Consider the global warming environment discussed in class, where each rm gains utility as a function of their consumptions, faces costs according to the current stock of greenhouse gases, and greenhouse gases are persistent across periods according to a transition equation. In particular, suppose that the utility function is linear uiECCit), and the costs of global warming are quadratic in the current stock of greenhouse gases C(g) = 92. The transition equation is Q: = \"gt1 + Clt + r32t- A. Write down the expression for per-period net utility. B. Formulate the social optimality problem when there is just one more period of emission left. What is the socially optimal net utility level V1(g)? C. Formulate the social optimality problem when there are two periods left. What is the socially optimal consumption rule? What is the socially optimal net utility level V2 (g)? D. Repeat the pmw'ompmbiemr 3 mmaiigperiodr (y'emirrim: Formulate the social optimality problem when there are three periods left. What is the socially optimal consumption rule? What is the socially optimal net utility level V3 (g)? E. What can you infer about the general case of T remaining emissions periods? What if there are an innite number of periods? F. Are we able to use the trick discussed in class to solve this problem? Why or why not? Does the global optimal consumption level depend on the inherited greenhouse gas stock 9? G. Formulate the \"Business as Usual\" problem when there is just one more period of emissions left. What is the BAU net utility level W1(g)? Is it higher or lower than V1(g)? H. Formulate the BAU problem when there are two periods left. What is the BAU equilibrium consumption rule? What is the BAE equilibrium net utility level V2 (g)? 1. Repeat the previous problem for 3 remaining periods of emission: Formulate the BAU problem when there are three periods left. What is the BAU equilibrium consumption rule? What is the BAE equilibrium net utility level V3(g)? J. What can you infer about the general case of T remaining emission periods? What if there are an innite number of periods? Does the BAU consumption level depend on the inherited greenhouse gas stock 9? Is it higher or lower than the socially optimal consumption amount