The Ohio State University Sungmin Park Problem 4 (10 points). Consider an economy in the short run described by the following system of equations: Y = C+I+G. C = 200 + 0.5 . (Y - T). I = 300 - 50r, M = 0.5Y - 50 . (r + Ex) T = 200, G = 200, M = 1000, En = 0, where Y is the output, C is the consumption, I is the investment, G is the government purchases, r is the real interest rate, M is the money supply, P is the price level, and Ex is the expected inflation rate. (a) Suppose P = 2.5. Derive the equation for the IS curve. Derive the equation for the LM curve. Draw both of these curves on a figure with Y on the horizontal axis and r on the vertical axis. What is the equilibrium interest rate and output? (b) Derive the equation for the aggregate demand curve. Draw the aggregate demand curve on a new figure with Y on the horizontal axis and P on the vertical axis. Suppose P = 2.5 and draw the short-run aggregate supply curve. Suppose that the economy's output is currently at long-run level and draw the long-run aggregate supply curve