Consider a two-period economy: A rm produces output LY ) with capital (K) according to the following production function Y; = 2.th3'5 in which 2: 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 byrro = %+(15)KoK1 311d by'zn =Y1+(15)K1. Thegoalofthisrm is to maximize the present value of prots so + (1/(1 + T))7l'1 by choosing K1, given K0, \"r. 20., and 21. Suppose that K0 = 16, that 2:0 = :51 = 1. that 6 = 0.10, and that r = 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 I] to achieve this value of K 1? Calculate 7m. What do you conclude? c) Suppose that 21 is expected to fall. How will investment be affected in period 0? Ebcplain. d) Suppose that 20 falls. Explain why a fall in 20 does not directly affect investment. Ebcplain why investment may nevertheless ll in equilibrium (hint: what happens to 7' when 20 falls?). e) Suppose that investment is added to aggregate demand in period 0 (Le. ADO = Cr) + In + Go). Use a graph of the goods market to describe what would happen to investment if the government increases G0. Will Y0 increase? What about Y1