Problems for Second Review Session

by Vitaliy

  1. The estimated Okun’s law for the US is given by:

ut – ut-1 = -0.4(gyt – 3%).

  1. What growth rate of output leads to an increase in the unemployment rate of 1% per year? How can the unemployment rate increase even though the growth rate of output is positive?
  2. What rate of growth output do we need to decrease unemployment by two percentage points over the next four years?
  3. Suppose that we experience a second baby boom. How do you expect Okun’s law to change if the rate of growth of the labor force increases by two percentage points?
  1. Suppose that the economy can be described by the following three equations:

ut – ut-1 = -0.4(gyt – 3%) Okun’s law

Phillips curve

gyt = gmt - aggregate demand

  1. Reduce the three equations to two by substituting gyt from the AD equation into Okun’s law.

Assume initially that ut = ut-1 = 5%, gmt = 13% and = 10%. Now suppose that this year’s money growth is permanently reduced from 13% to 0%.

  1. Compute the impact on unemployment and inflation this year and next year.
  2. Compute the values of unemployment and inflation in the medium run.
  1. Suppose that the Phillips curve is given by:

where K is a constant, and that .

Suppose that initially unemployment is equal to the natural rate and =12%. The authorities decide in year t that 12% inflation is too high and that they will maintain the unemployment rate one percent above the natural rate of unemployment until the inflation rate decreases to 2%.

  1. Solve for the natural rate of unemployment as a function of the constant K. What is the sacrifice ratio? How does the sacrifice ratio depend on the natural rate of unemployment?
  2. Compute the rate of inflation for years t and t+1.
  3. For how many years must the authorities keep the unemployment rate above the natural rate of unemployment? Is the implied sacrifice ratio consistent with your answer to (a)?

Now suppose that people know that the authorities want to lower inflation to 2%, but they are not sure of the authorities’ willingness to accept an unemployment rate above the natural rate of unemployment. So, their expectation of inflation is a weighted average of the target of 2% and last year’s inflation, that is,

, where b is the weight they put on the government’s target of 2%.

  1. Let b = 0.25. How long will it take before the inflation rate is no higher than 2%? What is the sacrifice ratio now?
  2. Suppose that after the government’s policy has been in effect for one year, people believe the authorities completely. So, they now set their expectations according to . From what year onward can the authorities let the unemployment rate return to the natural rate?
  3. What advice would you give to a policy maker interested in lowering the rate of inflation by increasing the rate of unemployment as little and for as short a time period as possible?
  1. Suppose that the Phillips curve is given by , where is the markup. Suppose that unemployment is initially at its natural rate. Suppose now that an oil shock increases , but that the monetary authority continues to keep the unemployment rate at its previous value.
  2. What will happen to inflation?
  3. What should the monetary authority do instead?
  1. This question focuses on the medium run. Suppose = 7%, un = 6% and = 2%.
  2. What will gyt and ut be in the medium run? Briefly explain.
  3. Calculate what the rate of inflation and adjusted nominal money growth will be in the medium run.
  4. Suppose the central bank decides to reduce from 7% to 3%. Using the original numbers in problem 5, answer the following questions.
  5. What happens to gyt and ut in the medium run as a result of the decrease in money growth?
  6. What happens to the rate of inflation and to adjusted nominal money growth in the medium run as a result of the reduction in money growth?
  1. Suppose the central bank wishes to reduce inflation by 8%.
  2. Calculate the point-years of excess unemployment needed to reduce inflation by 8% for each of the following values of : 1.5, 1.4, 1.15 and 1.
  3. What happens to the point-years of excess unemployment as decreases in size. Briefly explain.
  1. Let = 0.5, = 2%.
  2. To reduce ut by 2%, what must gyt be?
  3. To increase ut by 3%, what must gyt be?
  1. Suppose = 18%, un = 6%, = 1, = 3%, = 0.5. Assume in year 0 that u = 6% and that central bank decides that it wants to begin a disinflation in year 1 to reduce inflation to 3%. Assume that the desired path of inflation is: inflation starts at 18% in year 0 (before the change in monetary policy) and decreases 3% a year until it reaches 3%.
  2. Given this information, construct a table similar to Table 9-1 in the textbook. Include in your table for years 0-8 the values of inflation, unemployment, output growth and money growth.
  3. Briefly explain the path of each variable in your table.

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