would someone be able to help me solve this problem? b) to e)

Exercise 4: Consider a two-period economy: A rm produces output (Y) with capital (K ) according to the following production function Y; = 223K735 in which zt is an index of total factor productivity in period t. A portion 6 of the capital stock used in the production func- tion needs to be repaired each period and new capital installed in any period t becomes productive a period later only. Prots in period 0 and in period 1 are respectively given by 71'0 = Yb + (1 6)K0 K1 and by 7T1 = Y1 + (1 6)K1. The goal of this rm is to maximize the present value of prots 7T0 + (1 / (1 + T))7T1 by choosing K1, given K0, \"r, 2:0, and 21. Suppose that K0 2 16, that 20 = 21 = 1, that 6 = 0.10, and that 7\" = 0.10. a) Explain what the marginal product of capital measures. Explain what the user cost of capital is. Why is it optimal for the rm to choose K1 so that the marginal product of capital in period 1 is equal to the user cost of capital? b) Find the optimal value of K1. How much does this rm need to invest in period 0 to achieve this value of K1? Calculate 7m. What do you conclude? c) Suppose that 2:1 is expected to fall. How will investment be affected in period 0? Explain. d) Suppose that 2:0 falls. Ebiplai why a fall in 2:0 does not directly affect investment. Explain why investment may nevertheless fall in equilibrium (hint: what happens to 7' when 20 falls?). e) Suppose that investment is added to aggregate demand in period 0 (i.e. ADD 2 03' (r) I I0 + GO). Use a graph of the goods market to describe what would happen to investment if the government increases GO. Will Yb increase? What about Y1