Question 4 (25 points) Topics 8 & 9 Macroland is a closed economy that can be described by the IS-LM model. Long-run level of output: YFE = 30000 Consumption: C = 8250 + 0508' T) 400r Investment: I = 5000 100r Government spending: G = 6500 Taxes: T = 5500 Real money demand: L(r, Y) = 0.2Y 5 0r Note: Interest rate, r, is expressed in percentage points, i.e., if r = 7.5, then r = 7.5%. Keep your answers to 3 decimal points if necessary. a) Derive the IS and LM equations in terms of the exogenous variables. (4 points) b) In the initial (long-run) equilibrium, the central bank sets the level of nominal money to 40600. Find the resulting long-run equilibrium values of real interest rate, investment, and price level. (3 points) c) The economy is initially in its long-run equilibrium as shown in part (b). Now, with the rolling out of COVID-l9 vaccine, businesses become more optimistic about the future economic outlook. As a result, autonomous investment changes by 3%. Find the new short-run equilibrium values of real output, real interest rate, and investment. Compute the new long-run equilibrium values of real interest rate, investment, and price level. (10 points) d) (Continued from part c) Suppose the central bank wants to increase the short-run level of output in part (c) by 1000 via a change in the level of money supply. Find the level of money supply that would achieve the goal. What will be the new (short-run) equilibrium level of real interest rate? (8 points)