# ECO-500 – A firm’s product sells for \$4 per unit in a highly competitive market

A firm’s product sells for \$4 per unit in a
highly competitive market. The firm produces output using capital (which it
rents at \$25 per hour) and labor (which is paid a wage of \$30 per hour under a
contract for 20 hours of labor services). Complete the following table and use
that information to answer the questions that follow.

Instruction:
Round your answers for Average Product of Capital and Average Product of Labor
to 2 decimal places.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Capital

Labor

Output

Marginal Product of Capital MPK

Average Product of Capital APK

Average Product of Labor APL

Value Marginal Product of Capital
VMPK

0

20

0

1

20

50

2

20

150

3

20

300

4

20

400

5

20

450

6

20

475

7

20

475

8

20

450

9

20

400

10

20

300

11

20

150

. Identify the fixed and variable
inputs.

Capital and labor are fixed
inputs.

Capital is the fixed input and
labor is the variable input.

Capital and labor are variable
inputs.

Labor is the fixed input and
capital is the variable input.

What are the firm’s fixed costs?

\$

c. What is the variable cost of producing 475 units of output?

\$

d. How many units of the variable input should be used to maximize profits?

e. What are the maximum profits this firm can earn?

\$

f. Over what range of the variable input usage do increasing marginal returns
exist?

From to

g. Over what range of the variable input usage do decreasing marginal returns
exist?

From to

h. Over what range of input usage do negative marignal returns exist?

From to

2. An economist estimated that the cost function of
a single-product firm is:

C(Q) = 100 + 20Q + 15Q2 + 10Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output.

\$

b. The variable cost of producing 10 units of output.

\$

c. The total cost of producing 10 units of output.

\$

d. The average fixed cost of producing 10 units of output.

\$

e. The average variable cost of producing 10 units of output.

\$
f. The average total cost of producing 10 units of
output.

\$

g. The marginal cost when Q = 10.

A manager hires labor and rents
capital equipment in a very competitive market. Currently the wage rate is
\$15 per hour and capital is rented at \$8 per hour. If the marginal product of
labor is 45 units of output per hour and the marginal product of capital is
65 units of output per hour, should the firm increase, decrease, or leave
unchanged the amount of capital used in its production process?

The
firm should increase capital.

The
firm should leave capital unchanged.

The
firm should decrease capital.

The World of Videos operates a retail
store that rents movie videos. For each of the last 10 years, World of
Videos has consistently earned profits exceeding \$37,000 per year. The
store is located on prime real estate in a college town. World of Videos
pays \$2,100 per month in rent for its building, but it uses only 50 percent
of the square footage rented for video rental purposes. The other portion
of rented space is essentially vacant. Noticing that World of Videos only
occupies a portion of the building, a real estate agent told the owner of
World of Videos that she could add \$1,650 per month to her firm’s profits
by renting out the unused portion of the store. While the prospect of
adding an additional \$1,650 to World of Videos’s bottom line was enticing,
the owner was also contemplating using the additional space to rent video
games. What is the opportunity cost of using the unused portion of the
building for video game rentals?

\$

Hyundai Heavy Industries Co. is
one of Korea’s largest industrial producers. According to an article in BusinessWeek
Online, the company is not only the world’s largest shipbuilder but
also manufactures other industrial goods ranging from construction
equipment and marine engines to building power plants and oil refineries
worldwide. Despite being a major industrial force in Korea, several of the
company’s divisions are unprofitable, or “bleeding red ink” in the words of
the article. Indeed, last year the power plant and oil refineries building
division recorded a \$105 million loss, or 19 percent of its sales. Hyundai
Heavy Industries recently hired a new CEO who is charged with the mission
of bringing the unprofitable divisions back to profitability. According to BusinessWeek,
Hyundai’s profit-driven CEO has provided division heads with the following
ultimatum: “…hive off money-losing businesses and deliver profits
within a year—or else resign.”

Suppose you are the head of the marine engine division and that it has been
unprofitable for 7 of the last 10 years. While you build and sell in the
competitive marine engines industry, your primary customer is Hyundai’s
profitable ship-building division. This tight relationship is due, in large
part, to the technical specifications of building ships around engines.
Suppose that in our end-of-year report to the CEO you must disclose that
while your division reduced costs by 10 percent, it still remains
unprofitable. Which of the following, if true, would be valid arguments you
could make to the CEO when explaining why your division should not be
shut down.

There
are cost complementarities and diseconomies of scale.

There
are constant returns to scale and economies of scope.

There
are cost complementarities and constant returns to scale.

There
are cost complementarities and economies of scope.

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