Environmental: Let the initial stock of greenhouse gasses be represented as S1 = E1 , where E1 is the initial level of emissions. Suppose we are interested in the accumulation of greenhouse gasses over the next two periods, i.e. t = 2 and t = 3. Assume that greenhouse gasses dissipate from period t to t+1 at a rate of . Further assume that emissions grow at a constant rate g from period t to t+1. a. (3 pts) Find the evolution of greenhouse gas stock over the next two periods, i.e. S2 and S3 . [NOTE: Your solution should be in terms of g, , and E1 for full credit] b. (4 pts) Suppose the federal government can invest in next-generation technology to mitigate damages associated with increased greenhouse gas stock. The per-period benefit (avoided damages due to investment) is given by the function Bt = St . Suppose that the investment is simply a per-period payment c. Find the net present value of the investment opportunity (assume that the investment decision is applicable to all periods, i.e. 1, 2, and 3). [NOTE: Your solution should be in terms of , c, g, , E1 , and discount rate R for full credit] c. (3 pts) For what values of would the government decide to invest in this technology? [NOTE: Your solution should be an inequality for in terms of c, g, , E1 , and discount rate R for full credit]