2. (20 points) Consider the following investment decision. The rm's future output is given by Y} : Z! (Kr)0.4 (NI)U.6 , where: Y' is future output; K ' is future capital; N ' = 1977.9 is future labor, measured in hours per year; and z' = 0.08 is future total factor productivity. Capital evolves according to K' = (1d)K+I, where: K = 296 is current capital; d = 0.07 is the depreciation rate and I denotes investment. The rm chooses future capital to maximize V = 2 (1K)\" (000-6 wN [K' (1 d)K] 1 z' (K')0'4 (N')0'6 w'N' + (1 d)K'] . +1lr where r = 0.03 is the real interest rate. (a) (4 points) Compute the optimal value of K'. After you compute the desired future capital, compute the desired investment. (b) (4 points) Suppose z (K)0'4 (N)0'6 wN w'N' = 0. Show that the value of K ' computed in part (a) is indeed the optimal value of K ' by completing the following table: Y' = I = K' 2' (K')0'4 (N')0'6 (1 d) K' K ( 291.000 value from part (a) 300.000 (c) (2 points) Suppose that current capital, K, increases from 296 to 308. What is desired investment now? (d) (4 points) Suppose that 2.\" increases to 0.082, while K is back at its original value of 296. Compute the new optimal value of K' and the new desired investment. (e) (2 points) Suppose that 2' increases to 0.082, while K , increases from 296 to 308. What is desired investment now? (f) (4 points) On a single graph, show how the changes you considered in parts (c), (d) and (e) shift the desired investment schedule. You should clearly label the four curves: one for part (a), one for part (c), one for part ((1), and one for part (e), and include the values of desired investment at \"r = 0.03 under each case