Question 3 Assume that the current stock of CO2 held in the atmosphere is s0 (measured in Gt), and evolves according to: st = st1 + et where st is the stock at the end of period t. To simplify the analysis, consider 20-year increments, so that t = 0 is today, t = 1 represents the next 20 years, t = 2 the following 20 years and so on. The persistence rate of CO2 in the atmosphere is (the amount remaining after 20 years). Assume that emissions are et every 20 years. The total damages over a 20 year period are Dt = 0.01s 2t,where st is the end-of-period stock of CO2. 1. Write the stock of CO2 in the atmosphere at the end of period t = 1, 2, 3, 4, 5 as a function of s0 and emissions in each period. 2. Find an expression for the marginal damage done in period t = 5 from emissions released during period 2, e1. Generalize your expression to find the marginal damage done in period t from e1. 3. Calculate the marginal damage done over the next 100 years by e1. Assume that the social discount rate is 0.3, s0 = 5000, et = 1000 and = 0.9. Marginal damages are measured at the end of each period (so that we discount t = 1 once). 4. The social discount rate used in part 3 is high, because it is representing a long period of 20 years. It is equivalent to an annual rate of around 0.014 (or 1.4%). If we used a higher discount rate, would the damages you calculated in part 3 be lower or higher? Give an intuitive explanation for your answer.