Economics 314: Suggested Solutions to HW 2
TA: Romita Mukherjee
September 21, 2008
1
[Page 5, 3, NQ 1]
(a) If real GDP=$7 trillion, then real GDP after 10 years=($7 trillion)
*
(1
.
025)
10
=$8.96
trillion.
(b) If real GDP grows by $0.175 trillion per year: real GDP=$7 trillion +
(0.175)*10=$8.75. The answer in part (a) is greater than $8.75 trillion
since the growth is compounded over time.
2
[page 5, 3, NQ 3]
(a) Initial output is given by:
Y
=
AK
β
L
1

β
= 5
*
(400)
0
.
3
(100)
0
.
7
= 758
.
(b) Total Compensation to Employees=(1

β
)
Y
= (0
.
7)
*
758 = 531
.
(c) Increase labor and capital by 50%, we get changed Y as
Y
= 5
*
(600)
0
.
3
*
(150)
0
.
7
= 1137
,
which is 50% greater than 758.
3
[page 5, 3, (NQ 4)]
(a) Using Cobb Douglas production function with
K
= 200,
L
= 100,
A
= 2,
and
β
= 0
.
4, we have:
Intensive form:
y
=
Ak
β
= 2
*
(200
/
100)
0
.
4
= 2
.
64
(b) With
k
= 4
, y
= 2
*
(4)
0
.
4
= 3
.
48
1
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(c) The answer to part (b) does not depend on how the value of
k
changed
since
y
is a function of
k
itself.
4
[page 6, 3, NQ 5]
(a)
Y
1988
= (10)(1000)
0
.
3
(500)
0
.
7
= 6165
.
Y
1998
= (11)(1100)
0
.
3
(600)
0
.
7
= 7916
.
Δ
Y
Y
=
7916

6156
6156
= 29%
.
(b) Using growth accounting equation:
Δ
Y
Y
=
Δ
A
A
+
β
Δ
K
K
+ (1

β
)
Δ
L
L
Δ
Y
Y
≈
10 + (0
.
3)(10) + (0
.
7)(20) = 27%
.
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 Fall '07
 MBIEKOP
 Economics, Macroeconomics, Cobb Douglas, Cobb Douglas production, douglas production function

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