Econ302
Homework Assignment 3
Solution
1.
Trisha's Fashion Boutique production function for dresses is
(
29
1
1
3
2
,
,
=
y K L
K L
where
K
is the
number of sewing machines and
L
is the amount of labor hours employed.
Trisha pays $15 per labor
hour and sells each dress for $87.50.
Also, Trisha currently has 4 sewing machines.
Fill in the table
below.
How many units of labor will Trisha employ before the value of the marginal product of
labor is less than the cost of a labor hour?
y
L
L
MP
(
29
$87.50
L
MP
1
20
40
60
80
Solution:
1/ 2
(1/3) 1
1/ 2
2/3
1/ 2
2/3
2/3
1
1
3
3
3
3
L
y
MP
K L
K L
L
K
K
L
L


=
=
=
=
=
y
L
2
3
.
3
=
L
K
MP
L
(
29
$87.50
L
MP
2
1
0.666667
58.33333
5.428835
20
0.09048
7.917
6.839904
40
0.05700
4.9874
7.829735
60
0.04350
3.80612
8.617739
80
0.03590
3.14188
To find the number of units of labor that Trisha will employ, we need to find L
such that the value of the marginal product of labor is at least as much as the
wage rate.
87.5*MPL >= 15
2
3
4
15*
15.
3
L
K
We get L = 7.
1
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View Full Document2.
In Example 6.3 in the textbook, wheat is produced according to the production function
q = 100K
0.8
L
0.2
.
a.
Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and
the marginal product of capital are both decreasing.
For fixed labor and variable capital:
K
= 4
⇒
q
= (100)(4
0.8
)(49
0.2
) = 660.22
K
= 5
⇒
q
= (100)(5
0.8
)(49
0.2
) = 789.25
⇒
MP
K
= 129.03
K
= 6
⇒
q
= (100)(6
0.8
)(49
0.2
) = 913.19
⇒
MP
K
= 123.94
K
= 7
⇒
q
= (100)(7
0.8
)(49
0.2
) = 1,033.04
⇒
MP
K
= 119.85.
For fixed capital and variable labor:
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 Spring '08
 TOOSSI
 Economics, Marginal product, Economics of production, Parttime, Trisha

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