Environmental Economics and Policy Studies

, Volume 17, Issue 2, pp 185–210 | Cite as

Untapped fossil fuel and the green paradox: a classroom calibration of the optimal carbon tax

  • Frederick van der PloegEmail author
Research Article Energy and Climate Economics and Policy


A classroom model of global warming, fossil fuel depletion and the optimal carbon tax is formulated and calibrated. It features iso-elastic fossil fuel demand, stock-dependent fossil fuel extraction costs, an exogenous interest rate and no decay of the atmospheric stock of carbon. The optimal carbon tax reduces emissions from burning fossil fuel, both in the short and medium run. Furthermore, it brings forward the date that renewables take over from fossil fuel and encourages the market to keep more fossil fuel locked up. A renewables subsidy induces faster fossil fuel extraction and thus accelerates global warming during the fossil fuel phase, but brings forward the carbon-free era, locks up more fossil fuel reserves and thus ultimately curbs cumulative carbon emissions and global warming. For relatively large subsidies social welfare is more likely to fall as the economic costs rises more than proportionally with the size of the subsidy. Our calibration suggests that such subsidies are not a good second-best alternative for the carbon tax. Of course, such subsidies are required if markets fail to internalize learning-by-doing externalities in renewable production.


Global warming Social cost of carbon Optimal carbon tax Renewable Energy transitions 

JEL Classification

D81 H20 Q31 Q38 



Support from the European Research Council for the Advanced Instigator Grant ‘Political Economy of Green Paradoxes’ is gratefully acknowledged. I have benefited from many helpful discussions with Armon Rezai and Cees Withagen and useful comments from Florian Habermacher, SamWills, Niko Jaakkola and two anonymous referees


  1. Acemoglu D, Aghion P, Bursztyn L, Hemous D (2012) The environment and directed technical change. Am Econ Rev 102(1):131–166CrossRefGoogle Scholar
  2. Ackerman F, Stanton EA (2012) Climate risks and carbon prices: revising the social cost of carbon. Economics 6(10):1–25Google Scholar
  3. Allen MR, Frame DJ, Mason CF (2009a) The case for mandatory sequestration, Nature Geosci pp 813–814Google Scholar
  4. Allen MR, Frame DJ, Huntingford C, Jones CD, Lowe JA, Meinshausen M, Meinshausen N (2009b) Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458:1163–1166CrossRefGoogle Scholar
  5. BP (2012) Statistical review of world energy, London, UKGoogle Scholar
  6. de Mooij R, Parry IWH, Keen M (eds) (2012) Fiscal policy to mitigate climate change—a guide for policy makers. International Monetary Fund, WashingtonGoogle Scholar
  7. Gerlagh R, Liski M (2013) Carbon prices for the next thousand years, mimeo., Tilburg UniversityGoogle Scholar
  8. Golosov M, Hassler J, Krusell P, Tsyvinski A (2014) Optimal taxes on fossil fuel in general equilibrium. Econometrica 81(2):41–88Google Scholar
  9. Hanemann WM (2008) What is the economic cost of climate change? eScholarship. University of California, BerkeleyGoogle Scholar
  10. Hassler J, Krusell P, Olovsson P (2011) Energy-saving directed technical change, mimeo., University of StockholmGoogle Scholar
  11. Hassler J, Krusell P (2012) Economics and climate change: integrated assessment in a multi-region world, J. Schumpeter Lecture, University of StockholmGoogle Scholar
  12. Helm D (2012) The carbon crunch: how we’re getting climate change wrong—and how to fix it. Yale University Press, New Haven and LondonCrossRefGoogle Scholar
  13. Herfindahl OC (1967) Depletion and economic theory. In: Gaffney M (ed) Extractive resources and taxation. University of Wisconsin Press, Wisconsin, pp 63–90Google Scholar
  14. Hope CW (2006) The marginal impact of CO2 from PAGE 2002: an integrated assessment model incorporating the IPCC’s five reasons for concern. Integr Assess 6:1–16Google Scholar
  15. Hübler M, Baumstark L, Leimbach M, Edenhofer O, Bauer N (2012) An integrated assessment model with endogenous growth. Ecol Econ 83:118–131CrossRefGoogle Scholar
  16. IMF (2013) Energy subsidy reform: lessons and implications. International Monetary Fund, WashingtonGoogle Scholar
  17. IPCC (2007) Fourth assessment report. Intergovernmental Panel of Climate Change, GenevaGoogle Scholar
  18. IPCC (2014) Fourth assessment report. Intergovernmental Panel of Climate Change, GenevaGoogle Scholar
  19. Liski M, Tahvonen O (2004) Can carbon tax eat OPEC’s rents. J Environ Eco Manage 47(1):1–12CrossRefGoogle Scholar
  20. Nordhaus WD (2008) A Question of balance: economic modeling of global warming. Yale University Press, New HavenGoogle Scholar
  21. Otto A, Otto FEL, Boucher O, Church J, Hegerl G, Forster PM, Gillett NP, Gregory J, Johnson GC, Knutti R, Lewis N, Lohmann U, Marotzke J, Myhre G, Shindell D, Stevens B, Allen MR (2013) Energy budget constraints on climate change, Nature Geosci, pp 1–2Google Scholar
  22. Rezai A, van der Ploeg F (2013) Abandoning fossil fuel: how fast and how much, research paper 123. University of Oxford, OxCarreGoogle Scholar
  23. Rezai A, Foley D, Taylor L (2012) Global warming and economic externalities. Econ Theor 49:329–351CrossRefGoogle Scholar
  24. Sinn HW (2008) Public policies against global warming. Int Tax Publ Finance 15(4):360–394CrossRefGoogle Scholar
  25. Stern NH (2007) The economics of climate change—the stern review. Oxford University Press, OxfordCrossRefGoogle Scholar
  26. The Economist (2013) Unburnable fuel—energy firms and climate change, The Economist, 4 May.|c&fsrc=scn/tw_app_iphoneGoogle Scholar
  27. Tol R (2002) Estimates of the damage costs of climate change, part I: benchmark estimates. Environ Resour Econ 22:47–73CrossRefGoogle Scholar
  28. van der Ploeg F, Withagen C (2012a) Is there really a Green Paradox? J Environ Eco Manage 64(3):342–363CrossRefGoogle Scholar
  29. van der Ploeg F, Withagen C (2012b) Too much coal, too little oil. J Publ Eco 96:62–77CrossRefGoogle Scholar
  30. van der Ploeg F, Withagen C (2014) Growth, renewables and the optimal carbon tax. Int Eco Rev 55(1):283–311CrossRefGoogle Scholar
  31. Weitzman ML (2012) GHG targets as insurance against catastrophic climate damages. J Publ Eco Theory 14(2):221–244CrossRefGoogle Scholar

Copyright information

© Society for Environmental Economics and Policy Studies and Springer Japan 2014

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of OxfordOxfordUK
  2. 2.VU University AmsterdamAmsterdamThe Netherlands

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