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An economic model of metapopulation dynamics

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  • Stefano BOSI
  • David DESMARCHELIER

Abstract

In this paper, we aim to model the impact of human activities on the wildlife habitat in a general equilibrium framework by embedding the Levins model (1969) of metapopulation dynamics into a Ramsey model (1928) with a pollution externality. In the long run, as in Levins (1969), two steady states coexist: a zero one with mass extinction and anotherone with positive wildlife when the migration rate of the metapopulation exceeds the rate of extinction. A green tax always increases the wildlife and lowers the consumption demand. It is welfare-improving if and only if agents overweight the wildlife. In the short run, we show that a sufficiently negative effect of wildlife habitat on consumption demand can lead to the emergence of a limit cycle near the positive steady state through a Hopf bifurcation. We show also that the negative pollution effect on wildlife habitat works as a destabilizing force in the economy by promoting limit cycles.

Suggested Citation

  • Stefano BOSI & David DESMARCHELIER, 2017. "An economic model of metapopulation dynamics," Working Papers of BETA 2017-22, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2017-22
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    References listed on IDEAS

    as
    1. Stefano Bosi & David Desmarchelier, 2018. "Limit Cycles Under a Negative Effect of Pollution on Consumption Demand: The Role of an Environmental Kuznets Curve," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(2), pages 343-363, February.
    2. Benchekroun, Hassan & Withagen, Cees, 2011. "The optimal depletion of exhaustible resources: A complete characterization," Resource and Energy Economics, Elsevier, vol. 33(3), pages 612-636, September.
    3. Bosi, Stefano & Desmarchelier, David, 2019. "Local bifurcations of three and four-dimensional systems: A tractable characterization with economic applications," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 38-50.
    4. Roe, Brian & Teisl, Mario F. & Levy, Alan & Russell, Matthew, 2001. "US consumers' willingness to pay for green electricity," Energy Policy, Elsevier, vol. 29(11), pages 917-925, September.
    5. Stefano Bosi & David Desmarchelier, 2017. "Local Bifurcations of Three and Four-Dimensional Systems: A Tractable Characterization with Economic Applications," EUSP Department of Economics Working Paper Series Ec-02/17, European University at St. Petersburg, Department of Economics.
    6. Benchekroun, Hassan & Withagen, Cees, 2011. "The optimal depletion of exhaustible resources: A complete characterization," Resource and Energy Economics, Elsevier, vol. 33(3), pages 612-636, September.
    7. Rinnan, D. Scott, 2018. "Population persistence in the face of climate change and competition: A battle on two fronts," Ecological Modelling, Elsevier, vol. 385(C), pages 78-88.
    8. Lafuite, A.-S. & Loreau, M., 2017. "Time-delayed biodiversity feedbacks and the sustainability of social-ecological systems," Ecological Modelling, Elsevier, vol. 351(C), pages 96-108.
    9. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    10. Loehle, Craig, 2018. "Disequilibrium and relaxation times for species responses to climate change," Ecological Modelling, Elsevier, vol. 384(C), pages 23-29.
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    More about this item

    Keywords

    metapopulation dynamics; pollution; Ramsey model; Hopf bifurcation.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth

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