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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Exact Analytical Solutions of Selected Behaviourist Economic Growth Models with Exogenous Climate Damages

Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 251--261 | DOI:10.5890/DNC.2016.09.005

Dmitry V. Kovalevsky

Nansen International Environmental and Remote Sensing Centre, 14th Line 7, office 49, Vasilievsky Island, 199034 St. Petersburg, Russia

Saint Petersburg State University, Universitetskaya Emb. 7-9, 199034 St. Petersburg, Russia

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Abstract

Capital dynamics are calculated for (i) the AK model with output reduced by climate damages, (ii) the AK model with climate-dependent depreciation rate, and (iii) the Solow–Swan model with output given either by the Cobb–Douglas production function or by the constant elasticity of substitution (CES) production function and reduced by climate damages. The climate projections used as model inputs are exogenous. Simple analytical parametrisations for temperature dynamics are assumed (either linear or exponential temperature growth). The quadratic and the Nordhaus climate damage functions are considered. Exact analytical solutions for capital dynamics are derived in closed form (with the exception of the Solow–Swan model with CES production function). Numerical examples are provided for illustrative purposes. As the unabated climate change with unlimited temperature growth is assumed, the long-runmodel dynamics are dramatic: the capital converges to zero at infinite time, and the economy collapses.

Acknowledgments

The reported study was supported by the Russian Foundation for Basic Research, research project No. 13-06-00368-a.

