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
ut − ut −1 = −0.4(g yt − 3% )
a. What growth rate of output gyt leads to an increase in the unemployment rate
(ut − ut −1 ) of 1% per year? _____________________________________________.
How is it possible for the unemployment rate to rise (ut − ut −1 > 0 ) 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 ut − ut −1 = __________ 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 (ut − ut −1 ) . 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:
ut − ut −1 = −0.4(g yt − 3% )
π t − π t −1 = −(ut − 0.05)
g yt = g mt − π t
Okun’s Law
Phillips Curve
Aggregate Demand
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
t–1
t
t+1
t+2
t+3
πt
u
(Use PC)
gyt
(Use OL)
gmt
(Use AD)
8
4
4
4
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.
Problem 6
Credibility and Disinflation
Suppose that the Phillips Curve is given by
π t − π e = −(ut − 0.05)
Equation 1
And expected inflation is given by
π te = π t −1
Equation 2
a. What is the sacrifice ratio in this economy (see p. 190) ____________________.
sacrifice ratio =
point - years of excess unemployment
decrease in inflation
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
t–1
t
t+1
t+2
t+3
u
πt
= π t −1 − (ut − 0.05)
0.12
t+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,
π te = β 2% + (1 − β )π t −1
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).
u
Year
t–1
t
t+1
t+2
t+3
t+4
t+5
un =
πt
= β 0.02 + (1 − β )π t −1 − (ut − 0.05)
0.12
(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
π te = 2%
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
t–1
un =
t
t+1
t+2
t+3
t+4
t+5
(Stop when inflation ≤ 2%)
f.
πt
= β 0.02 + (1 − β )π t −1 − (ut − 0.05)
(β = 0.25)
(β =1)
(β =1)
(β =1)
(β =1)
(β =1)
0.12
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, unemployment, and aggregate activity in the short-run and the medium run.
Suppose the Phillips Curve is specified as
π t − π e = −α (ut − u n )
Okun’s Law is specified as
ut − u n = − β (g yt − g y )
Finally, Aggregate Demand is
g yt = g mt − π t
a. Plug Okun’s Law into the Phillips curve to derive the Inflation-Adjustment
curve (see the slides), solving for π t = __________________________________.
b. Draw the Inflation-Adjustment curve below (see the slides).
Label the axes and the curve.
The intercept = ____________________, and the slope = ___________________.
(Check your work with the slides).
c. On the graph above, draw the Aggregate Demand curve (and label it).
Expected inflation is given by π te = 0.03 and the natural rate of unemployment is given
by un=0.05. The normal rate of output growth is given by g y = 0.02 . Take α = 1 and
β = 0.02 .
d. Using the numbers above, the intercept of the I-A curve is = ______________,
the slope is = ______________. Rewrite the I-A curve, using these numbers:
π t = _______________________________________________________________.
In the graph above, identify the point on the I-A curve where π t = π e .
e. Plug the I-A curve into the AD curve and find a numerical equation for the
short-run growth rate of output gyt = __________________.
Suppose g mt = 0.05 . Then gyt = __________ and g yt − g y = _______________.
Suppose g mt = 0.08 . Then gyt = __________ and g yt − g y = _______________.
Suppose g mt = 0 . Then gyt = __________ and g yt − g y = __________________.
f.
Plugging your answers to (e) into the I-A curve,
If g mt = 0.05 . Then πt = __________ and π t − π e = _______________________.
If g mt = 0.08 . Then πt = __________ and π t − π e = _______________________.
If g mt = 0 . Then πt = __________ and π t − π e = _________________________.
g. Suppose the Central Bank increases gmt. In the short run, what will happen to
output growth, gyt?_______________. What will happen to inflation? _______
_______. Draw what happens (shifting the appropriate curve and labeling
the new values of output growth and inflation.
h. In the short run, expected inflation will ________________________________.
So π t − π e is now ______________ (zero/positive/negative). What will happen in
the medium run to expected inflation? _________________________________.
What will this do to the I-A curve? Draw this, labeling everything.
i.
In the medium run, π t − π e = ________. Use this on the I-A function and find
medium-run output growth, gyt =_____. In the medium run, g yt − g y = ____.
This implies that, for a given growth rate of the nominal money supply gmt, in
the medium run, π t = ___________. (This should be an equation, derived
from the AD curve.)
j.
Using your equation for medium run inflation,
If g mt = 0.05 , then π t = __________ . (This should be a number).
If g mt = 0.08 , then π t = __________ .
If g mt = 0 , then π t = __________ .
This should tell you that, in the medium run, any value of inflation is
compatible with medium-run output growth, gyt =_____.