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Econ 31402
Fall 2009
Problem Set 8
Answer Key
1. (a) Equating aggregate demand to shortrun aggregate supply gives:
300+10
M
P
±
= 500+
P
P
,
300+(10
±
1000
P
) = 500+
P
50
,
10000
P
= 150+
P
.
Multiplying both sides of the equation by
P
and rearranging gives
P
2
150
P
10
;
000 = 0
, which can be factored as
(
P
50)(
P
+ 200) = 0
.
This has the nonnegative solution
P
= 50
.
Since
P
e
is also
50
, the expected price level equals the actual price level, so output
is at its fullemployment level of
500
and the unemployment rate is at the natural
rate of
6%
. These are the longrun equilibrium values of the three variables as
well.
(b) When the nominal money supply increases unexpectedly to
1260
, we again equate
aggregate demand to shortrun aggregate supply, which gives:
300+10
M
P
±
= 500+
P
P
,
300+(10
±
1260
P
) = 500+
P
50
,
12600
P
= 150+
P
.
Multiplying both sides of the equation by
P
and rearranging gives
P
2
150
P
12
;
600 = 0
, which can be factored as
(
P
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 Spring '07
 MBIEKOP
 Macroeconomics

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