Foundations of International Macroeconomics
1
Workbook
2
Maurice Obstfeld, Kenneth Rogo
ff
, and Gita Gopinath
Chapter 7 Solutions
1.
(The word °equiproportionate± in the third line of the statement of this
exercise should be °lumpsum.±)
(a) With the introduction of tax
°
nanced government spending in the Weil
(1989a) model, the period budget constraint for a family of vintage
υ
is given
by
k
υ
t
+1
= (1 +
r
t
)
k
υ
t
+
w
t
−
τ
−
c
υ
t
(where
τ
is the lumpsum tax) instead of by eq. (30) in Chapter 7. We write
the above expression in average per capita terms as
k
t
+1
−
k
t
=
f
(
k
t
)
−
c
t
−
g
1 +
n
−
nk
t
1 +
n
,
(1)
giving the analog of eq. (32) in the chapter. Here we have used the balanced
budget constraint
g
=
τ
.
The introduction of government expenditure there
fore shifts the
∆
k
= 0 locus down by
g/
(1 +
n
) in the phase diagram for per
capita consumption and the capitallabor ratio (
°
gure 7.7 on p. 449). The
presence of tax
°
nanced government spending does not a
ff
ect eq. (33) in the
text:
c
t
+1
= [1 +
f
0
(
k
t
+1
)] [
β
c
t
−
n
(1
−
β
)
k
t
+1
]
.
(2)
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
75
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(b) Figure 7.1 shows the phase diagram.
In that
°
gure, an unanticipated
permanent rise in
g
shifts the
∆
k
= 0 schedule down.
At the instant the
shock occurs, consumption declines immediately from point
A
to point
B
.
In subsequent periods, there is a gradual decumulation of capital, and con
sumption continues to decline until the new steady state
A
0
is reached at
lower levels of fl
c
and
fl
k.
The decline in
fl
k
represents a °crowding out± e
ff
ect
of balancedbudget government spending.
(c) As can be seen in
°
gure 7.2, the impact e
ff
ect of the announcement is an
immediate decline in consumption from
c
0
to
c
1
. The economy then moves
along an °unstable± path relative to the initial steady state. Along that path,
c
gradually declines while
k
increases until the economy reaches point
D
on
date
T
. Point
D
lies on the stable path corresponding to the new constant
level of
g
.
After date
T
,
c
and
k
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 Winter '08
 YuChinChe
 Macroeconomics, Thermodynamics, Dynamic Equilibrium, Steady State, per capita consumption

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