PROBLEMS
TEXTBOOK
Problem 1
Nimbus, Inc., makes brooms and then sells them door- to-door. Here is the relationship
between the number of workers and Nimbus’s output in a given day:
Workers
Output
0
0
1
20
2
50
3
90
4
120
5
140
6
150
7
155
Marginal
Product
Total
Cost
Average
Total
Cost
Marginal
Cost
a. Fill in the column of marginal products. What pattern do you see? How might you
explain it?
b. A worker costs $100 a day, and the firm has fixed costs of $200. Use this information
to fill in the column for total cost.
c. Fill in the column for average total cost. (Recall that ATC = TC/Q.) What pattern do
you see?
d. Now fill in the column for marginal cost. (Recall that MC = �TC/�Q.) What pattern
do you see?
e. Compare the column for marginal product and the column for marginal cost. Explain
the relationship.
f. Compare the column for average total cost and the column for marginal cost. Explain
the relationship.
Answer:
Table of costs:
Workers
Output
0
1
2
3
0
20
50
90
Marginal
Product
--20
30
40
Total
Cost
$200
300
400
500
Average
Total Cost
--$15.00
8.00
5.56
Marginal
Cost
--$5.00
3.33
2.50
4
5
6
7
120
140
150
155
30
20
10
5
600
700
800
900
5.00
5.00
5.33
5.81
3.33
5.00
10.00
20.00
a. See the table for marginal product. Marginal product rises at first, then declines
because of diminishing marginal product.
b. See the table for total cost.
c.
See the table for average total cost. Average total cost is U-shaped. When quantity is
low, average total cost declines as quantity rises; when quantity is high, average total
cost rises as quantity rises.
d. See the table for marginal cost. Marginal cost is also U-shaped, but rises steeply as
output increases. This is due to diminishing marginal product.
e. When marginal product is rising, marginal cost is falling, and vice versa.
f.
When marginal cost is less than average total cost, average total cost is falling; the
cost of the last unit produced pulls the average down. When marginal cost is greater
than average total cost, average total cost is rising; the cost of the last unit produced
pushes the average up.
Problem 2
Your aunt is thinking about opening a hardware store. She estimates that it would cost
$500,000 per year to rent the location and buy the stock. In addition, she would have to quit
her $50,000 per year job as an accountant.
a. Define opportunity cost.
b. What is your aunt’s opportunity cost of running a hardware store for a year? If your
aunt thought she could sell $510,000 worth of merchandise in a year, should she open
the store? Explain.
Answer:
a. The opportunity cost of something is what must be given up to acquire it.
b. The opportunity cost of running the hardware store is $550,000, consisting of
$500,000 to rent the store and buy the stock and a $50,000 opportunity cost,
because your aunt would quit her job as an accountant to run the store. Because the
total opportunity cost of $550,000 exceeds revenue of $510,000, your aunt should
not open the store, as her profit would be negative.
Problem 3
You are the Chief Financial Officer for a firm that sells digital music players. Your firm has
the following average total cost schedule:
Quantity
600 players
601
Average Total Cost
$300
301
Your current level of production is 600 devices, all of which have been sold. Someone calls
desperate to buy one of your music players. The caller offers $550 for it. Should you accept
the offer? Why or why not?
Answer:
At an output level of 600 players, total cost is $180,000 (600 × $300). The total cost of
producing 601 players is $180,901. Therefore, you should not accept the offer of $550,
because the marginal cost of the 601st player is $901.