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Econ 100B: Tang
Winter Quarter 2009
Homework 2: Ch 6 and Ch 7
Due Thursday January 22, at the beginning of class.
Please write your name and PID on your homework.
1) Say the production function for a foam fingers is given by:
3
3
2
2
600
L
K
L
K
q

=
.
If K=1, over what range of L will the function have diminishing marginal product of
labor?
2
3
1200
L
L
MP
L

=
L
L
MP
L
6
1200

=
∂
∂
so
L
MP
will be diminishing when L>200
2) Say the production function for stuffed penguins is given by:
2
2
2
.
8
.
L
K
KL
q


=
a. Graph the total and average product of labor curves if K=10.
Find the
level of labor that maximizes average product and the number of stuffed
penguins produced with that level of labor.
2
2
.
80
10
L
L
TP


=
L
L
AP
L
80
2
.
10


=
Take derivative w/ respect to labor, and set to 0, solve for L to find where
AP reaches max.
AP is maximized where L=20.
Q=40.
b. Graph the marginal product of labor curve, again assuming K=10.
Find
the level of labor where MP
L
=0.
L
MP
L
4
.
10

=
MP=0 at L=25
c. How would your answers change if K=20?
AP is maximized where L=40.
Q=160.
MP=0 at L=50
d. Does the function exhibit decreasing, constant, or increasing returns to
scale?
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 Spring '09
 TANG
 Microeconomics

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