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Solution HW2
1.
To calculate the steadystate level ratio of income per capita, we first find the steadystate level for each
country and then divide. The steadystate level ratio for Country X to Y is given by:
1
1
1
,
,
X
Xs
s
XX
X
Y
Ys
s
Y
YY
y
An
yA
n
α
γ
δ
−
−
⎡⎤
⎢⎥
⎛⎞
+
=
⎜⎟
⎝⎠
+
⎣⎦
We now substitute in the values
20%,
0,
n
=
=
and
5%
X
=
for Country X, and for Country Y, we use
the values
5%,
4%,
n
==
and
5%.
Y
=
Also, set
1/3
=
and
.
X
Y
AA
=
This yields,
1
1
(1/ 3)
1
2
3
1
2
,
,
0.2
43
6
00
.
0
5
2.68.
0.05
5
5
0.04
0.05
9
s
s
y
y
⎧⎫
−
⎨⎬
⎩⎭
+
=
≈
⎢⎥⎝⎠
+
Therefore, we conclude the ratio of Country X to Y in their steadystate levels of income per capita to be near
2.68.
2.
TFR
=
4.
NRR
=
(1/2)
×
[(1 child)
×
(Probability of reaching age 25)
+
(1 child)
×
(Probability of reaching age 28)
+
(1
child)
×
(Probability
of
reaching
age
32)
+
(1
child)
×
(Probability
of
reaching
age 35)]
Substituting in the given information, we get
NRR
=
(1/2)
×
[(2/3)
+
(2/3)
+
(1/3)
+
(1/3)]
=
1
b. NRR
=
(1/2)
×
[(1)
+
(1)
+
(1/2)
+
(1/2)]
=
1.5
c. TFR
=
2
NRR
=
(1/2)
×
[(1/2)
+
(1/2)
+
(1/2)
×
(1/2)
+
(1/2)
×
(1/2)]
=
.75
3.
The payment to human capital is the difference between the total wage and the wage for raw labor. Given the
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 Spring '10
 DR.RAHULA

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