ECON 202, SPRING 2008
Malhar Nabar
Answer Key # 2
Posted: February 29
Note
: There are six questions in total. You may consult with other students, but please turn in
your own individual answer sheet with the names of all group members listed on the front page.
1.
Solow Model: Theory
Country C and Country D have the following production function
Y
=
K
1
3
L
2
3
The two countries have identical growth rates for the labor force and share an identical depre
ciation rate of capital, but country C invests 20% of output per year while Country D invests 5%
of output per year. Suppose the countries have reached their steady states. Calculate the following
steady state ratios:
k
C
k
D
and
y
C
y
D
The production function in per worker terms
y
=
k
1
=
3
The capital accumulation equation is
k
=
sk
1
=
3
(
n
+
)
k
In steady state,
k
= 0
and the steady state level of the per worker capital stock
k
s
(
k
)
1
=
3
(
n
+
)
k
= 0
)
k
=
s
n
+
±
1
1
±
1
=
3
=
s
n
+
±
3
2
This general formula applies to both countries (since they share the same aggregate production
function). Their steady state ratio
k
C
k
D
therefore is
k
C
k
D
=
s
c
s
D
±
3
2
=
&
0
:
2
0
:
05
±
3
2
= 4
3
2
= 8
And their steady state ratio
y
C
y
D
follows as
y
C
y
D
=
k
C
k
D
±
1
=
3
= 8
1
=
3
= 2
1
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Solow Model with technological progress
Chapter 8, problems and applications, #2.
We are given the following data
Capital Share of GDP (
) = 0.3
Growth rate of Output (n+g) = 0.03
Depreciation rate (
±
) = 0.04
a.
In the steady state, the investment per worker is exactly equal to the breakeven investment per
worker (using the hint provided):
s
e
y
= (
n
+
g
+
±
)
e
k
Also note that
e
k
e
y
=
K
el
Y
el
=
K
Y
= 2
:
5
Substituting in the relevant values from the above table, we see that
s
= (
n
+
g
+
±
)
e
k
e
y
= 0
:
175
Note that although the book refers to this as the saving rate what the author really has in mind
is the investment rate. In a closed economy it doesn±t matter since saving and investment are
equal. But it is more correct to talk about the investment rate in the Solow Model rather than
the saving rate. This is the constant fraction of output that±s invested in each time period.
b.
Recall that the capital share of income is given by
=
MPK
K
Y
So from this
MPK
=
(
K=Y
)
= 0
:
12
c.
In the golden rule steady state,
MPK
GR
= (
n
+
g
+
±
) = 0
:
07
Comparing with (b) we see that
current MPK > MPK
GR
. Due to diminishing marginal
returns to capital, we can conclude that the current steady state capital per e²ective worker
is lower than the golden rule steady capital per e²ective worker (i.e. we are to the left of the
steady state).
2
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 Spring '08
 Nabar
 Economics, Steady State

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