Long Question 1: (70 points) Consider the short run model of Chapters 1 1 and 12. The national income identity is given by Y = Cq + h + Gt + EX, - IM, (1) Where Y is real actual output, Ct is consumption, It is investment, Gt is government spending, EX. is exports, and IM, is imports (all in period t). Assume that the "demand" variables are given by: Ct/ 7, = ac (2) Gt/ = ag (3) (4 ) IMt/ = dim (5) 1/p. = al - b(R - ) (6) Where ac , ag , dex , dim , a; , g and b are given positive parameters. Moreover, Y represents potential output, Y, is short-run output, R, is the real interest rate, and r is the marginal product of capital or just the long run interest rate. a) Combine equations (2)-(6) with (1) to obtain the IS curve. This curve should have short run output on the left-hand side and the real interest rate on the right-hand side. Recall from the lectures that we defined short run output as Y, = . In other words, short run output is the percentage difference of actual output from the potential. (15 points)