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Appendix A

Solution Algorithm

Step A. Find the Economy s Steady State

Guess K-, compute the supply of capital Xs, update Kei+1 = 0.8Xe + 0.2Ks, and iterate until \KeM -- Щ | < Ј.

Step B. Find T

The price of energy at T satisfies

Let us set x at 1 and find a date T at which cumulative oil consumption exceeds oil reserves, but at date T -- 1 cumulative oil consumption is less than oil reserves. Then in step C we iterate on x to equalize cumulative oil consumption and oil reserves at time T. We also define

some large value, M, by which time the model converges to its steady state.

Step B1. Set T = 0.

Step B2. Set x = 1.

Step B3. Guess K't, te [1, T + 1].

Step B4. Given the value of K'T+1 in the non-oil regime, find a transition path from T + 1 to the steady state by iterating over the path of capital. Guess K't , te [T + 2, M - 1], update K/+1 = 0.8Kj + 0.2Kts, te [T + 2, M- 1], iterate until || K/+1 - Kj ||^< є, te [T + 2, M- 1]. The converged solution provides paths for all variables at t є [T + 2, M - 1].

Step B5. Guess

Step B6. For t < T and given the path for price of energy, determine the allocation of total capital and labor between clean energy and final goods production sectors using the bisection method to solve the nonlinear system of equations (30)-(33). Compute rt and update the guess

of the price path for energy:

t < T.

Step B7. Fixed point iterations on price of energy. Repeat step B6 until

Step B8. Compute capital supply Update the path of capital K/+1 = 0.8Kt + 0.2Kf, U= [1, T + 1].

Step B9. Repeat steps B4-B8 until

Step B10. Compute YP.

Step B11. If and repeat steps B2-B10, else stop

Step C. Find Transition Path

We have found date T at which cumulative oil consumption exceeds oil reserves. But at date T - 1 cumulative oil consumption is less than oil reserves. Now we will solve for the transition path that entails equalization of cumulative oil consumption and oil reserves at T. At steps B3-

B10 we have a mapping Define a function

Solve the equation g(x) = 0, [1, - ] using the bisection method, where x- is some upper bound for x. For each xt we need to iterate on steps B3-B10.

Appendix B

Supplementary Figures

Note. Solid line indicates baseline. Dotted line indicates transition with the double growth rate gB. Ot -- oil, pt -- price of energy, Vt

Figure B1 The Transition with Faster Technical Progress in Clean Energy (Detrended Variables) Note. Solid line indicates baseline. Dotted line indicates transition with the double growth rate gB. Ot -- oil, pt -- price of energy, Vt -- value of oil company, Jt -- CO2 concentration, Dt -- damages, фt -- absolute tax per unit of oil, St -- clean energy production, nt -- rental price of land, Qt -- value of land, Et -- total energy consumption, Kt -- total capital, Ks,t -- clean energy sector's capital, Ky,t -- final goods production sector's capital, wt -- real wage rate, rt -- real interest rate, Yt -- final output, ct y -- consumption of young households, ct o -- consumption of old households, gY -- steady state growth rate of output, gS -- steady state growth rate of clean energy

Figure B2 Transition with Faster Technical Progress in the Final Goods Sector (Detrended Variables) Note. Solid line indicates baseline. Dotted line indicates transition with the double growth rate gZ. Ot -- oil, pt -- price of energy, Vt -- value of oil company, Jt -- CO2 concentration, Dt -- damages, фt -- absolute tax per unit of oil, St -- clean energy production, nt -- rental price of land, Qt -- value of land, Et -- total energy consumption, Kt -- total capital, Ks,t -- clean energy sector's capital, Ky,t -- final goods production sector's capital, wt -- real wage rate, rt -- real interest rate, Yt -- final output, ct y -- consumption of young households, ct o -- consumption of old households, gY -- steady state growth rate of output, gS -- steady state growth rate of clean energy.

Figure B3 The Transition with Faster Economy Wide Technical Progress (Detrended Variables) Note. Solid line indicates baseline. Dotted line indicates transition with the double growth rates gB and gZ, and thus gY. Ot -- oil, pt -- price of energy, Vt -- value of oil company, Jt -- CO2 concentration, Dt -- damages, фt -- absolute tax per unit of oil, St -- clean energy production, nt -- rental price of land, Qt -- value of land, Et -- total energy consumption, Kt -- total capital, Ks,t -- clean energy sector's capital, Ky,t -- final goods production sector's capital, wt -- real wage rate, rt -- real interest rate, Yt -- final output, ct y -- consumption of young households, ct o -- consumption of old households, gY -- steady state growth rate of output, gS -- steady state growth rate of clean energy.

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