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Over-exploitation of open-access natural resources and global indeterminacy in an economic growth model


  • Angelo Antoci

    () (Universita' degli Studi di Sassari)

  • Marcello Galeotti

    () (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Paolo Russu

    (Universita' degli Studi di Sassari)


In this paper we use global analysis techniques to investigate 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 steady state which is, in fact, a poverty trap, coexisting with another steady state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the economy state variables are close enough to those of the attractive point, then there exists a continuum of equilibrium orbits approaching the poverty trap and one orbit approaching the saddle-point.

Suggested Citation

  • Angelo Antoci & Marcello Galeotti & Paolo Russu, 2009. "Over-exploitation of open-access natural resources and global indeterminacy in an economic growth model," Working Papers - Mathematical Economics 2009-05, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:flo:wpaper:2009-05

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    References listed on IDEAS

    1. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, July.
    2. Perrings, Charles, 1989. "Environmental bonds and environmental research in innovative activities," Ecological Economics, Elsevier, vol. 1(1), pages 95-110, February.
    3. Perrings,Charles, 1987. "Economy and Environment," Cambridge Books, Cambridge University Press, number 9780521340816, March.
    4. Costanza, Robert & Perrings, Charles, 1990. "A flexible assurance bonding system for improved environmental management," Ecological Economics, Elsevier, vol. 2(1), pages 57-75, April.
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    Cited by:

    1. Been-Lon Chen & Yu-Shan Hsu & Kazuo Mino, 2013. "Can consumption habit spillovers be a source of equilibrium indeterminacy?," Journal of Economics, Springer, vol. 109(3), pages 245-269, July.

    More about this item


    environmental externalities; indeterminacy; history versus expectations; global analysis of dynamic systems;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products

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