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Natural cycles and pollution

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  • Stefano Bosi
  • David Desmarchelier

Abstract

In this paper, we study a competitive Ramsey model where a pollution externality, coming from production, impairs a renewable resource which affects the consumption demand. A proportional tax, levied on the production level, is introduced to finance public depollution expenditures. In the long run, two steady states may coexist, the one with a low resource level, the other with a high level. Interestingly, a higher green tax rate lowers the resource level of the low steady state, giving rise to a Green Paradox (Sinn, 2008). Moreover, the green tax may be welfareimproving at the high steady state but never at the low one. Therefore, at the latter, it is optimal to reduce the green tax rate as much as possible. Conversely, the optimal tax rate is positive when the economy experiences the high steady state. This rate is unique. In the short run, the two steady states may collide and disappear through a saddle-node bifurcation. Since consumption and natural resources are substitutable goods, a limit cycle may arise around the high stationary state. To the contrary, this kind of cycles never occur around the low steady state whatever the resource effect on consumption demand. Finally, focusing on the class of bifurcations of codimension two, we find a Bogdanov-Takens bifurcation.

Suggested Citation

  • Stefano Bosi & David Desmarchelier, 2016. "Natural cycles and pollution," Working Papers of BETA 2016-53, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2016-53
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    References listed on IDEAS

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    Cited by:

    1. Takuma Kunieda & Kazuo Nishimura, 2021. "Pollution, Human Capital, and Growth Cycles," Creative Economy, in: Kazuo Nishimura & Masatoshi Murase & Kazuyoshi Yoshimura (ed.), Creative Complex Systems, chapter 0, pages 85-99, Springer.
    2. David DESMARCHELIER & Alexandre MAYOL, 2020. "To seed, or not to seed," Working Papers of BETA 2020-04, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    3. Stefano Bosi & David Desmarchelier, 2017. "A simple method to study local bifurcations of three and four-dimensional systems: characterizations and economic applications," Working Papers of BETA 2017-07, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    4. Can Askan Mavi, 2017. "What Can Abrupt Events Tell Us About Sustainability ?," Working Papers hal-01628682, HAL.
    5. Mavi, Can Askan, 2019. "What can catastrophic events tell us about sustainability?," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 70-83.
    6. 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.
    7. Maxime MENUET & Alexandru MINEA & Patrick VILLIEU & Anastasios XEPAPADEAS, 2021. "Growth, Endogenous Environmental Cycles, and Indeterminacy," LEO Working Papers / DR LEO 2889, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    8. Maxime Menuet & Alexandru Minea & Patrick Villieu & Anastasios Xepapadeas, 2020. "Economic Growth and the Environment: A Theoretical Reappraisal," DEOS Working Papers 2031, Athens University of Economics and Business.
    9. David Desmarchelier & Alexandre Mayol, 2022. "To seed, or not to seed? An endogenous labor supply approach in a simple overlapping generation economy," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 25-38, January.
    10. Can Askan Mavi, 2019. "What can catastrophic events tell us about sustainability?," Post-Print halshs-02142121, HAL.

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    More about this item

    Keywords

    nature; logistic dynamics; Ramsey model; depollution; saddle-node bifurcation; Hopf bifurcation; Bogdanov-Takens bifurcation.;
    All these keywords.

    JEL classification:

    • 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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