Elsevier, vol. 30(1), pages 97-110, March.
  22. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2005. "Consumption of private goods as substitutes for environmental goods in an economic growth model," MPRA Paper 13664, University Library of Munich, Germany.
  23. Bennett, R.L. & Farmer, R.E.A., 1999. "Indeterminacy with Non-Separable Utility," Economics Working Papers eco99/34, European University Institute.
  24. Jess Benhabib & Kazuo Nishimura & Tadashi Shigoka, 2008. "Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 337-355.
  25. Kazuo Mino & Kazuo Nishimura & Koji Shimomura & Ping Wang, 2008. "Equilibrium dynamics in discrete-time endogenous growth models with social constant returns," Economic Theory, Springer, vol. 34(1), pages 1-23, January.
  26. Wirl, Franz & Feichtinger, Gustav, 2005. "History dependence in concave economies," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 390-407, August.
  27. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62, pages 124.
  28. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
  29. Kazuo Nishimura & Carine Nourry & Alain Venditti, 2008. "Indeterminacy in aggregate models with small externalities: an interplay between preferences and technology," Working Papers halshs-00281428, HAL.
  30. Benhabib, Jess & Nishimura, Kazuo, 1998. "Indeterminacy and Sunspots with Constant Returns," Journal of Economic Theory, Elsevier, vol. 81(1), pages 58-96, July.
  31. Krugman, Paul, 1991. "History versus Expectations," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 651-67, May.
  32. Lopez, Ramon E. & Anriquez, Gustavo & Gulati, Sumeet, 2007. "Structural change and sustainable development," Journal of Environmental Economics and Management, Elsevier, vol. 53(3), pages 307-322, May.
  33. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60.
  34. Antoci, Angelo & Sodini, Mauro, 2009. "Indeterminacy, bifurcations and chaos in an overlapping generations model with negative environmental externalities," MPRA Paper 13750, University Library of Munich, Germany.
  35. Ayong Le Kama, Alain D., 2001. "Sustainable growth, renewable resources and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1911-1918, December.
  36. Wirl Franz, 1995. "The Cyclical Exploitation of Renewable Resource Stocks May Be Optimal," Journal of Environmental Economics and Management, Elsevier, vol. 29(2), pages 252-261, September.
  37. D'Alessandro, Simone, 2007. "Non-linear dynamics of population and natural resources: The emergence of different patterns of development," Ecological Economics, Elsevier, vol. 62(3-4), pages 473-481, May.
  38. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  39. Caulkins, Jonathan P. & Feichtinger, Gustav & Johnson, Michael & Tragler, Gernot & Yegorov, Yuri, 2005. "Skiba thresholds in a model of controlled migration," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 490-508, August.
  40. Itaya, Jun-ichi, 2008. "Can environmental taxation stimulate growth? The role of indeterminacy in endogenous growth models with environmental externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1156-1180, April.
  41. Wirl, Franz, 2004. "Sustainable growth, renewable resources and pollution: Thresholds and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1149-1157, March.
  42. Xavier Raurich-Puigdevall, 2000. "Global indeterminacy in an endogenous-growth model with public capital," Journal of Economics, Springer, vol. 71(3), pages 255-280, October.
  43. Gardner Brown, 2000. "Renewable Natural Resource Management and Use Without Markets," Discussion Papers in Economics at the University of Washington 0025, Department of Economics at the University of Washington.
  44. Gardner Brown, 2000. "Renewable Natural Resource Management and Use Without Markets," Working Papers 0025, University of Washington, Department of Economics.
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