Managerial Economics & Business Strategy Michael Baye 9e - Test Bank

Managerial Economics & Business Strategy Michael Baye 9e – Test Bank

Instant Download – Complete Test Bank With Answers

Sample Questions Are Posted Below

Chapter 05

The Production Process and Costs

Multiple Choice Questions

Suppose the marginal product of labor is 8 and the marginal product of capital is 2. If the wage rate is $4 and the price of capital is $2, then in order to minimize costs the firm should use:
more capital and less labor.
B.more labor and less capital.
C. three times more capital than labor.
D. none of the answers are correct.

Answer: B
Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application

Difficulty: 02 Medium

Suppose the production function is Q = min {K, 2L}. How much output is produced when 4 units of labor and 9 units of capital are employed?
2
B. 4
C.8
D. 9

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the production function is given by Q = 3K + 4L. What is the average product of capital when 10 units of capital and 10 units of labor are employed?
3
B. 4
C.7
D. 45

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose the production function is given by Q = 3K + 4L. What is the marginal product of capital when 10 units of capital and 10 units of labor are employed?
3
B. 4
C. 11
D. 45

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose the production function is given by Q = min{K, L}. How much output is produced when 10 units of labor and 9 units of capital are employed?
0
B. 4
C.9
D. 13

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the production function is given by Q = min {K, L}. How much output is produced when 4 units of labor and 9 units of capital are employed?
0
B.4
C. 9
D. 13

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose the production function is given by Q = 3K + 4L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?
3
B. 4
C. 11
D. 45

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 01 Easy

Suppose the production function is given by Q = 3K + 4L. What is the average product of capital when 5 units of capital and 10 units of labor are employed?
3
B. 4
C.11
D. 45

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

For the cost function C(Q) = 100 + 2Q + 3Q², the marginal cost of producing 2 units of output is:
2.
B. 3.
C. 12.
D.14.

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

For the cost function C(Q) = 100 + 2Q + 3Q², the average fixed cost of producing 2 units of output is:
100.
B.50.
C. 3.
D. 2.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

For the cost function C(Q) = 100 + 2Q + 3Q², the total variable cost of producing 2 units of output is:
16.
B. 12.
C. 4.
D. None of the answers are correct.

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

If a firm’s production function is Leontief and the wage rate goes up, the:
firm must use more labor in order to minimize the cost of producing a given level of output.
B. firm must use more capital in order to minimize the cost of producing a given level of output.
C. firm must use less labor in order to minimize the cost of producing a given level of output.
D.cost minimizing combination of capital and labor does not change.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 03 Hard

Which of the following statements is incorrect?
Fixed costs do not vary with output.
B. Sunk costs are those costs that are forever lost after they have been paid.
C.Fixed costs are always greater than sunk costs.
D. Fixed costs could be positive when sunk costs are zero.

Answer: C

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w = $40, r = $100, MP_L = 20, and MP_K = 40 the firm:
is cost minimizing.
B. should use less L and more K to cost minimize.
C.should use more L and less K to cost minimize.
D. is profit maximizing but not cost minimizing.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The production function Q = L^.5K^.5 is called:
Cobb Douglas.
B. Leontief.
C. linear.
D. None of the answers are correct.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The production function for a competitive firm is Q = K^.5L^.5. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at 25 units. The profit-maximizing quantity of labor is:
1.
B. 2.
C. 10.
D.None of the answers are correct.

Answer: D

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w = $40, r = $100, MP_L = 4, and MP_K = 40 the firm:
is cost minimizing.
B. should use less L and more K to cost minimize.
C.should use more K and less L to cost minimize.
D. is profit maximizing but not cost minimizing.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

If the production function is Q = K^.5L^.5 and capital is fixed at 1 unit, then the average product of labor when L = 25 is:
2/5.
B.1/5.
C. 10.
D. None of the answers are correct.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

For a cost function C = 100 + 10Q + Q², the marginal cost of producing 10 units of output is:
10.
B. 200.
C. 210.
D.None of the answers are correct.

