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Economics 154a, Spring 2005
Intermediate Macroeconomics
Problem Set 10: Answer Key
April 25, 2005
1. This problem studies a version of the Solow growth model developed in Chapter 6 of
the textbook. Suppose that aggregate output in period t is given by:
Y
t
=
K
0
.
3
t
N
0
.
7
...
(a) Calculate the steadystate capital stock implied by the law of motion for ag
gregate capital. Calculate the level of steadystate consumption implied by the
steadystate capital stock.
..
ANSWER
: The steady state capital stock is the value for capital
K
*
such that
K
*
= (1

d
)
K
*
+
sY
(
K
*
). Note that we have assumed
N
t
=
N
= 1, so we
simply plug it in:
K
*
= (1

d
)
K
*
+
sY
(
K
*
) = (1

0
.
1)
K
*
+ 0
.
2(
K
*
)
0
.
3
(1)
0
.
7
K
*
(0
.
1) = 0
.
2(
K
*
)
0
.
3
(
K
*
)
0
.
7
= 0
.
2
/
0
.
1
K
*
= (0
.
2
/
0
.
1)
1
/
0
.
7
= 2
.
69
To obtain consumption, simply ﬁnd which part of output (the steady state output
given by steady state capital
K
*
) is not saved but consumed:
C
*
=
Y
*

I
*
= (1

s
)
Y
*
= 0
.
8
×
2
.
69
0
.
3
= 0
.
8
×
1
.
34 = 1
.
07
(b) Suppose that s increases to 0.25. What is the new steadystate capital stock?
What is the new level of steadystate consumption?
ANSWER
: Clearly, substituting 0.25 instead of 0.2 in the equation above gives:
K
*
= 2
.
5
1
/
0
.
7
= 3
.
70
C
*
= 0
.
75
×
3
.
70
0
.
3
= 0
.
75
×
1
.
48 = 1
.
11
1
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View Full Document (c) Describe in qualitative terms the dynamic behavior of the capital stock after the
increase in the savings rate (assume that the economy is in a steady state before
the increase). Support your answer using an appropriate diagram.
ANSWER
: Qualitatively, when the rate of saving increases, there is less output
available for consumption and more for investment out of the original output,
Y
(
K
*
), so that consumption falls ﬁrst, while capital starts growing until it reaches
its new steady state
ˆ
K
*
. Consumption in this new steady state might be above or
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This homework help was uploaded on 04/06/2008 for the course ECON 154 taught by Professor Bjoernbruegemann during the Spring '07 term at Yale.
 Spring '07
 BjoernBruegemann
 Macroeconomics

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