QUESTION 2: EFFICIENT INVESTMENT Norway and Uganda are small open economies and face the real interest rates (it = 0.1) in the international borrowing market. Normay's production function in terms of capital and production per worker is: or = Auk" (2) Uganda's production function in terms of capital and production per worker is: a = Auk\" (3) Wherek: K/L,q = Q/L and AN >Au. Suppose that both countries produce a numeraire good with price equal to 1. a) Calcalate the marginal product of capital for each comtry. b) Setup the profit maximization problem of each c0untry using the production functions in equations (2) and (3) and take the first order condition. c) Use the rst order condition in b) and the production function to derive a linear equation for q as a function of k. What does this line represent? d) let 9 = 1/ 2, AN = 2 and Au = 1. Graph (on the same graph) both countries' production functions and the line you derived in c). e) Calculate the prot maximizing level of capital for each c0untry and indicate them on the graph