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

For a cost function C = 100 + 10Q + Q², the average variable cost of producing 20 units of output is:
10.
B. 20.
C.30.
D. None of the answers are correct.

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

For a cost function C = 100 + 10Q + Q², the average fixed cost of producing 10 units of output is:
10.
B. 5.
C. 1.
D. None of the answers are correct.

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Which of the following conditions is true when a producer minimizes the cost of producing a given level of output?
The MRTS is equal to the ratio of input prices.
B. The marginal product per dollar spent on all inputs is equal.
C. The marginal products of all inputs are equal.
D.The MRTS is equal to the ratio of input prices, and the marginal product per dollar spent on all inputs is equal.

Answer: D

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

If the production function is Q = KL and capital is fixed at 1 unit, then the marginal product of labor when L = 25 is:
¼.
B. 1/10.
C. 15.
D.None of the answers are correct.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The production function for a competitive firm is Q = K^.5L^.5. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing quantity of labor is:
2/5.
B.1.
C. 10.
D. None of the answers are correct.

Answer: B

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The production function for a competitive firm is Q = K^.5L^.5. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit and costs $2. The maximum profits are:
3.
B. 10.
C. 15.
D. None of the answers are correct.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The feasible means of converting raw inputs such as steel, labor, and machinery into an output are summarized by:
land.
B. production.
C. capital.
D.technology.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The recipe that defines the maximum amount of output that can be produced with K units of capital and L units of labor is the:
production function.
B. technological constraint.
C. research and development schedule.
D. total product.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The creation of a new product is referred to as:
process innovation.
B. independent research and development.
C.product innovation.
D. patent disclosure.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Which of the following is NOT a means of acquiring product and process innovations?
Independent research and development
B.Mass production of the existing product
C. Reverse engineering
D. Hiring employees of innovating firms

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Inputs a manager may adjust in order to alter production are:
all factors.
B.variable factors.
C. long-run factors.
D. fixed factors.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

What is the average product of labor, given that the level of labor equals 10, total output equals 1200, and the marginal product of labor equals 200?
20
B.120
C. 6
D. 2,000

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 01 Easy

The change in total output attributable to the last unit of an input is the:
total product.
B. average product.
C.marginal product.
D. marginal return.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

If the last unit of input increases total product, we know that the marginal product is:
positive.
B. negative.
C. zero.
D. indeterminate.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Total product begins to fall when:
marginal product is maximized.
B. average product is below zero.
C. average product is negative.
D.marginal product is zero.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

What is the value marginal product of labor if: P = $10, MP_L = $25, and AP_L = 40?
$10,000
B. $1,000
C. $400
D.$250

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

It is profitable to hire units of labor as long as the value of marginal product:
is less than wage.
B. exceeds average product.
C. equals price.
D.exceeds wage.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Given the following table, how many workers should be hired to maximize profits?

Labor

Marginal

Product Labor

VMP_L

Wage

$32

$100

$128

$100

$64

$100

-1

$-4

$100

-12

$-48

$100

1
B.2
C. 3
D. 4

Answer: B

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Firm managers should use inputs at levels where the:
Marginal benefit equals marginal cost.
B. Price equals marginal product.
C. Value marginal product of labor equals wage.
D.Marginal benefit equals marginal cost and value marginal product of labor equals wage.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Given the linear production function Q = 10K + 5L, if Q = 10,000 and K = 500, how much labor is utilized?
600 units
B. 800 units
C. 500 units
D.1,000 units

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Given the Leontief production function Q = min{5.5K, 6.7L}, how much output is produced when K = 40 and L = 35?
220
B. 234.5
C. 192.5
D. 268

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the production function is given by Q = K^1/2L^1/2, and that Q = 30 and K = 25. How much labor is employed by the firm?
49
B. 6
C.36
D. 25

