Fall 2017 Econ 204 Vamsi Vakulabharanam Assignment 3 3 Questions, Max Points: 10 Due: Monday, December 11, 2017 in the Classroom at 8 AM. Please show your calculations step by step. Please write your name, section and TA name on your answer sheet. 1. (The IS-LM-PC model): Assume the following relations characterize the goods market: () ! = 100 + 0.5! () ! = 100 + 0.25 ! 200( ! + ! ) () ! = 100; ! = 200 ! = 0.1 10% (a) Derive the IS curve (as a relation between Yt and rt). (b) Assume the LM curve is given by rt = 0.1 (i.e. in period t, the central bank sets the real interest rate at 10 %). What is the short-run equilibrium level of output (Yt )? (c) Suppose that L = 1000 and un = 0.05 (where L: total population, un=natural rate of unemployment). Calculate the value of potential output (Yn). How does Yn compare to the short-run equilibrium level of output (Yt )? (d) Calculate the natural rate of interest (rn). How does rn compare to rt? Label this example as one of the cases covered in lectures. (e) Consider that the Phillips Curve is given by: [! !!! = 0.0005 (! ! )] , with !!! = 0.05 Calculate the change in inflation in period t. (f) Draw the IS-LM-PC graph. (g) Assume neither the government nor the central bank intervene until period t+4. Calculate the inflation rates from period t+1 through period t+3 (i.e. !!! , !!! , !!! ). Describe briefly the situation of the economy toward the end of period t+3, based on the output gap and the time-path of the inflation rate from period t+1 through period t+3. (g) Given the state of this economy toward the end of period t+3, what choice would you advise to policymakers for period t+4? (Choose among A, B, C and D). Explain why. A. The central bank should conduct a contractionary monetary policy in period t+4, thus raising the real interest rate target. B. The central bank should conduct an expansionary monetary policy in period t+4, thus lowering the real interest rate target. C. The government should implement a fiscal consolidation in period t+4. D. The government should intervene by expanding government spending and/or reducing overall taxes in period t+4. 2. (The IS-LM-PC model): Suppose that the following behavioral relations characterize the goods market in period t: () ! = 60 + 0.5! () ! = 90 + 0.25 ! 200( ! + ! ) () ! = 500; ! = 100 ! = 0 (a) Derive the IS curve (as a relation between Yt and rt ). (b) Assume the LM curve is given by r t = 0.05 (i.e. in period t, the central bank sets the real interest rate at 5 %). What is the short-run equilibrium level of output (Yt )? (c) Suppose that L = 2950 and un = 0.20 (where L: total population, un=natural rate of unemployment). Calculate the value of potential output (Yn). How does Yn compare to the short-run equilibrium level of output (Yt )? (d) Calculate the natural rate of interest (rn). How does rn compare to rt? (e) Consider that the Phillips Curve is given by: [! !!! = 0.05 (! ! )] Calculate the change in inflation in period t. (f) Draw the IS-LM-PC graph. (g) Assume that the government intervenes in period t+1 by conducting a fiscal policy consolidation. This one-time intervention can be seen as a 5 % decrease of government spending. i. Derive the new IS and calculate the new short-run equilibrium in period t+1? How does !!! compare to Yn? ii. Calculate the new natural rate of interest (rn) in period t+1. Assuming that the central bank does not change the initial real interest rate target, how would the new rn compare to rt+1? (j) Redraw the IS-LM-PC graph and represent the effects of this policy shift. (k) Given the state of this economy toward the end of period t+1, what choice would you advise to policymakers for period t+2? (Choose among A, B, C and D). Explain why. A. The central bank should conduct a contractionary monetary policy in period t+2, thus raising the real interest rate. B. The central bank should conduct an expansionary monetary policy in period t+2, thus lowering the real interest rate. C. The government should continue its program of fiscal consolidation in period t+2. D. The government should reverse its program of fiscal consolidation in period t+2. 3. Open Economy Consider an economy where C = 200 + 0.25(Y-T) I = 200 + 0.25Y-1000i G = 350, T = 300 = = .05 X = 0.4Y* and IM = 0.2Y, (real exchange rate) = 2 Y* (foreign output) = 1000 a. Calculate the multiplier if the economy is closed and the multiplier if the economy opens up. Explain the economic intuition why the two are different with 3-5 sentences. b. Solve for the equilibrium level of income (Y) for the open economy (Yopen) and calculate the trade balance (NX). c. If government follows an expansionary fiscal policy and G changes by 60, calculate the change in Y for both the closed economy (Yclosed) the open economy (Yopen). Assume no change in the foreign output (Y*). Calculate the new trade balance. d. If this economy has flexible exchange rate regime, how would the exchange rate respond to a fiscal expansion policy? Appreciation or Depreciation? Explain why. e. Suppose the interest rate in the foreign economy is 2%, and an investor expects the domestic currency to depreciate relative to the foreign currency by 4%, in which bond market in those two economies should the investor invest