ECON 202, FALL 2007
Malhar Nabar
October 4, 2007
MID TERM I
Instructions.
The maximum score is 75. Please answer all FOUR questions. Show all your work.
Simply writing down an answer (even if it happens to be the correct one) without an adequate
demonstration of how you arrived at your answer will not get you full credit. Partial credit will be
calculator. GOOD LUCK!
1.
(Ten Points)
Growth Accounting in the Solow Model
An economy described by the Solow Model has the following production function
Y
=
K
1
=
3
(
eL
)
2
=
3
;
where
Y
is aggregate output,
K
is aggregate capital,
L
is aggregate labor, and
e
is an index of
technology. The economy is in a steady state with the labor force growing at 1.2% per year and
technology growing at 1.8% per year. What fraction of the growth in total output is accounted for
by technological progress?
Rewrite the production function as
Y
=
e
2
=
3
±
K
1
=
3
L
2
=
3
=
AK
1
=
3
L
2
=
3
:
Take logs and di/erentiate with respect to time to get
d
ln
Y
dt
=
d
ln
A
dt
+
1
3
d
ln
K
dt
+
2
3
d
ln
L
dt
;
which can be reexpressed as
g
Y
=
g
A
+
1
3
g
K
+
2
3
g
L
to get the relationship between the growth rates of aggregate output, aggregate capital, technology
and labor. Since the economy is in a steady state,
g
Y
=
g
K
=
g
e
+
g
L
= 3%
:
The fraction of the
growth in total output accounted for by technological progress is the component of output growth left
over after the contributions of capital accumulation and labor force growth are taken into account.
It is given by
g
A
g
Y
=
g
Y
1
3
g
K
+
2
3
g
L
±
g
Y
=
0
:
03
(0
:
01 + 0
:
008)
0
:
03
=
0
:
012
0
:
03
= 40%
over and above the contributions of capital accumulation and the growth rate of the labor force.
Note: you cannot take the steady state growth rate of 3% and simply calculate the fraction as
g
e
g
Y
=
0
:
018
0
:
03
= 60%
:
This calculation would ignore the fact that the aggregate capital stock is also
growing and therefore contributing to output growth.
1
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(Twenty Points)
Solow Model with technological progress and population growth
A country is described by the Solow Model with per e/ective worker production function
e
y
=
e
k
0
:
5
:
The investment rate is 15%, the depreciation rate is 1%, the labor force grows at the annual rate
of 1%, and technology grows at the annual rate of 2%.
a. (Eight points)
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