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Pollution effects on disease transmission and economic stability

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  • Stefano Bosi
  • David Desmarchelier

Abstract

In this article, we embed a model of disease spread into a Ramsey model. A stock of pollution, viewed as a productive externality, affects both the disease transmission and the consumption demand. An eco‐friendly government levies a proportional Pigouvian tax on production to depollute. We show the coexistence of two steady states in the long run: a disease‐free and an endemic steady state. At the endemic steady state, a higher green‐tax rate always reduces the pollution level. In the short run, we show the existence of limit cycles (through a Hopf bifurcation) as well as more complex dynamics of codimension two (a Gavrilov‐Guckenheimer bifurcation). We complete the study with a numerical illustration of these bifurcations and a new facet of the Green Paradox: a higher tax rate can allow more scope for cycles by lowering the critical aversion to pollution and, thus, contribute to destabilization of the economy and promotion of the intergenerational inequalities.

Suggested Citation

  • Stefano Bosi & David Desmarchelier, 2021. "Pollution effects on disease transmission and economic stability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(2), pages 169-189, June.
    • Handle: RePEc:bla:ijethy:v:17:y:2021:i:2:p:169-189
    DOI: 10.1111/ijet.12213
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    References listed on IDEAS

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    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. Seegmuller, Thomas & Verchere, Alban, 2004. "Pollution as a source of endogenous fluctuations and periodic welfare inequality in OLG economies," Economics Letters, Elsevier, vol. 84(3), pages 363-369, 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. Samer Atallah, 2018. "Political transition in resource economies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 14(3), pages 233-256, September.
    5. 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.
    6. Fernández, Esther & Pérez, Rafaela & Ruiz, Jesús, 2012. "The environmental Kuznets curve and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1700-1717.
    7. 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.
    8. Hans-Werner Sinn, 2008. "Public policies against global warming: a supply side approach," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 15(4), pages 360-394, August.
    9. Junxi Zhang, 1999. "Environmental sustainability, nonlinear dynamics and chaos," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 489-500.
    10. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    11. Antoine Le Riche, 2017. "Macroeconomic volatility and trade in OLG economies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 13(4), pages 401-425, December.
    12. Philippe Michel & Gilles Rotillon, 1995. "Disutility of pollution and endogenous growth," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 6(3), pages 279-300, October.
    13. Stefano Bosi & David Desmarchelier, 2018. "Pollution and infectious diseases," International Journal of Economic Theory, The International Society for Economic Theory, vol. 14(4), pages 351-372, December.
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    Cited by:

    1. Guillaume Morel, 2020. "A note on pollution and infectious disease," Economics Bulletin, AccessEcon, vol. 40(4), pages 2723-2733.
    2. 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.
    3. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2021. "COVID-19 and a Green Recovery?," Economic Modelling, Elsevier, vol. 104(C).
    4. Guillaume MOREL, 2020. "PA note on pollution and infectious diseases," Working Papers of BETA 2020-22, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    5. Guillaume MOREL, 2020. "A note on pollution and infectious disease," Working Papers of BETA 2020-38, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.

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    More about this item

    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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