of Department Economics University of California Berkeley
Fall 2007 Economics 100B Professor Olney
Problem Set #5 (15 points possible; 3 percent of course grade) Due: To Your GSI In Section, Monday November 19 & Tuesday November 20
Your answers should be written on the answer sheet provided. Staple your work (on 8x11 paper) to the back of your answer sheet. You must attach your work or you will receive no points. Be sure to write your section day/time and GSI's name at the top of the answer sheet. Write your name at the top of every attached page. Late problem sets will be penalized 5 points per day. No problem sets are accepted after the solutions are posted. Your submitted work must be your own: Problem sets that are identical (in whole or in part) to another problem set will receive a score of zero (0).
Problem sets should NOT be left in GSI mailboxes. Papers can be stolen from those mailboxes. We are not responsible for problem sets that are not handed directly to your GSI. 1. (2.5 points total) Suppose real money demand can be described by the equation Md/P = 0.5Y - 20,000i. Suppose the real money supply is 4,000. A. (1 point) When income is 10,000, what is the equilibrium nominal interest rate? When instead income is 11,000, what is the equilibrium nominal interest rate? B. ( point) Suppose the real money supply is increased by 10 percent. If income remains 10,000, what is the new equilibrium nominal interest rate? C. ( point) Explain why bond prices and interest rates are inversely related. D. ( point) The central bank decides to decrease nominal interest rates. What effect will this have on the real money supply? Why? 2. (2 points total) Suppose the economy can be described by the following equations. C = $600 billion + 0.75YD G = $3,000 billion GX = $2,500 billion - 10,000r T = 400 + 0.2Y I = $2,000 billion - 20,000r IM = 0.2Y A. (1 point) Derive the equation for the IS curve. When the real interest rate is 3 percent, what is the equilibrium value of real output? If instead the real interest rate is 6 percent, then what is the equilibrium value of real output? B. (1 point) Suppose the government decides to increase spending and pay for the spending with increased taxes. So government spending G is increased to $4,000 billion and the marginal tax rate is raised to 30 percent. What is the new IS equation? Graph the IS equations from parts (a) and (b). 3. (3 points total) The Phillips Curve equation can be described by the equation = e - (u - u*) + ss. A. (1 point) Suppose the expected inflation rate is 3 percent, = 0.6, the natural rate of unemployment is 5 percent, and there are no supply shocks. When the unemployment rate is 5 percent, what is the inflation rate? When the unemployment rate is 10 percent, what is the inflation rate? B. (1 point) Explain why the inflation rate increases when the unemployment rate decreases. C. ( point) Draw a Phillips Curve and label it PC1. Label the point on PC1 when u=u* and there are no supply shocks. Suppose the expected inflation rate increases. Draw the new Phillips Curve on the same set of axes and label it PC2. D. ( point) Draw a Phillips Curve and label it PC1. Label the point on PC1 when u=u* and there are no supply shocks. Suppose wages and prices become more flexible. Draw the new Phillips Curve on the same set of axes and label it PC2.
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Department of Economics University of California, Berkeley Problem Set #5
Fall 2007 Professor Olney Page 2
4. (2.5 points total) t The Taylor rule can be described by the equation r = r0 + r( - ). Suppose the Fed's "normal" baseline value of the real interest rate is 3 percent, r = , and the Fed's target inflation rate is 2 percent. A. (1 point) If the actual inflation rate is 2 percent, what real interest rate will the Fed set? If instead the actual inflation rate is 5 percent, what real interest rate will the Fed set? B. ( point) Explain the why Fed would increase the real interest rate if the inflation rate rose. C. (1 point) Draw a graph of the Taylor rule and label it TR1. Suppose the composition of the FOMC changes and becomes more "dovish." Draw the new Taylor rule and label it TRdove. Suppose instead the composition of the FOMC changes and becomes more "hawkish." Draw the new Taylor rule and label it TRhawk. 5. (1 point total) t Starting from the Taylor rule, r = r0 + r( - ) A0 I r + X r - r the IS equation, Y = 1 - MPE 1 - MPE and Okun's Law u = u * - 0.4
Y - Y * Y*
derive the equation for the monetary policy reaction function: u = u0 + ( - t) 6. (2 points total) Suppose inflationary expectations are static (never change). Suppose the economy can be described by the following: Fed's target inflation rate = 2% MPE = 0.6 u* = 4% expected inflation rate = 2% A0 = 4,900 Y* = 10,000 r = supply shocks = 0 Ir = 20,000 =2 r0 = 3% Xggr = 10,000 A. (1 point) What are the equilibrium values of the inflation rate and the unemployment rate? What real interest rate does the Fed set? What is the equilibrium value of real output? B. (1 point) Suppose autonomous consumption falls by 200. If the Fed didn't change interest rates, what would be the new equilibrium value of real output? The Fed, though, will take action. What are the new equilibrium values of the inflation rate and the unemployment rate? What real interest rate does the Fed set? 7. (2 points total) Suppose inflationary expectations are static (never change). For each part, draw an initial MPRF and Phillips Curve, with initial equilibrium at u=u*=uo and = e = t . Then, for each part, show the effect of the event described. A. ( point) The government increases its spending. B. ( point) There is a negative supply shock a war disrupts oil production and raises oil prices. C. ( point) International wealth-holders flee from the dollar, moving some of their wealth out of dollardenominated assets. D. ( point) The subprime mortgage crisis leads to drops in autonomous consumption and autonomous investment spending.
GSI's Name _______________________________ Section Day/Time _____________________
Department of Economics University of California, Berkeley
Your Name_________________________
Fall 2007 Professor Olney
Write your answers in the space indicated. Be sure to attach your work. Answer sheets without work attached will receive a score of zero (0). Possible points for each answer are given in parentheses.
Answer Sheet for Problem Set #5
For all questions, show your work on your attached pages.
1a. () Y=10,000 Y i = _________ 1b. () new i = _________ 1c. () Explain. (Short on space?
Use your attached pages.)
() Y=11,000 Y i = _________
1d. () Real money supply will increase / decrease / stay the same (circle one) 1d. Explain. (Short on space?
Use your attached pages.)
2a. () IS equation: Y = ___________ - ___________ r. () r = 3 percent Y Y = _____________ r = 6 percent Y Y = ________________ 2b. () new IS equation: Y = ___________ - ___________ r. () Draw both IS equations in one graph on your attached pages. 3a. () u = 5% Y = __________ 3b. (1) Explain. (Short on space?
Use your attached pages.)
() u = 10 % Y = __________
3c. () Draw your graph on your attached pages. 3d. () Draw your graph on your attached pages.
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Department of Economics University of California, Berkeley Problem Set #5
Fall 2007 Professor Olney Page 2
4a. (1) = 2% Y r = _____________ 4b. () Explain. (Short on space?
Use your attached pages.)
= 5% Y r = _____________
4c. (1) Draw your graph on your attached pages. (one graph, three Taylor rules) 5a. (1) Show your derivation on your attached pages. 6a. (1) = _________ and u = __________. r = _________. Y = __________. 6b. (1) if no Fed action, Y = ____________. with Fed action, = __________ and u = _______. r = _________. 7a. () 7c. ()
7b. ()
7d. ()