Let the following represent the structure of a SMALL OPEN ECONOMY with PERFECT CAPITAL MOBILITY and FIXED EXCHANGE RATE REGIME: C = Ca + 0.75(Y-T), Ca = 90, T= 40+0.2Y, G=45, IP = 75 - 5r, NX = 80 - 0.1Y - 5e, (M/P)D = 0.2Y-2r, MS/P = 80. a)Assume that initially foreign and domestic interest rates are equal so that r = rf and let the foreign exchange rate e=4. Find the IS and LM equations. b)Find the equilibrium income, interest rate and net exports c) Suppose autonomous planned consumption, Ca, goes down from 90 to 60. (C1) Write down the new IS curve, after the shift in autonomous planned consumption. d) Let domestic interest rates and world interest rates briefly diverge: capital investors have not reacted yet, and neither has the government or central bank. Use the new IS curve and the LM curve to calculate the new output and domestic interest rate. e) What is the new output Y and interest rate r? What factors adjust to get the economy here? (Hint: Recall that the economy has a fixed exchange rate, and perfect capital mobility.)