(25 points). Consider a standard onesector Solow model with a xed savings rate .5. Output is produced via the production function Y; = Knga As usual, labor is inelastically supplied and grows at the exogenous rate 71 (i.e., Lt+1 = Suppose that each unit of output produced generates 9; units of 'pollution', and that due to exogenous technological progress in pollution abatement, 9: decreases over time at rate 9,; (i.e., Qt+1/Qt = 1/ (1 + 9.1)). In addition, suppose that there is an 'abatement technology' that allows resources to be diverted into pollution reduction. Specically, if 9 represents the share of output used in pollution reduction, then not pollution emission, E3, is given by E1; = G(9)Qtn (1) where (1(9) is assumed to be a positive, decreasing function. For simplicity, assume that 9 is constant and exogenous. As usual, for notational convenience, let 3;; represent net output available for consumption and capital accumulation per capita. That is, (1 6)Y L Similarly, let k and e be capital and net pollution emission per capita. Using this notation, we have the following 'green Solow' model: y: y: = (1 9),\"? Akt+1 = 5(1 6M? (6 + n)kt e; = a(9)9k rxzx 05m UV where 6 is the depreciation rate of capital. Evidently, from equation (2), the economy will converge to a unique steady state k, = 36*. From equation (3), it is then clear that in the steady state (ie, when is; is constant), pollution grows at a constant rate, 95, given by AEt+1 1 + in. 95' = = E; 1 + 9,] 1mnga Of course, during the transition to the steady state, pollution may be growing either faster or slower than this. Now, let's dene 'sustainable' growth to be a situation where ya 2 71. That is, pollution remains bounded. (a) It is often claimed that the time path of pollution within economies follows a socalled 'Environmental Kuznets Curve' (EKC), with pollution rising as the economy develops, and then eventually falling once the economy becomes wealthy enough (i.e., it traces out an inverted Ushape when plotted against either time or per capita income). Consider a sustainable economy, where 913