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Answers to Practice Exercises on Chapter 11
Analytical Exercise 2
If the prevailing expectations in the economy are rational expectations, labour contracts
do not overlap, and if workers, managers, and investors have sufficient foreknowledge of
the change in policy, then it will affect the price level and the inflation rate, but not the
level of real GDP or unemployment.
Analytical Exercise 3
It would raise inflation, and raise the price level.
Analytical Exercise 6
Suppose half the contracts are signed at the beginning of the period and half the contracts
in the middle of the period. In the figure below the initial full employment equilibrium is
at point A, with the monetary policy reaction function at MPFR and0the Phillips Curve at
PC 0 Suppose after all the contracts are signed at the beginning of the period, the central
bank announces that it will lower its target interest rate r* starting in the second half of
the period. (That this policy is expansionary was discussed in Analytic Exercise #7 of
Chapter 10.) The announcement of the policy will affect labour contract negotiations in the middle of
the period. As only half of the workers and firms are engaged in labour negotiations, they
will be worried about their position relative to the other half of workers and firms; and
they will not raise the wage rates in order to stay competitive. As a result in the middle of
the period wages will increase by a very small amount, and the Phillips curve will shift
up by a small amount, to PC . The 1eduction in r* will also shift up the monetary policy
reaction function to MPRF . The 1quilibrium in the second half of the period will be at
point B. Hence, the anticipated expansionary policy will reduce the unemployment rate
even though expectations are rational.
Policy Exercise 6
a. In year zero, actual ieflation is equal to expected inflation. The Phillips curve equation:
πt=π −βt×(u −u *) t t
tells us that this is true only when unemployment is at its natural rate of six percent. So in
year zero unemployment is six percent. According to the MPRF-Taylor Rule equation as
it stands in year zero, unemployment is six percent only when inflation is 2%. So
inflation in year zero is 2%.
b. If the economy has rational expectations, then because the shift in policy was known
and anticipated beforehand, expected inflation will be equal to actual inflation. From the
Phillips curve equation, this holds only when unemployment is six percent. So
unemployment is six percent in year one and for every year thereafter.
The MPRF equation:
ut = u0t φ × (π t π ' t)
with parameter values for year one and thereafter substituted into it:
ut = 0.004+ 0.4 × (π t .02 )
tells us that unemployment is six percent only when inflation is seven percent. So u =.06 t
and π t.07 at all times t greater than or equal to one.
The government’s attempt to pursue an expansionary policy has, under rational
expectations, no effect at all on unemployment, but serves to raise the inflation rate from
2 to 7% per year.
c. If the economy has adaptive expectations, then this year’s expected inflation is last
year’s actual inflation. Substituting in this definition of adaptive expectations and the
values of the parameters produces the two adaptive-expectation equations:
π = π − 0.5× (u −.06)
t t−1 t
ut= 0.004+ 0.4 × (π t .02 )
Substituting the second equation into the first to solve for the path over time of inflation
produces:
π = (5/6)π + (7/600)
t t−1 And once inflation in any year is known, calculating unemployment can be done by
straightforwardly applying the MPRF equation:
u = 0.004+ 0.4 × π − .02 )
t t
Beginning to calculate this equation for t=1, for the first year in which the policy is in
effect, and then calculating forward in time for 35 years tells us that inflation and
unemployment follow the following path over time:
AN EXPANSIONARY POLICY UNDER ADAPTIVE EXPECTATIONS
Year Unemployment Inflation
0 0.06 0.02
1 0.043333333 0.028333333
2 0.046111111 0.035277778
3 0.048425926 0.041064815
4 0.050354938 0.045887346
5 0.051962449 0.049906121
6 0.05330204 0.053255101
7 0.054418367 0.056045918
8 0.055348639 0.058371598
9 0.056123866 0.060309665
10 0.056769888 0.061924721
11 0.05730824 0.063270601
12 0.057756867 0.064392167
13 0.058130722 0.065326806
14 0.058442269 0.066105672
15 0.058701891 0.066754726
16 0.058918242 0.067295605
17 0.059098535 0.067746338
18 0.059248779 0.068121948
19 0.059373983 0.068434957
20 0.059478319 0.068695797
21 0.059565266 0.068913164
22 0.059637721 0.069094304
23 0.059698101 0.069245253
24 0.059748418 0.069371044
25 0.059790348 0.06947587
26 0.05982529 0.069563225
27 0.059854408 0.069636021
28 0.059878674 0.069696684
29 0.059898895 0.069747237
30 0.059915746 0.069789364
31 0.059929788 0.06982447
32 0.05994149 0.069853725
33 0.059951242 0.069878104
34 0.059959368 0.06989842
35 0.05996614 0.06991535 The first year of the policy sees the economy boom—unemployment falls to 4.33%--and
inflation rise slightly. Thereafter every year sees the adaptive expectations of the
economy revise expected inflation upward slightly. The new higher level of expected
inflation induces the central bank to raise interest rates and so raise unemployment, and
over time the economy heads for the same equilibrium—inflation at 7%, unemployment
at 6%--as in the rational expectations economy of part b. But while the long-run
equilibrium in which actual equals expected inflation comes immediately under rational
expectations, it is reached only in the long run under adaptive expectations.
d. Under static expectations, expected inflation remains at 2%, and so in year one the
economy attains the same unemployment-inflation configuration—4.33% for
unemployment, 2.83% for inflation—attained under adaptive expectations. But because
expectations of inflation are static, the economy remains at that point thereafter.
Policy Exercise 7
a. The initial level of unemployment is the same as it was in question 4: 6%. (So is the
initial level of inflation: 2%).
b. Under rational expectations, as argued in the answer to question 4 above,
unemployment is always 6% as long as the economic policies of the government are
understood and anticipated. Moreover, expected inflation is equal to actual inflation.
Since the central bank has raised its target inflation rate to 4%, and since that is the
inflation rate consistent with 6% unemployment, actual inflation and expected inflation
jump immediately to that 4% level as well.
c. The logic is the same as in part c of question 4 above, only this time it is the central
bank’s tolerance for inflation that has shifted. The Phillips curve and MPRF equations
from year one on are:
π t π t−1− 0.5× (u −t06)
u t= 0.06+ 0.4 × π t .04 )
Substituting this second equation into the first produces an equation for the dynamic path
over time of the inflation rate:
π t (5/6)π t−1+ (2/300)
And once inflation in any year is known, calculating unemployment can be done by
straightforwardly applying the MPRF equation:
u t 0.06+ 0.4 × π t .04 )
Beginning to calculate this equation for t=1, for the first year in which the policy is in
effect, and then calculating forward in time for 35 years tells us that inflation and
unemployment follow the following path over time:
AN EXPANSIONARY POLICY UNDER ADAPTIVE EXPECTATIONS
Year Unemployment Inflation
0 0.06 0.02 1 0.053333333 0.023333333
2 0.054444444 0.026111111
3 0.05537037 0.028425926
4 0.056141975 0.030354938
5 0.056784979 0.031962449
6 0.057320816 0.03330204
7 0.057767347 0.034418367
8 0.058139456 0.035348639

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