Problem set 5

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Problem set 5
Macroeconomı́a II
2017
Exercise 1. (Blanchard). Even in the absence of collective bargaining, workers do have some bargaining power
that allows them to receive wages higher than their reservation wage. Each worker’s bargaining power depends both
on the nature of the job and on the economy-wide labor market conditions. Let’s consider each factor in turn.
a. Compare the job of a delivery person and a computer network administrator. In which of these jobs does a
worker have more bargaining power? Why?
b. For any given job, how do labor market conditions affect a worker’s bargaining power? Which labor-market
variable would you look at to assess labor-market conditions?
c. Suppose that for given labor-market conditions [the variable you identified in part (b)], worker bargaining
power throughout the economy increases. What effect would this have on the real wage in the medium run? in the
short run? What de termines the real wage in the model described in this chapter 7?
Exercise 2. (Blanchard). a. The Phillips curve is πt = πet + (m+ z) − αut. Rewrite this relation as a relation
between the deviation of the unemployment rate from the natural rate, inflation, and expected inflation.
b. In chapter 7, we derived the natural rate of unemployment. What condition on the price level and the
expected price level was imposed in that derivation? How does it relate to the condition imposed in part a?
c. How does the natural rate of unemployment vary with the markup?
d. How does the natural rate of unemployment vary with the catchall term z ?
e. Identify two important sources of variation in the natural rate of unemployment across countries and across
time.
Exercise 3. (Blanchard). 5. Mutations of the Phillips curve Suppose that the Phillips curve is given by
πt = πet + 0.1 − 2ut
and expected inflation is given by
πet = (1 − θ)π + θπt−1
and suppose that θ is initially equal to 0 and π is given and does not change. It could be zero or any positive value.
Suppose that the rate of unemployment is initially equal to the natural rate. In year t, the authorities decide to
bring the unemployment rate down to 3% and hold it there forever.
a. Determine the rate of inflation in periods t + 1, t + 2, t + 3, t + 4, t + 5. How does it compare to π?
b. Do you believe the answer given in (a)? Why or why not? (Hint: Think about how people are more likely
to form expectations of inflation.) Now suppose that in year t + 6, u increases from 0 to 1. Suppose that the
government is still determined to keep u at 3% forever.
c. Why might θ increase in this way?
d. What will the inflation rate be in years t + 6, t + 7, and t + 8?
e. What happens to inflation when θ = 1 and unemployment is kept below the natural rate of unemployment?
f. What happens to inflation when θ = 1 and unemployment is kept at the natural rate of unemployment?
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Exercise 4. (Blanchard). The macroeconomic effects of the indexation of wages Suppose that the Phillips
curve is given by
πt − πet = 0.1 − 2ut
where
πet = πt−1
Suppose that inflation in year t - 1 is zero. In year t, the central bank decides to keep the unemployment rate at 4%
forever.
a. Compute the rate of inflation for years t, t + 1, t + 2, and t + 3.
Now suppose that half the workers have indexed labor contracts.
b. What is the new equation for the Phillips curve?
c. Based on your answer to part (b), recompute your answer to part (a).
d. What is the effect of wage indexation on the relation between π and u?
Exercise 5. (adapted from Blanchard). The two paths to the medium-run equilibrium explored in chapter 9
make two different assumptions about the formation of the level of expected inflation. One path assumes the level of
expected inflation equals lagged inflation. The level of expected inflation changes over time. The other path assumes
the level of expected inflation is anchored to a specific value and never changes. Begin in medium-run equilibrium
where actual and expected inflation equals 2% in period t.
a. Suppose there is an increase in consumer confidence in period t + 1 (and that it make people more willing to
consume, everything else constant). How does the IS curve shift? Assume that the central bank does not change the
real policy rate. How will the short-run equilibrium in period t + 1 compare to the equilibrium in period t?
b. Consider the period t + 2 equilibrium under the assumption that πet+2 = πt+1. If the central bank leaves the
real policy rate unchanged, how does actual inflation in period t + 2 compare to inflation in period t + 1? How
must the central bank change the nominal policy rate to keep the real policy rate unchanged? Continue to period t
+ 3. Making the same assumption about the level of expected inflation and the real policy rate, how does actual
inflation in period t + 3 compare to inflation in period t + 2.
c. Consider the period t + 2 equilibrium making the assumption that πet+2 = π. If the central bank leaves the
real policy rate unchanged, how does actual inflation in period t + 2 compare to inflation in period t + 1? How
must the central bank change the nominal policy rate to keep the real policy rate unchanged? Continue to period t
+ 3. Making the same assumption about the level of expected inflation and the real policy rate, how does actual
inflation in period t + 3 compare to inflation in period t + 2?
d. Compare the inflation and output outcomes in part b to that in part c.
e. Which scenario, part b or part c, do you think is more realistic. Discuss.
f. Suppose in period t + 4, the central bank decides to raise the real policy rate high enough to return the
economy immediately to potential output and to the period t rate of inflation. Explain the difference between central
bank policies using the two assumptions about expected inflation in part b and part c.
