- = With carbon input equal to 8.36GtC in 2010, we obtain (8.36 / 2.13) / 63 0.062. σ = = Finally, given 1 1 L A = we can back out A = 34.67.
Paper not yet in RePEc: Add citation now
Ackerman, F., Stanton, E., 2012. Climate risks and carbon prices: revising the social cost of carbon. Economics, The Open-Access, Open-Assessment E-Journal, 6, 2012-10.
- AK A L F R Z Z Z Z Ï‘ Ï‘ Ï‘ α α β β σ − − − −       +   = − +       ï£ ï£¸ ï£ ï£¸   We set the share of capital to α = 0.35, the energy share parameter to β = 0.05, and the elasticity of factor substitution to 1 Ï‘ = . World GDP in 2010 is 63 $trillion. The energy intensity of output σ is calibrated to current energy use. In the Leontief case energy demand (only fossil fuel initially) is 0 0 0. F D Z σ
Paper not yet in RePEc: Add citation now
- Appendix B: Necessary optimality conditions for the simple model We use a version of Golosov et al. (2014) which conflates coal, oil and natural gas into one fossil fuel source, Ft . The SCC is derived assuming that ( / ) ln( / ) t t t t U C L C L = , δ = 1, ( ) ( ) , t E E t D E e γ − − = 1 0 , t t t t t Z A L K H α υ α υ − − = and ( ) 1/ 1 2 t t t H F R χ χ χ κ κ = + with 1/ (1 ) 0 ε χ ≡ − > the elasticity of factor substitution. Only labor is needed to extract fossil fuel or produce renewable energy: Ft = AFt LFt and Rt = AR,t LR,t. Labor is perfectly mobile between the final goods and energy sectors: (B.1) 0 / / . t t t Ft t Rt L L F A R A =+ + where Lt denotes the exogenous aggregate supply of labor. The carbon cycle is still given by (3)-(5).
Paper not yet in RePEc: Add citation now
Brock, W., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory, 4, 3, 479-513.
- Following Golosov et al. (2014), the decay rate for the transient stock of atmospheric carbon is 0.0228 ϕ = and 0.2, L ϕ = so that 20% of carbon emissions stay up ‘forever’ in the atmosphere and the remainder has a mean life of about 300 years The parameter 0 0.393 ϕ = is calibrated so that about half of the carbon impulse is removed after 30 years. We set 0 103 P E = GtC and 0 699 T E = GtC. We suppose an equilibrium climate sensitivity of ω = 3.
Paper not yet in RePEc: Add citation now
Gerlagh, R., Liski, M., 2012). Carbon prices for the next thousand years. CESifo Working Paper Series No. 3855. CESifo, Munich.
Golosov, M., Hassler, J., Krusell, P., Tsyvinski, A., 2014. Optimal taxes on fossil fuel in general equilibrium. Econometrica, 82, 1, 41-88.
Hassler, J., Krusell, P., 2012. Economics and climate change: integrated assessment in a multi-region world. Journal of the European Economic Association, 10(5), 974-1000.
- IEA, 2008. World Energy Outlook 2008. http://www.iea.org/textbase/nppdf/free/2008/weo2008.pdf.
Paper not yet in RePEc: Add citation now
- IPCC, 2007. Climate Change 2007, the Fourth IPCC Assessment Report. http://www.ipcc.ch/ipccreports/ar4-syr.htm Nordhaus, W., 2008. A Question of Balance: Economic Models of Climate Change. Yale University Press, New Haven, Connecticut.
Paper not yet in RePEc: Add citation now
Iverson, T., 2013. Optimal carbon taxes with non-constant time preference. Mimeo., Colorado State University.
- Nordhaus (2008) assumes an upper limit for carbon-based fuel of 6000 GtC in the DICE-07. 4
Paper not yet in RePEc: Add citation now
- Nordhaus (2008) supposes that with global warming of 2.5o C damages are 1.7% of world GDP and uses this to calibrate: 2 2 1 1 ( ) . 1 0.00284 1 ( /18.8) t t t D T T T = = + + Weitzman (2010) argues that global warming damages rise more rapidly at higher levels of mean global temperature. With climate damages equal to 50% of world GDP at 6o C and 99% at 12.5o C, Ackerman and Stanton (2012) calibrate 2 6.76 1 ( ) . 1 ( / 20.2) ( / 6.08) t t t D T T T = + + The extra term in the denominator captures potentially catastrophic losses at high temperatures. Computational implementation The transversality condition for the model is 1 2 lim ( ) 0.
Paper not yet in RePEc: Add citation now
- Population in 2010 (L1) is 6.5 billion people. Following Nordhaus (2008) and UN projections population growth is given by 0.35 8.6 2.1 t t L e− = − . Population growth starts at 1% per year and falls below 1% percent per decade within six decades and flattens out at 8.6 billion people. Without loss of generality the efficiency of labor 0.2 3 2 L t t A e− = − starts out with 1 1 L A = and an initial Harrod-neutral rate of technical progress of 2% per year. The efficiency of labor stabilizes at 3 times its current level. 3
Paper not yet in RePEc: Add citation now
Rezai, A., 2011. The opportunity cost of climate policy: a question of reference. Scandinavian Journal of Economics, 113, 885-903.
Rezai, A., van der Ploeg, F., 2013. Abandoning fossil fuel: how fast and how much? OxCarre Research Paper 123, University of Oxford.
- Since 2 2 (1000) / (4000) (4000 /1000) 4 G G γ γ = = and 0.75 4 2.8 = . A5 Output before damages is ( ) 1 1 1/ 1 1/ 1 1 1/ (1 ) ( ) ( ) , L t t t t t t F R Z AK A L ϑ ϑ α α ϑ β β σ − − − − +   = − +     0, 0 1 ϑ α ≥ < < and 0 1. β < < This is a constant-returns-to scale CES production function in energy and a capitallabor composite with ϑ the elasticity of substitution, β the share the parameter for energy, and σ the carbon intensity of output. The capital-labor composite is defined by a constant-returns-to-scale CobbDouglas function with α the share of capital, A total factor productivity and L t A the efficiency of labor. The two types of energy are perfect substitutes in production. Damages are calibrated so that they give the same climate damages for the initial levels of output and mean temperature. It is convenient to rewrite production before damages as 1 1 1/ 1 1/ 1 1/ 1 0 0 0 ( ) (1 ) . L t t t t t t
Paper not yet in RePEc: Add citation now
- Stocks of carbon-based energy sources are notoriously hard to estimate. IPCC (2007) assumes in its A2scenario that 7000 GtCO2 (with 3.66 tCO2 per tC this equals 1912 GtC) will be burnt with a rising trend this century alone. We roughly double this number to get our estimate of 4000 GtC for initial fossil fuel reserves.
Paper not yet in RePEc: Add citation now
- The initial capital stock is set to 200 (US$ trillion), which is taken from Rezai and van der Ploeg (2013). We set δ to be 0.5 per decade, which corresponds to a yearly depreciation rate of 6.7%.
Paper not yet in RePEc: Add citation now