The overall price level is a weighted average of the prices set by the two types of firms:
P
=
sEP
+ (1 –
s
)[
P
+
a
(
Y
–
Y
)].
Rearranging:
P
=
EP
+ [
a
(1 –
s
)/
s
](
Y
–
Y
).
a.
If no firms have flexible prices, then
s
= 1. The above equation tells us that
P
=
EP
.
That is, the aggregate price level is fixed at the expected price level: the aggregate
supply curve is horizontal in the short run, as assumed in Chapter 9.
b.
If desired relative prices do not depend at all on the level of output, then
a
= 0 in
the equation for the price level. Once again, we find
P
=
EP
: the aggregate supply
curve is horizontal in the short run, as assumed in Chapter 9.
2. The economy has the Phillips curve:
π
=
π
–1
–0.5(
u
– 0.06).
a.
The natural rate of unemployment is the rate at which the inflation rate does not
deviate from the expected inflation rate. Here, the expected inflation rate is just
last period’s actual inflation rate. Setting the inflation rate equal to last period’s
inflation rate, that is,
π
=
π
–1
, we find that
u
= 0.06. Thus, the natural rate of
unemployment is 6 percent.
b.
In the short run (that is, in a single period) the expected inflation rate is fixed at
the level of inflation in the previous period,
π
–1
. Hence, the shortrun relationship
between inflation and unemployment is just the graph of the Phillips curve: it has
a slope of –0.5, and it passes through the point where
π
=
π
–1
and
u
= 0.06. This is
shown in Figure 13–1. In the long run, expected inflation equals actual inflation,
so that
π
=
π
–1
, and output and unemployment equal their natural rates. The long
run Phillips curve thus is vertical at an unemployment rate of 6 percent.
146
Answers to Textbook Questions and Problems
LRPC
SRPC
u
0.06
Unemployment
Inflation
0.5
π
−
1
π
Figure 13–1
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To reduce inflation, the Phillips curve tells us that unemployment must be above
its natural rate of 6 percent for some period of time. We can write the Phillips
curve in the form
π
–
π
–1
= 0.5(
u
– 0.06).
Since we want inflation to fall by 5 percentage points, we want
π
–
π
–1
= –0.05.
Plugging this into the lefthand side of the above equation, we find
–0.05 = –0.5(
u
– 0.06).
We can now solve this for
u
:
u
= 0.16.
Hence, we need 10 percentage points of cyclical unemployment above the natural
rate of 6 percent.
Okun’s law says that a change of 1 percentage point in unemployment trans
lates into a change of 2 percentage points in GDP. Hence, an increase in unem
ployment of 10 percentage points corresponds to a fall in output of 20 percentage
points. The sacrifice ratio is the percentage of a year’s GDP that must be forgone
to reduce inflation by 1 percentage point. Dividing the 20 percentagepoint
decrease in GDP by the 5 percentagepoint decrease in inflation, we find that the
sacrifice ratio is 20/5 = 4.
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 Spring '08
 Staff
 Economics, Inflation, Unemployment, natural rate, unemployment rates

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