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Given the production function Q = min {4K, 3L}, what is the average product of capital when 8 units of capital and 16 units of labor are used?
16
B. 2
C.4
D. 32

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

For the production function Q = 5.2K + 3.8L, if K = 16 and L = 12, we know that MP_K is:
16.
B.5.2.
C. 3.8.
D. 12.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The combinations of inputs that produce a given level of output are depicted by:
indifference curves.
B. budget lines.
C. isocost curves.
D.isoquants.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Isoquants are normally drawn with a convex shape because:
inputs are perfectly substitutable.
B. inputs are perfectly complementary.
C.inputs are not perfectly substitutable.
D. inputs are not perfectly complementary.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The absolute value of the slope of the isoquant is the:
marginal rate of technical substitution.
B. marginal product of capital.
C. marginal rate of substitution.
D. value marginal product of labor.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The production function is Q = K^.6 L^.4. The marginal rate of technical substitution is:
2/3 K^-1 L.
B. K^-1 L^-1.
C.2/3 K L^-1.
D. K^.4 L^-.6.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

The Leontief production function implies:
straight-line isoquants.
B. convex-shaped isoquants.
C. A positive MRTS.
D.L-shaped isoquants.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

In order for isoquants to have a diminishing marginal rate of substitution, they must be:
L-shaped.
B. straight lines.
C. vertical.
D.None of the preceding statements is correct.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Changes in the price of an input cause:
isoquants to become steeper.
B.slope changes in the isocost line.
C. parallel shifts of the isocost lines.
D. changes in both the isoquants and isocosts of equal magnitude.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Which of the following sets of economic data is minimizing the cost of producing a given level of output?
MP_L = 20, MP_K = 40, w = $16, r = $32.
B. MP_L = 20, MP_K = 40, w = $32, r = $16.
C. MP_L = 40, MP_K = 20, w = $16, r = $32.
D. MP_L = 40, MP_K = 40, w = $16, r = $32.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

In order to minimize the cost of producing a given level of output, a firm manager should use more inputs when:
that input’s price rises.
B.that input’s price falls.
C. that input’s price remains the same.
D. the prices of other inputs fall.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Fixed costs exist only in:
the long run.
B. capital-intensive markets.
C.the short run.
D. labor-intensive markets.

Answer: C

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Costs that change as output changes are:
variable costs.
B. fixed costs.
C. sunk costs.
D. None of the preceding statements is correct.

Answer: A

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Costs that are forever lost after they have been paid are:
production costs.
B. fixed costs.
C.sunk costs.
D. variable costs.

Answer: C

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose you are a manager of a factory. You purchase five (5) new machines at one million dollars each. If you can resell two of the machines for $500,000 and three of the machines for $200,000, what are the sunk costs of purchasing the machines?
$5 million
B. $500,000
C.$3.4 million
D. $1.6 million

Answer: C

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

According to the table below, what is the total cost of producing 125 units of output?

1,000

350

1,000

700

1,000

1,050

125

1,000

1,400

145

1,000

1,750

160

1,000

2,100

1,000
B. 2,050
C. 1,400
D.2,400

Answer: D

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

According to the table below, what is the average variable cost of producing 50 units of output?

1,000

350

1,000

700

1,000

1,050

125

1,000

1,400

145

1,000

1,750

160

1,000

2,100

21
B. 34
C.14
D. 20

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

According to the table below, what is the average total cost of producing 160 units of output?

1,000

350

1,000

700

1,000

1,050

125

1,000

1,400

145

1,000

1,750

160

1,000

2,100

12.98
B. 16.31
C. 22.04
D.19.38

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

According to the table below, what is the marginal cost of producing 90 units of output?

1,000

350

1,000

700

1,000

1,050

125

1,000

1,400

145

1,000

1,750

160

1,000

2,100

5.32
B.8.75
C. 11.67
D. 21.00

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

According to the table below, at what level of output is marginal cost minimized?

