C H A P T E R 1 4
A Dynamic Model of Aggregate Demand and Aggregate Supply
| 429
A Shift in Monetary Policy
Suppose that the central bank decides to reduce its target for the inflation rate.
Specifically, imagine that, in period t,
p
t
* falls from 2 percent to 1 percent and
thereafter remains at that lower level. Let’s consider how the economy will react
to this change in monetary policy.
Recall that the inflation target enters the model as an exogenous variable in
the dynamic aggregate demand curve. When the inflation target falls, the DAD
The Dynamic Response to a Demand
Shock
This figure shows the responses
of the key variables over time to a posi-
tive 1-percent demand shock that lasts
for five periods.
F I G U R E
1 4 - 9
Y
t
101.0
100.5
100.0
99.5
99.0
e
t
2.0
1.5
1.0
0.5
0.0
–0.5
–1.0
–1.5
–2.0
r
t
3.0%
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
p
t
3.5%
3.0
2.5
2.0
1.5
1.0
0.5
0.0
i
t
6.0%
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Time
Time
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
Time
Time
Time
(a) Demand Shock
(b) Output
(c) Real Interest Rate
(d) Inflation
(e) Nominal Interest Rate
curve shifts to the left, as shown in Figure 14-10. (To be precise, it shifts down-
ward by exactly 1 percentage point.) Because target inflation does not enter the
dynamic aggregate supply equation, the DAS curve does not shift initially. The
economy moves from its initial equilibrium, point A, to a new equilibrium, point
B. Output and inflation both fall.
Monetary policy is, not surprisingly, key to the explanation of this outcome.
When the central bank lowers its target for inflation, current inflation is now above
the target, so the central bank follows its policy rule and raises real and nominal
interest rates. The higher real interest rate reduces the demand for goods and ser-
vices. When output falls, the Phillips curve tells us that inflation falls as well.
Lower inflation, in turn, reduces the inflation rate that people expect to pre-
vail in the next period. In period t
+ 1, lower expected inflation shifts the dynam-
ic aggregate supply curve downward, to DAS
t
+1
. (To be precise, the curve shifts
downward by exactly the fall in expected inflation.) This shift moves the econ-
omy from point B to point C, further reducing inflation and expanding output.
Over time, as inflation continues to fall and the DAS curve continues to shift
430
|
P A R T I V
Business Cycle Theory: The Economy in the Short Run
A Reduction in Target Inflation
A permanent reduction in target infla-
tion in period t shifts the dynamic aggregate demand curve to the left
from DAD
t
−1
to DAD
t
,
t
+1
, . . . . Initially, the economy moves from point
A to point B. Both inflation and output fall. In the subsequent period,
because expected inflation falls, the dynamic aggregate supply curve
shifts downward. The economy moves from point B to point C in period
t
+ 1. Over time, as expected inflation falls and the dynamic aggregate
supply curve repeatedly shifts downward, the economy approaches a
new equilibrium at point Z. Output returns to its natural level Y
−
all
, and
inflation ends at its new, lower target (
p
t
*,
t
+1, . . .
= 1 percent).
F I G U R E
1 4 - 1 0
Inflation,
p
p
p
t
p
t – 1
= 2%
p
final
= 1%
Income, output, Y
A
C
Z
B
DAS
t + 1
DAS
final
DAD
t – 1
DAS
t – 1,
t
Y
t
Y
t – 1
=
Y
final
2. . . . causing
output to fall . . .
1. A reduction in target inflation shifts
the DAD curve downward, . . .
3. . . . and
inflation to
fall as well.
Y
all
4. In subsequent
periods, lower
expected inflation
shifts the DAS
curve downward.
DAD
t,
t + 1…
5. Eventually, the economy
approaches a final equilibrium, with
output at its natural level and
inflation at its new, lower target.
C H A P T E R 1 4
A Dynamic Model of Aggregate Demand and Aggregate Supply
| 431
toward DAS
final
, the economy approaches a new long-run equilibrium at point
Z, where output is back at its natural level (Y
final
=
Y−
all
) and inflation is at its new
lower target (
p
t
*,
t
+1, . . .
= 1 percent).
Figure 14-11 shows the response of the variables over time to a reduction in tar-
get inflation. Note in panel (e) the time path of the nominal interest rate i
t
. Before
the change in policy, the nominal interest rate is at its long-run value of 4.0 percent
(which equals the natural real interest rate
r of 2 percent plus target inflation
p
t
*
−1
of 2 percent). When target inflation falls to 1 percent, the nominal interest rate rises
The Dynamic Response to a
Reduction in Target Inflation
This fig-
ure shows the responses of the key vari-
ables over time to a permanent reduc-
tion in the target rate of inflation.
F I G U R E
1 4 - 1 1
Y
t
101.0
100.5
100.0
99.5
99.0
p
t
*
3.0
2.5
2.0
1.5
1.0
0.5
0.0
r
t
3.0%
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
p
t
3.5%
3.0
2.5
2.0
1.5
1.0
0.5
0.0
i
t
6.0%
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Time
Time
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
t – 2
t + 2
t + 6
t + 10
t + 4
t + 8
t + 12
t
Time
Time
Time
(a) Inflation Target
(b) Output
(c) Real Interest Rate
(d) Inflation
(e) Nominal Interest Rate
to 4.2 percent. Over time, however, the nominal interest rate falls as inflation and
expected inflation fall toward the new target rate; eventually, i
t
approaches its new
long-run value of 3.0 percent. Thus, a shift toward a lower inflation target increas-
es the nominal interest rate in the short run but decreases it in the long run.
We close with a caveat: Throughout this analysis we have maintained the
assumption of adaptive expectations. That is, we have assumed that people form
their expectations of inflation based on the inflation they have recently experi-
enced. It is possible, however, that if the central bank makes a credible
announcement of its new policy of lower target inflation, people will respond
by altering their expectations of inflation immediately. That is, they may form
expectations rationally, based on the policy announcement, rather than adap-
tively, based on what they have experienced. (We discussed this possibility in
Chapter 13.) If so, the dynamic aggregate supply curve will shift downward
immediately upon the change in policy, just when the dynamic aggregate
demand curve shifts downward. In this case, the economy will instantly reach its
new long-run equilibrium. By contrast, if people do not believe an announced
policy of low inflation until they see it, then the assumption of adaptive expec-
tations is appropriate, and the transition path to lower inflation will involve a
period of lost output, as shown in Figure 14-11.
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