Reference no: EM133556894

Case: Stock Pollution Assume that the current stock of CO2 held in the atmosphere is s0 in Gt, and evolves according to: st = δst-1 + et where st is the stock at the end of period t. To simplify the analysis, consider 50-year increments, so that t=0 is today, t=1 represents the next 50 years, t=2 the following 50 years and so on. The persistence rate of CO2 in the atmosphere is δ (the amount remaining after 50 years). Assume that emissions are constant at et every 50 years. The total damages over a 50 year period are: Dt = 0.02s 2 t where st is the end-of-period stock of CO2.

Question 1. Write the stock of CO2 in the atmosphere at the end of period t = 1, 2, 3 as a function of s0 and emissions in each period.

Question 2. Find an expression for the marginal damage done in period t=3 from emissions released during period 1, e1.

Question 3. Suppose that s0=4000 and emissions each period are constant at et = 2000 for t = 1, 2, 3. Also assume that δ = 0.8. What is the present value of damages caused by a small increase in emissions in period 1? Assume that the social discount rate for a 50 year period is 0.6, and that marginal damages are measured at the end of each period (so that we discount t=1 once).

Question 4. How much should society as a whole be willing to pay to reduce emissions in period 1 by a small amount, based on the damage that these emissions would do over 150 years?