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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) Capital Labor Output 0 20 0 1 20 20 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 (6) (7) Value Marginal Marginal Average Average Product of Product of Product of Product of Capital Capital Capital APK Labor APL MPK VMPK 150 3 (5) 50 2 (4) 150 – – a. Identify the fixed and variable inputs. Labor is the fixed input and capital is the variable input. Capital and labor are variable inputs. Capital is the fixed input and labor is the variable input. – – Capital and labor are fixed inputs. b. 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 Problem 05-04 (Algo) An economist estimated that the cost function of a single-product firm is: C(Q) = 120 + 25Q + 30Q2 + 5Q3. 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. $ Problem 05-16 (Algo) 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 $36,000 per year. The store is located on prime real estate in a college town. World of Videos pays $2,300 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?

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)

Capital

Labor

Output

0

20

0

1

20
20
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

(6)

(7)

Value Marginal
Marginal
Average
Average
Product of
Product of
Product of Product of
Capital
Capital
Capital APK Labor APL
MPK
VMPK

150

3

(5)

50

2

(4)

150

a. Identify the fixed and variable inputs.
Labor is the fixed input and capital is the variable input.
Capital and labor are variable inputs.
Capital is the fixed input and labor is the variable input.

Capital and labor are fixed inputs.

b. 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
Problem 05-04 (Algo)
An economist estimated that the cost function of a single-product firm is:
C(Q) = 120 + 25Q + 30Q2 + 5Q3.
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.
$
Problem 05-16 (Algo)
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 $36,000 per year. The store is located
on prime real estate in a college town. World of Videos pays $2,300 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?

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