Problem 1 : Consider the following GDP equation , consumption function , exports function .imports function and investment function and use them to answer the following questions Yt = C+ + + + G+ + EX, -IM. = a; - b(R. - r); b >0 G = a,Yt EX = 0 IM = 0 (a) Derive the IS curve as a relation between short run output and the real interest rate gap Rt - r. (b) Find the government spending multiplier {) holding the real interest rate constant. (c) Is the multiplier derived in b) greater than one or smaller than one? Briefly provide intuition for your answer along with mathematical reasoning. (d) Consider the following MP curve where monetary policy and real interest rates now depends on the short-run output. Re - r = nY. Derive the AD curve. (e) Find the government spending multiplier f. ). If " is positive , is the multiplier higher or lower than in part c)