9. (1) Show that the UIP equation can be reexpressed as log 35 log 30 = [10 13) + (1; 1"1"3) + (1:3a 1';'3) where S; = Eg[33], if 2 Edit] and 1:3 = 1E0[1':] for t = 1,2, (2) Suppose that the foreign interest rate is determined by the foreign central bank as the following: .* _ no; )0: 31H '31 + errorl where errorg'H = 1:\" Et[1;"+1] is the prediction error at time t+ 1, and IE: [erro' +1] 2 0 for all t = U, 1, 2, The domestic central bank controls the domestic interest rate in one of the following policy rules: Rule A The domestic interest rate is equal to the lagged foreign interest rate. it+1 : 3": Rule B The domestic interest rate depends on the lagged foreign interest rate. 1t+1 = 1;\" + errort+1 Rule C The domestic interest rate is independent of the the foreign interest rate. it+1 : '51 + BTTOTtH where error + 1 is the monetary policy shock at time t+1, and Et [error +1) = 0 for all t = 0, 1, 2, ... Now suppose that the current foreign interest rate, decreases by 1%p whereas the current domestic interest rate, io is fixed. For each policy rule, compute the impact of the fall in i, on (log S5 - log So). (3) What is the implication of the findings from the Question 9-(2)