References

  1. [1]  Capellán-Pérez, I., González-Eguino, M., Arto, I., Ansuategi, A., Dhavala, K., Patel, P. and Markandya, A. (2014), New climate scenario framework implementation in the GCAM integrated assessment model. BC3 Working Paper Series 2014-04, Basque Centre for Climate Change (BC3), Bilbao, Spain.
  2. [2]  Edenhofer, O., Lessmann, K., Kemfert, C., Grubb, M. and Köhler, J. (2006), Induced technological change: Exploring its implications for the economics of atmospheric stabilization. Synthesis Report for the InnovationModeling Comparison Project, The Energy Journal, Special Issue: Endogenous Technological Change, 57-107.
  3. [3]  Hasselmann, K. (2013), Detecting and responding to climate change, Tellus B, 65, 20088.
  4. [4]  Hasselmann, K., Cremades, R., Filatova, T., Hewitt, R., Jaeger, C., Kovalevsky, D., Voinov, A. and Winder, N. (2015), Free-riders to forerunners, Nature Geoscience, 8, 895-898.
  5. [5]  Hasselmann, K. and Kovalevsky, D.V. (2013), Simulating animal spirits in actor-based environmental models, Environmental Modelling & Software, 44, 10-24.
  6. [6]  Kovalevsky,D.V., Kuzmina, S.I. and Bobylev, L.P. (2015), Impact of nonlinearity of climate damage functions on longterm macroeconomic projections under conditions of global warming, Discontinuity, Nonlinearity, and Complexity, 4, 25-33.
  7. [7]  Moss, S., Pahl-Wostl, C. and Downing, T. (2001), Agent-based integrated assessment modelling: the example of climate change, Integrated Assessment, 2, 17-30.
  8. [8]  Nordhaus, W.D. (1993), Rolling the ‘DICE’: An optimal transition path for controlling greenhouse gases, Resource and Energy Economics, 15, 27-50.
  9. [9]  Nordhaus,W.D. (2008), A Question of Balance, Yale University Press: New Haven & London.
  10. [10]  Nordhaus, W.D. and Yang, Z. (1996), RICE: A regional dynamic general equilibrium model of alternative climatechange strategies, The American Economic Review, 86, 741-765.
  11. [11]  Rovenskaya, E. (2010), Optimal economic growth under stochastic environmental impact: Sensitivity analysis. In: Dynamic Systems, Economic Growth, and the Environment, Vol. 12 of the series Dynamic Modeling and Econometrics in Economics and Finance, J.C. Cuaresma, T. Palokangas, A. Tarasyev (eds.), Springer, 79-107.
  12. [12]  Stanton, E.A., Ackerman, F., and Kartha, S. (2009), Inside the integrated assessment models: four issues in climate economics, Climate and Development, 1, 468-492.
  13. [13]  Stern, N. (2007), The Economics of Climate Change. The Stern Review, Cambridge University Press.
  14. [14]  Tol, R.S.J. (1992), On the uncertainty about the total economic impact of climate change, Environmental and Resource Economics, 53, 97-116.
  15. [15]  van der Ploeg, F. and Withagen, C. (2014), Growth, renewables, and the optimal carbon tax, International Economic Review, 55, 283-311.
  16. [16]  Voinov, A., Seppelt, R., Reis, S., Nabel, J.E.M.S. and Shokravi, S. (2014), Values in socio-environmental modelling: Persuasion for action or excuse for inaction, Environmental Modelling & Software, 53, 207-212.
  17. [17]  Weber, M., Barth, V., and Hasselmann, K. (2005), A multi-actor dynamic integrated assessment model (MADIAM) of induced technological change and sustainable economic growth, Ecological Economics, 54, 306-327.
  18. [18]  Wolf, S., Fürst, S., Mandel, A., Lass, W., Lincke, D., Pablo-Martí, F. and Jaeger, C. (2013), A multi-agent model of several economic regions, Environmental Modelling & Software, 44, 25-43.
  19. [19]  Solow, R.M. (1999), Neoclassical growth theory, In: Handbook on Macroeconomics, Vol. 1, Part A, J.B. Taylor, M. Woodford (eds.), Elsevier, 1999, 637-667.
  20. [20]  Barro, R.J. and Sala-i-Martin, X.I. (2003), Economic Growth, Second Edition, The MIT Press.
  21. [21]  von Neumann, J. (1937), Über ein Ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen, Ergebnisse eines Mathematische Kolloquiums, 8, translated by Karl Menger as “A model of general equilibrium”, Review of Economic Studies (1945), 13, 1-9.
  22. [22]  Knight, F.H. (1944), Diminishing returns from investment, Journal of Political Economy, 52, 26-47.
  23. [23]  Dietz, S. (2011), High impact, low probability? An empirical analysis of risk in the economics of climate change, Climatic Change, 108, 519-541.
  24. [24]  Nordhaus, W.D. (1992), The ‘DICE’ model: Background and structure of a dynamic integrated climate-economy model of the economics of global warming. Cowles Foundation Discussion Paper No. 1009. Cowles Foundation for Research in Economics, Yale University.
  25. [25]  Royce, B.S.H. and Lam S.H. (2013), The Earth’s climate sensitivity and thermal inertia. Department ofMechanical and Aerospace Engineering, Princeton University. Princeton, NJ, USA. Mimeo. URL: https://www.princeton. edu/~lam/documents/RoyceLam2010.pdf (accessed 15 December 2015).
  26. [26]  Kovalevsky, D.V., Kuzmina, S.I. and Bobylev, L.P. (2014), Projecting the global macroeconomic dynamics under highend temperature scenarios and strongly nonlinear climate damage functions, Russian Journal of Earth Sciences, 14, ES3001.
  27. [27]  Weitzman, M.L. (2012), GHG targets as insurance against catastrophic climate damages, Journal of Public Economic Theory, 14, 221-244.
  28. [28]  Sorger, G. (2003), On the multi-country version of the Solow–Swan model, The Japanese Economic Review, 54, 146- 164.
  29. [29]  Bretschger, L. and Valente, S. (2011), Climate change and uneven development, The Scandinavian Journal of Economics, 113, 825-845.
  30. [30]  Ikefuji, M. and Horii, R. (2012), Natural disasters in a two-sector model of endogenous growth, Journal of Public Economics, 96, 784-796.
  31. [31]  Kovalevsky, D.V. (2014), A climate-economic model with endogenous capital depreciation rate under uncertainty of temperature projections, Scientific Journal of KubSAU, No. 10(104). IDA [article ID]: 1041410089. URL: http: //ej.kubagro.ru/2014/10/pdf/89.pdf
  32. [32]  Solow, R.M. (1956), A contribution to the theory of economic growth, Quarterly Journal of Economics, 70, 65-94.
  33. [33]  Swan, T.W. (1956), Economic growth and capital accumulation, Economic Record, 32, 334-361.
  34. [34]  Novales, A., Fernández, E. and Ruíz, J. (2014), Economic Growth: Theory and Numerical Solution Methods, Second Edition, Springer.
  35. [35]  Guerrini, L. (2006), The Solow–Swan model with a bounded population growth rate, Journal of Mathematical Economics, 42, 14-21.
  36. [36]  Abel, A.B., Bernanke, B.S. and Croushore, D. (2013), Macroeconomics, Global Edition, Eighth Edition, Pearson.