Problem Set 5
THEORY OF PRODUCTION
1.
a. If a firm’s production function is given by F(L,K) =
3
9
18
K
L
+
, which is larger
AP
L
(8, 8) or AP
K
(8, 8)?
2.
a. What is the MRTS of the function F(L,K)= L
2
+ K?
b. Does this function exhibit diminishing MRTS?
c. Does this function exhibit increasing returns to scale?
3.
Suppose MP
L
(9, 20) =3 and AP
L
(9,20) = 6.
a. Is AP
L
(9,20) smaller than, larger than, or equal to AP
L
(10, 20)?
b. Is AP
L
(9, 20) smaller than, larger than, or equal to AP
K
(10, 20)?
4.
Suppose AP
L
(L, K) is always 17K.
a. What is F(L,K)?
b. What is MP
L
(L,K)?
c. Does F(L,K) exhibit diminishing MRTS?
5.
If MRTS(L,K) is always 3/2, draw the isoquants of F(L,K).
6.
Let F(L,K) = 5LK. When K rises does MP
L
rise or fall? Can you think of a reason
why this might be a good description of a real firm’s production?
7.
My firm digs ditches. Its production inputs are workers and shovels and its output,
measured in cubic feet per day, is ditches. Each worker needs a shovel (the ground is