Workbook For Chapter 9 Of Blanchard Macroeconomics. Problem 2 As shown by equation (9.2), the estimated Okun’s Law for the United States is given by ()%34.01−−=−− ytttguu a. What growth rate of output gyt leads to an increase in the unemployment rate ()1−−ttuu of 1% per year? _____________________________________________. How is it possible for the unemployment rate to rise ()01>−−ttuu even though output is growing at a positive rate? b. Suppose we wanted to decrease unemployment by 2 percentage points. But we will do it over the next four years. Then the decrease in unemployment in each of the next four years will be =−−1ttuu __________ so that the total change is 2 percentage points. Given your answer, solve for the value of gyt that will give you that value of ()1−−ttuu . gyt = __________________________ c. Suppose that the U.S. experiences a second baby boom, increasing rate of growth of the labor force by two percentage points. Rewrite Okun’s Law if an increase in the labor force leads to a proportionate increase in potential output. ____________________________________________________________. Problem 3 Suppose that the economy can be described by the following three equations:()()tmtyttttytttgguguuπππ−=−−=−−−=−−−05.0%34.011 a. What is the natural rate of unemployment for this economy? ______________. b. Suppose that the unemployment rate has been equal to the natural rate for two years, and the inflation rate is 8%. What is the growth rate of output? __________. (Hint: use Okun’s Law.) What is the growth rate of the money supply? __________. (Hint: Use the AD function). c. Suppose the conditions are as in (b) when, in year t, the authorities use monetary policy to reduce the inflation rate to 4% in year t and keep it there. What must happen to the unemployment rate; the growth rate of output, and the growth rate of the money supply in years t, t+1, t+2, …? Year πt u (Use PC) gyt (Use OL) gmt (Use AD) t – 1 8 t 4 t + 1 4 t + 2 4 t + 3 4 Hint: these values will change from year to year, so make sure to fill the entire table. Problem 5 Part (a) should be pretty obvious if you use the equation the book provides. Hint for part (b). The monetary authority is assumed to want to keep the inflation rate constant. What policy can it follow that will do so in the presence of an oil shock that raises the markup? (What a timely question, with oil prices at $64 per barrel and gasoline at $3.00 per gallon!) In the long run, a policy of keeping inflation low, at whatever cost to unemployment, can be shown to produce both unemployment at the natural rate and low inflation. For example, see Figure 9-4. Okun’s Law Phillips Curve Aggregate DemandProblem 6 Credibility and Disinflation Suppose that the Phillips Curve is given by ()05.0−−=−tetuππ Equation 1 And expected inflation is given by 1−=tetππ Equation 2 a. What is the sacrifice ratio in this economy (see p. 190) ____________________. inflation in decreasentunemployme excess of years-pointratio sacrifice = Suppose that unemployment is initially equal to the natural rate and π = 12%. The central bank decides that 12% inflation is too high and that, starting in year t, it will maintain the unemployment rate one percentage point above the natural rate for as long as it takes to bring inflation down to 2%. b. Compute the rate of inflation for years t, t+1, t+2. Rewrite the Phillips curve (equation 1) using equation 2 above: ___________________________________. Using the Phillips curve, un = ____________ so the government announcement that it will aim for an “unemployment rate one percentage point above the natural rate” means that u = _____________ until inflation falls to 2%. Use this information and the rewritten equation to fill the following table: Year u πt ()05.01−−=− ttuπ t – 1 0.12 t t + 1 t + 2 t + 3t + 4 t + 5 t + 6 t + 7 t + 8 t + 9 t + 10 t + 11 t + 12 t + 13 (Stop when inflation = 2%) c. For how many years must the Central Bank keep unemployment above the natural rate of unemployment? _________. This means that the economy had to endure ___________ point-years of unemployment to reduce inflation by 10 percentage points. What is the implied sacrifice ratio (see p. 190)? ___________. Is it consistent with your answer to (a)? ____________________. Now suppose that people know that the central bank wants to lower inflation to 2%. But they are not sure of the central bank’s willingness to accept an unemployment rate above the natural rate of unemployment. So, their expectations of inflation are formed according to a weighted average of the target of 2% and last years inflation, that is, 1)1(%2−−+=tetπββπ where β is the weight they put on the central bank’s target of 2%. d. Let β = 0.25. How long will it take before the inflation rate is equal to 2% if u – un = 0.01? Fill in the following table (you may want to use Excel). Year u πt ()05.0)1(02.01−−−+=− ttuπββ t – 1 un = 0.12 t t + 1 t + 2 t + 3 t + 4 t + 5(Stop when inflation ≤ 2%) What is the sacrifice ratio? _____________. Why is it different from your answer in (c) ________________________________________________________ ___________________________________________________________________. Suppose that after the policy has been in effect for one year, people believe that the central bank is indeed committed to reducing inflation to 2%, raising β to 1. So, from t+1 on, they now set their expectations according to %2=etπ e. From what year onward can the central bank let the unemployment rate return to the natural rate? ________________. What is the sacrifice ratio now?_______________________________________________________________. Year u πt ()05.0)1(02.01−−−+=− ttuπββ t – 1 un = 0.12 t (β = 0.25) t + 1 (β =1) t + 2 (β =1) t + 3 (β =1) t + 4 (β =1) t + 5 (β =1) (Stop when inflation ≤ 2%) f. What advice would you give to a central bank that wants to lower the rate of inflation by increasing the rate of unemployment as little and for as short a time period as possible? ______________________________________________ ___________________________________________________________________ ___________________________________________________________________. Additional Problem Inflation,