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A one-sector model of economic growth with a nonlinear production function and related environmental quality

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Abstract

In this paper we suggest a stylized one-sector optimization model of national economic growth with a nonlinear production function and environmental quality control. A steady-state point of the Hamilton system is found analytically, while the optimal trajectory is constructed numerically. And finally, we adjust the model to the Russian economy.

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References

  1. Aseev, S.M. and Kryazhimskii, A.V., The Pontryagin Maximum Principle and Problems of Optimal Economic Growth, Tr. Mat. Inst. Steklov., 2007, vol. 257, pp. 5–271.

    MathSciNet  Google Scholar 

  2. Krasovskii, A.A., Methods for Solving Optimal Control Problems with Infinite Horizon, Cand. Sci. (Phys.-Math.) Dissertation, Yekaterinburg, 2008.

    Google Scholar 

  3. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1983.

    MATH  Google Scholar 

  4. Rovenskaya, E.A., A Model of Economic Growth and Related Environmental Quality, Mat. Teor. Igr Pril., 2011, vol. 3, no. 3, pp. 67–84.

    MATH  Google Scholar 

  5. Usova, A.A., Property Analysis of Hamilton Systems and Price Functions in Dynamic Growth Models, Cand. Sci. (Phys.-Math.) Dissertation, Yekaterinburg, 2012.

    Google Scholar 

  6. Acemoglu, D., Introduction to Modern Economic Growth, Cambridge: MIT Press, 2009.

    MATH  Google Scholar 

  7. Ariga, J.M., Internalizing Environmental Quality in a Simple Endogenous Growth Model, 2002, http://fsg.afre.msu.edu/kenya/o_papers/environmental_qualit_and_growth.pdf.

    Google Scholar 

  8. Ayong le Kama, A. and Shubert, K., The Consequences of an Endogenous Discounting Depending on Environmental Quality, 2002 World Congress of Environmental and Resource Economics, Monterey, California, 2002.

    Google Scholar 

  9. Bartz, S. and Kelly, D.L., Economic Growth and the Environment: Theory and Facts, Resource Energy Econom., 2008, vol. 30, no. 2, pp. 115–149.

    Article  Google Scholar 

  10. Jouvet, P.-A., Miche, P., and Rotillon, G., Optimal Growth with Pollution: How to Use Pollution Permits?, J. Econom. Dynamics Control, 2005, vol. 29, no. 9, pp. 1597–1609.

    Article  MATH  Google Scholar 

  11. Savin, V.V. and Rovenskaya, E.A., Remarks on Fair Wealth Accumulation in Russia, Environ., Develop. Sustainability, 2011, vol. 13, no. 5, pp. 923–937.

    Article  Google Scholar 

  12. Wei, W., Alvarez, I., and Martin, S., Sustainability Analysis: Viability Concepts to Consider Transient and Asymptotical Dynamics in Socio-Ecological Tourism-Based Systems, Ecological Model., 2013, vol. 251, pp. 103–113.

    Article  Google Scholar 

  13. World Bank Database, http://data.worldbank.org/.

Download references

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Correspondence to E. A. Rovenskaya.

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Original Russian Text © E.A. Rovenskaya, 2012, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2012, No. 4, pp. 73–92.

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Rovenskaya, E.A. A one-sector model of economic growth with a nonlinear production function and related environmental quality. Autom Remote Control 76, 2078–2090 (2015). https://doi.org/10.1134/S0005117915110168

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  • DOI: https://doi.org/10.1134/S0005117915110168

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