y' +(1-d)K' Suppose a firm optimizes the two-period profit function: V = Y - 1+-+ 1+r Current output is given by Y = zka, and future output is given by Y' = z'(K)a. Recall that K' = (1 - d)K+ 1. a) Let z = 2, z' = 4, K = 100, d = 0.1, r= 0.05, and a = 0.5. What is the optimal level of investment, 1*, that maximizes the two-period profit function? b) Now suppose the interest rate rises from r = 0.05 to r = 0.10. What is the new optimal level of investment? c) Now suppose that current capital K rises from K = 100 to K =150. What is the new optimal level of investment (evaluated at the original interest rate of r = 0.05)? y' +(1-d)K' Suppose a firm optimizes the two-period profit function: V = Y - 1+-+ 1+r Current output is given by Y = zka, and future output is given by Y' = z'(K)a. Recall that K' = (1 - d)K+ 1. a) Let z = 2, z' = 4, K = 100, d = 0.1, r= 0.05, and a = 0.5. What is the optimal level of investment, 1*, that maximizes the two-period profit function? b) Now suppose the interest rate rises from r = 0.05 to r = 0.10. What is the new optimal level of investment? c) Now suppose that current capital K rises from K = 100 to K =150. What is the new optimal level of investment (evaluated at the original interest rate of r = 0.05)