number of employed workers is 47.5 million (502.5). (iv) The employment/population
ratio is 47.5% (47.5/100).
3.
6 points
The
average annual growth rates
for each of the 6 decades.
Using the exact method
Econ303
Homework 2 Answer
2
Average annual growth rate in
50
s
= (
15773
13244
)
1
/
10

1 = 1
.
76%
Average annual growth rate in
60
s
= (
20994
15773
)
1
/
10

1 = 2
.
90%
Average annual growth rate in
70
s
= (
25752
20994
)
1
/
10

1 = 2
.
06%
Average annual growth rate in
80
s
= (
32275
25752
)
1
/
10

1 = 2
.
28%
Average annual growth rate in
90
s
= (
39744
32275
)
1
/
10

1 = 2
.
10%
Average annual growth rate in
00
s
= (
42311
39744
)
1
/
10

1 = 0
.
63%
Using the approximating method
Average annual growth rate in
50
s
=
ln(15773)

ln(13244)
10
= 1
.
75%
Average annual growth rate in
60
s
=
ln(20994)

ln(15773)
10
= 2
.
86%
Average annual growth rate in
70
s
=
ln(25752)

ln(20994)
10
= 2
.
04%
Average annual growth rate in
80
s
=
ln(32275)

ln(25752)
10
= 2
.
26%
Average annual growth rate in
90
s
=
ln(39744)

ln(32275)
10
= 2
.
08%
Average annual growth rate in
00
s
=
ln(42311)

ln(39744)
10
= 0
.
63%
4.
8 points
The production function takes the following form
Y
=
F
(
K, L
) =
AK
0
.
4
L
0
.
6
The expressions for marginal product of labor and marginal product of capital are as
follows.
MP
L
= 0
.
6
·
AK
0
.
4
L

0
.
4
MP
K
= 0
.
4
·
AK

0
.
6
L
0
.
4
Table below are the values of the marginal product of labor
L=1
L=2
L=3
L=4
L=5
A
= 50 &
K
= 1000
475.4680
360.3373
306.3887
273.0846
249.7660
A
= 60 &
K
= 1000
570.5615
432.4048
367.6664
327.7016
299.7192
A
= 50 &
K
= 2000
627.3837
475.4680
404.2823
360.3373
329.5682
Econ303
Homework 2 Answer
3
When the total factor productivity increases, the marginal product of labor increases.
The marginal product of labor curve shifts up.
When the capital input increases, the marginal product of labor also increases. There
is complementarity between labor and capital.