ECO 3320-002
Managerial Economics
Lanlan Chu
Chapter5
Quiz 5
1.
An accountant for a car rental company was recently asked to report the firm’s
costs of producing various levels of output. The accountant knows that the most
recent estimate available of the firm’s cost function is C (Q ) = 100 + 10Q + Q 2 ,
where costs are measured in thousands of dollars and output is measured in
thousands of hours rented.
a. What is the average fixed cost of producing 2 units of output?
b. What is the average variable cost of producing 2 units of output?
c. What is the average total cost of producing 2 units of output?
d. What is the marginal cost of producing 2 units of output? (MC(Q)=10+2Q)
e. What is the relation between the answers to (a), (b), and (c) above? Is this a
general property of average cost curves?
Answer:
a. AFC(2) = 100/2 = $50.
b. AVC(2) = [(10)(2) + (2)2]/2 = $12.
c. ATC(2) = AFC(2) + AVC(2) = $62.
d. MC(2) = 10 + 2(2) = $14.
e. AVC + AFC = ATC. This holds for all output levels, not just Q = 2.
2. The following table summarizes the short-run production function for your firm.
Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is
$20 per unit. Complete the following table, and then answer the accompanying questions.
(1)
K
0
1
2
3
4
5
6
7
8
9
10
11
a.
b.
c.
d.
e.
(2)
L
5
5
5
5
5
5
5
5
5
5
5
5
(3)
Q
0
10
30
60
80
90
95
95
90
80
60
30
(4)
MPK
10
20
30
20
10
5
0
-5
-10
-20
-30
(5)
APK
10=Q/K
15
20
20
18
15.8
13.6
11.3
8.9
6
2.7
(6)
APL
(7)
VMPK
2=Q/L 50=MPK*P
6
100
12
150
16
100
18
50
19
25
19
0
18
-25
16
-50
12
-100
6
-150
Which inputs are fixed inputs? Which are the variable inputs?
How much are your fixed costs?
What is the variable cost of producing 30 units of output?
How many units of the variable input should be used to maximize profits?
What are your maximum profits?
Answer:
a. Labor is fixed and capital is variable input
b. FC=5*5=25
c. VC(30)=20*2=40
d. Six units because VMPK>P for all the first six units
e. Q*=95 when K=6
 TR=5*95=475
TVC=20*6=120 TFC=5*5=25
Profit=TR-TVC-TFC=475-120-25=330