Foundations of International Macroeconomics
1
Workbook
2
Maurice Obstfeld, Kenneth Rogo
ff
, and Gita Gopinath
Chapter 9 Solutions
1.
(a) In the problem, the government unexpectedly freezes the money
supply, which had previously been growing predictably at the proportional
rate
°
, at the
previous
period°s level
m
, say. Since the economy was initially
in a steady state, we have that
p
0
=
m
+ (1 +
η
)
°
, which, together with eq.
(12) in Chapter 9, implies that
q
0
=
e
0
−
m
−
(1 +
η
)
°.
(1)
(Recall that
y
,
i
∗
,
p
∗
≡
0
.
This problem di
ff
ers from the one in section 9.2.5
in that here, there is a forecast error in the level of the date 0 money supply,
whereas in the chapter, there is no surprise concerning the date 0 money
supply.) Let us reproduce eq. (18) from Chapter 9 (which assumes a constant
longrun real exchange rate):
e
t
−
e
flex
t
=
1
−
φδ
1 +
ψδη
(
q
t
−
q
)
.
For
t
= 0
,
we may use eq. (1) to eliminate
q
0
from the preceding equation:
e
0
−
e
flex
0
=
1
−
φδ
1 +
ψδη
[
e
0
−
m
−
(1 +
η
)
°
−
q
]
.
1
By Maurice Obstfeld (University of California, Berkeley) and Kenneth Rogo
ff
(Prince
ton University).
c
°
MIT Press, 1996.
2
c
°
MIT Press, 1998. Version 1.1, February 27, 1998. For online updates and correc
tions, see http://www.princeton.edu/ObstfeldRogo
ff
Book.html
96
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Observe that
e
flex
0
, the postdisturbance
°
exibleprice exchange rate, simply
equals
q
+
m
(because the money supply has been frozen at its date
t
=
−
1
level). The preceding equation therefore becomes
e
0
=
q
+
m
−
°
1
−
φδ
ψδη
+
φδ
¶
(1 +
η
)
°
=
e
flex
0
−
°
1
−
φδ
ψδη
+
φδ
¶
(1 +
η
)
°.
The e
ff
ect on the real exchange rate (relative to the economy°s initial path)
is the di
ff
erence
e
0
−
p
0
−
q
=
e
0
−
[
m
+ (1 +
η
)
°
]
−
q
, which, from the last
displayed equation equals
−
°
1
−
φδ
ψδη
+
φδ
¶
(1 +
η
)
°
−
(1 +
η
)
°
=
−
°
1 +
ψδη
ψδη
+
φδ
¶
(1 +
η
)
°.
Thus, there is an initial real appreciation on date 0, after which the real
exchange rate converges back to its longrun level
q
according to eq.
(13)
in Chapter 9. [The real appreciation is proportional to the total monetary
shock, equal to the moneysupply level shock,
−
°
, plus the moneysupply
growth rate e
ff
ect,
−
η
°
, with the same proportionality factor as in eq. (17),
Chapter 9.] From the aggregate demand equation in the chapter, eq. (3), we
see that output falls initially by a percentage equal to
δ
times the percentage
real appreciation, and then gradually rises back to its fullemployment level.
Footnote 17 in the chapter implies that the initial HomelessForeign real
interest di
ff
erential is the expected change in
q
after the shock hits. Equation
(13) in the chapter shows that
q
1
−
q
0
=
q
1
−
q
−
(
q
0
−
q
)
=
−
ψδ
(
q
0
−
q
)
=
ψδ
°
1 +
ψδη
ψδη
+
φδ
¶
(1 +
η
)
°.
Thus Home°s relative real interest rate rises, a result that also can be derived
from eq. (24) in Chapter 9.
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 YuChinChe
 Exchange Rate, Inflation

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