Section 7: Production and Costs
Question 1
1. Changes in the prices of key commodities have a significant impact on a company’s bottom
line. For virtually all companies, the price of energy is a substantial portion of their costs. In
addition, many industries—such as those that produce beef, chicken, high-fructose corn syrup
and ethanol—are highly dependent on the price of corn. In particular, corn has seen a
significant increase in price.
a. Explain how the cost of energy can be both a fixed cost and a variable cost for a company.
b. Suppose energy is a fixed cost and energy prices rise. What happens to the company’s
average total cost curve? What happens to its marginal cost curve? Illustrate your answer
with a diagram.
c. Explain why the cost of corn is a variable cost but not a fixed cost for an ethanol producer.
d. When the cost of corn goes up, what happens to the average total cost curve of an ethanol
producer? What happens to its marginal cost curve? Illustrate your answer with a diagram.
Solution 1
1. a. Energy required to keep a company operating regardless of how much output is produced
Question 2
2. Marty’s Frozen Yogurt is a small shop that sells cups of frozen yogurt in a university town.
Marty owns three frozen-yogurt machines. His other inputs are refrigerators, frozen-yogurt
mix, cups, sprinkle toppings, and, of course, workers. He estimates that his daily production
function when he varies the number of workers employed (and at the same time, of course,
yogurt mix, cups, and so on) is as shown in the accompanying table.
Quantity of labor
(workers)
Quantity of frozen
yogurt (cups)
0
0
1
110
2
200
3
270
4
300
5
320
6
330
a. What are the fixed inputs and variable inputs in the production of cups of frozen yogurt?
b. Draw the total product curve. Put the quantity of labor on the horizontal axis and the
quantity of frozen yogurt on the vertical axis.
c. What is the marginal product of the first worker? The second worker? The third worker?
Why does marginal product decline as the number of workers increases?
Solution 2
2. a. The fixed inputs are those whose quantities do not change as the quantity of output changes:
Question 3
3. The production function for Marty’s Frozen Yogurt is given in Problem 2. Marty pays each of
his workers $80 per day. The cost of his other variable inputs is $0.50 per cup of yogurt. His
fixed cost is $100 per day.
a. What is Marty’s variable cost and total cost when he produces 110 cups of yogurt? 200
cups? Calculate variable and total cost for every level of output given in Problem 2.
b. Draw Marty’s variable cost curve. On the same diagram, draw his total cost curve.
c. What is the marginal cost per cup for the first 110 cups of yogurt? For the next 90 cups?
Calculate the marginal cost for all remaining levels of output.
Solution 3
Question 4
4. Labor costs represent a large percentage of total costs for many firms. According to data from
the Bureau of Labor Statistics, U.S. labor costs were up 2.0% in 2015, compared to 2014.
a. When labor costs increase, what happens to average total cost and marginal cost? Consider
a case in which labor costs are only variable costs and a case in which they are both
variable and fixed costs.
An increase in labor productivity means each worker can produce more output. Recent data
on productivity show that labor productivity in the U.S. nonfarm business sector grew by
1.7% between 1970 and 1999, by 2.6% between 2000 and 2009, and by 1.1% between 2010
and 2015.
b. When productivity growth is positive, what happens to the total product curve and the
marginal product of labor curve? Illustrate your answer with a diagram.
c. When productivity growth is positive, what happens to the marginal cost curve and the
average total cost curve? Illustrate your answer with a diagram.
d. If labor costs are rising over time on average, why would a company want to adopt
equipment and methods that increase labor productivity?
Solution 4
Question 5
5. You have the information shown in the accompanying table about a firm’s costs. Complete the
missing data.
Solution 5
Question 6
6. Evaluate each of the following statements. If a statement is true, explain why; if it is false,
identify the mistake and try to correct it.
a. A decreasing marginal product tells us that marginal cost must be rising.
b. An increase in fixed cost increases the minimum-cost output.
c. An increase in fixed cost increases marginal cost.
d. When marginal cost is above average total cost, average total cost must be falling.
Solution 6
Question 7
7. Mark and Jeff operate a small company that produces souvenir footballs. Their fixed cost is
$2,000 per month. They can hire workers for $1,000 per worker per month. Their monthly
production function for footballs is as given in the accompanying table.
Quantity of labor
(workers)
Quantity of footballs
0
0
1
300
2
800
3
1,200
4
1,400
5
1,500
a. For each quantity of labor, calculate average variable cost (AVC), average fixed cost (AFC),
average total cost (ATC), and marginal cost (MC).
b. On one diagram, draw the AVC, ATC, and MC curves.
c. At what level of output is Mark and Jeff’s average total cost minimized?
Solution 7
Question 8
8. You produce widgets. Currently you produce four widgets at a total cost of $40.
a. What is your average total cost?
b. Suppose you could produce one more (the fifth) widget at a marginal cost of $5. If you do
produce that fifth widget, what will your average total cost be? Has your average total cost
increased or decreased? Why?
c. Suppose instead that you could produce one more (the fifth) widget at a marginal cost of
$20. If you do produce that fifth widget, what will your average total cost be? Has your
average total cost increased or decreased? Why?
Solution 8
Question 9
9. Don owns a small concrete-mixing company. His fixed cost is the cost of the concrete-
batching machinery and his mixer trucks. His variable cost is the cost of the sand, gravel,
and other inputs for producing concrete; the gas and maintenance for the machinery and
trucks; and his workers. He is trying to decide how many mixer trucks to purchase. He has
estimated the costs shown in the accompanying table based on estimates of the number of
orders his company will receive per week.
Quantity
of trucks
VC
FC
20
orders
40
orders
60 orders
2
$6,000
$2,000
$5,000
$12,000
3
7,000
1,800
3,800
10,800
4
8,000
1,200
3,600
8,400
a. For each level of fixed cost, calculate Don’s total cost for producing 20, 40, and 60 orders
per week.
b. If Don is producing 20 orders per week, how many trucks should he purchase and what will
his average total cost be? Answer the same questions for 40 and 60 orders per week.
Question 10
10. True or false? Explain your reasoning.
a. The short-run average total cost can never be less than the long-run average total cost.
b. The short-run average variable cost can never be less than the long-run average total cost.
c. In the long run, choosing a higher level of fixed cost shifts the long-run average total cost
curve upward.
Solution 10
Question 11
11. Wolfsburg Wagon (WW) is a small automaker. The accompanying table shows WW’s long–
run average total cost.
Quantity of cars
LRATC of
car
1
$30,000
2
20,000
3
15,000
4
12,000
5
12,000
6
12,000
7
14,000
8
18,000
a. For which levels of output does WW experience increasing returns to scale?
b. For which levels of output does WW experience decreasing returns to scale?
c. For which levels of output does WW experience constant returns to scale?
Solution 11
Question 12
WORK IT OUT Interactive step-by-step help with solving this problem can be found
online.
12. The accompanying table shows a car manufacturer’s total cost of producing cars.
Quantity of
cars
TC
0
$500,000
1
540,000
2
560,000
3
570,000
4
590,000
5
620,000
6
660,000
7
720,000
8
800,000
9
920,000
10
1,100,000
a. What is this manufacturer’s fixed cost?
b. For each level of output, calculate the variable cost (VC). For each level of output except
zero output, calculate the average variable cost (AVC), average total cost (ATC), and
average fixed cost (AFC). What is the minimum-cost output?
c. For each level of output, calculate this manufacturer’s marginal cost (MC).
d. On one diagram, draw the manufacturer’s AVC, ATC, and MC curves.
Solution 12
