Consider an economy described by the IS-LM model. The consumption function in this economy is given by C = 40 + 0.5(Y T). The investment function is I = 30 10r where r is the real interest rate. Government purchases (G) and taxes (T) are both equal to 20. The money demand function is given by (M/P)^d = Y 10i where i is the nominal interest rate. The money supply (M) is 200 and the price level (P) is 2. Expected inflation is equal to E = 0.

(a) Find the equation that describes the IS curve. [5 points]

(b) Find the equation that describes the LM curve. [5 points]

(c) Find the equilibrium interest rate r and the equilibrium level of output Y [10 points].

(d) Suppose that both consumers and investors become more pessimistic about the future, so that the consumption function changes to C = 10 + 0.5(Y T) while the investment function changes to I = 10 10r. Everything else remains the same as before. Compute the new equilibrium. [20 points]

(e) Can the central bank use the monetary policy to bring output back to the level you found in part (c)? [10 points]