Exercise 6. (adapted from Blanchard). A shock to aggregate supply will also have different outcomes when
there are different assumptions about the formation of the level of expected inflation. As in Question 5, one path
assumes that the level of expected inflation equals lagged inflation. The level of expected inflation changes over time.
The second path assumes the level of expected inflation is anchored to a specific value and never changes. Begin in
medium-run equilibrium where actual and expected inflation equal 2% in period t.
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a. Suppose there is a permanent increase in the price of oil in period t + 1. How does the PC curve shift?
Assume that the central bank does not change the real policy rate. How will the short-run equilibrium in period t +
1 compare to the equilibrium in period t? What happens to output? What happens to inflation?
b. Consider the period t + 2 equilibrium under the assumption that πet+2 = πt+1. If the central bank leaves the
real policy rate unchanged, how does actual inflation in period t + 2 compare to inflation in period t + 1? Continue
to period t + 3. Making the same assumption about the level of expected inflation and the real policy rate, how
does actual inflation in period t + 3 compare to inflation in period t + 2?
c. Consider the period t + 2 equilibrium under the assumption that πet+2 = π. If the central bank leaves the real
policy rate unchanged, how does actual inflation in period t + 2 compare to inflation in period t + 1? Continue to
period t + 3. Making the same assumption about the level of expected inflation and the real policy rate, how does
actual inflation in period t + 3 compare to inflation in period t + 2.
d. Compare the inflation and output outcomes in part b to that in part c.
e. In period t + 4, the central bank decides to change the real policy rate to return the economy as quickly as
possible to potential output and to the inflation rate of period t. Under which path for the formation of expected
inflation is the nominal policy rate of interest higher in period t + 4, the path from b or the path from c. Explain why,
when inflation expectations are anchored as in part c, the central bank can changethe policy rate to immediately
reach the new level of potential output and the period t level of inflation in period t + 4. Make the argument that is
not possible for the central bank to immediately hit both the new level of potential output and the period t level of
inflation in period t + 4 when expected inflation is equal to its lagged value.
Exercise 7. (Blanchard). Suppose the economy is operating at the zero lower bound for the nominal policy rate;
there is a large government deficit and the economy is operating at potential output in period t. A newly elected
government vows to cut spending and reduces the deficit in period t + 1, period t + 2 and subsequent periods.
a. Show the effects of the policy on output in period t + 1.
b. Show the effects of the policy on the change in inflation in period t + 1.
c. If expected inflation depends on past inflation, then what happens to the real policy rate in period t + 2?
How will this affect output in period t + 3?
d. How does the zero lower bound on nominal interest rates make a fiscal consolidation more difficult?
Exercise 8. (adapted from Blanchard). Consider the AS-AD model seen in class.Assume that the economy
starts at the natural level of output. Now suppose there is an increase in the price of oil.
a. In an AS–AD diagram, show what happens to output and the price level in the short run and the medium run.
b. What happens to the unemployment rate in the short run? In the medium run?
Suppose that the Federal Reserve decides to respond immediately to the increase in the price of oil. In particular,
sup pose that the Fed wants to prevent the unemployment rate from changing in the short run after the increase in
the price of oil. Assume that the Fed changes the money supply once – immediately after the increase in the price of
oil – and then does not change the money supply again.
c. What should the Fed do to prevent the unemployment rate from changing in the short run? Show how the
Fed’s action, combined with the decline in business confidence (underpreted as lower investment for any given level
of output and interest rates), affects the AS–AD diagram in the short run and the medium run.
d. How do output and the price level in the short run and the medium run compare to your answers from part
(a)?
e. How do the short-run and medium-run unemployment rates compare to your answers from part (b)?
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Exercise 9. (adapted from Blanchard). Consider two bonds, one issued in euros (e) in Germany, and one
issued in dollars ($) in the United States. Assume that both government securities are one-year bonds—paying the
face value of the bond one year from now. The exchange rate, E, stands at 0.75 euros per dollar. The face values
and prices on the two bonds are given by
Face Value Price
USA $ 10,000 $ 9,615.38
Germany e 10,000 e 9,433.96
a. Compute the nominal interest rate on each of the bonds.
b. Compute the expected exchange rate next year consistent with uncovered interest parity.
c. If you expect the dollar to depreciate relative to the euro, which bond should you buy?
d. Assume that you are a U.S. investor and you exchange dollars for euros and purchase the German bond today.
One year from now, it turns out that the exchange rate, E, is actually 0.72 (.72 euros buys one dollar) What is your
realized rate of return in dollars compared to the realized rate of return you would have made had you held the U.S.
bond?
e. Are the differences in rates of return in (d) consistent with the uncovered interest parity condition? Why or
why not?
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