1,000

350

1,000

700

1,000

1,050

125

1,000

1,400

145

1,000

1,750

160

1,000

2,100

90
B. 50
C. 125
D. 160

Answer: A

Learning Objective: 05-02

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Which curve(s) does the marginal cost curve intersect at the (their) minimum point?
Average total cost curve
B. Average fixed cost curve
C. Average variable cost curve
D.Average total cost curve and average variable cost curve

Answer: D

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Given a cost function C(Q) = 200 + 14Q + 8Q², what is the marginal cost function?
14 + 16Q
B. 14Q + 8Q²
C. 200 + 8Q²
D. 14 + 16Q²

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

What is implied when the total cost of producing Q₁ and Q₂ together is less than the total cost of producing Q₁ and Q₂ separately?
Economies of scale
B. Diminishing average fixed costs
C. Cost complementarity
D.Economies of scope

Answer: D

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

For the cost function C(Q) = 1000 + 14Q + 9Q² + 3Q³, what is the marginal cost of producing the fourth unit of output?
$42
B. $295
C.$230
D. $116

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

For the cost function C(Q) = 200 + 3Q + 8Q² + 4Q³, what is the average fixed cost of producing six units of output?
18.31
B. 212.61
C. 42.12
D.33.33

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Which of the following cost functions exhibits cost complementarity?
−4Q₁Q₂ + 8Q₁.
B. −4Q₂ + 8Q₁.
C. 6Q₁Q₂ − Q₁.
D. 4Q₂Q₁ + 8Q₁.

Answer: A

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

For the multiproduct cost function C(Q₁,Q₂) = 100 + 2Q₁Q₂ + 4Q₁², what is the marginal cost function for good one?
MC₁ = 2Q₂ + 4Q₁ − Q₂².
B.MC₁ = 2Q₂ + 8Q₁.
C. MC₁ = 100 + 2Q₁Q₂ + 4Q₁².
D. MC₁ = 4Q₁² − 2 Q₂².

Answer: B

Learning Objective: 05-05

Topic: Multiple-Output Cost Functions

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Which of the following cost functions exhibits economies of scope when three (3) units of good one and two (2) units of good two are produced?
C = 50 − 5Q₁Q₂ + 0.5Q₁² + Q₂².
C = 10 + 4Q₁Q₂ + Q₁² + Q₂².
C = 15 + 5Q₁Q₂ + 2Q₁ + 4Q₂.
C = 5 + Q₁Q₂ + Q₁²Q₂².

Answer: A

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The minimum average cost of producing alternate levels of output, allowing for optimal selection of all variables of production is defined by the:
long-run average total cost curve.
B. short-run average fixed cost curve.
C. short-run marginal cost curve.
D. long-run marginal cost curve.

Answer: A

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

A production function:
defines the minimum amount of output that can be produced with inputs such as capital and labor.
B. defines the average amount of output that can be produced with inputs such as capital and labor.
C.represents the technology available for turning inputs into output.
D. is determined only by the expenditures on R&D.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Which of the following is the most common source of technology?
Independent R&D
B. Licensing technology
C. Publications or technical meetings
D. Reverse engineering

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Variable factors of production are the inputs that a manager:
may adjust in order to alter sales.
B.may adjust in order to alter production.
C. cannot adjust in the short run.
D. cannot adjust in the long run.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The short run is defined as the time frame:
in which there are no fixed factors of production.
B.in which there are fixed factors of production.
C. less than one year.
D. less than three years.

Answer: B

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The long run is defined as:
the horizon in which the manager can adjust all factors of production.
B. the horizon in which there are only fixed factors of production.
C. the horizon in which there are both fixed and variable factors of production.
D. greater than one year.

Answer: A

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Which of the following is NOT a measure of productivity?
Total product
B. Marginal product
C.Average advertising
D. Input-output ratio

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 1 Easy

The marginal product of an input is defined as the change in:
average output attributable to the last unit of an input.
B.total output attributable to the last unit of an input.
C. total input attributable to the last unit of an output.
D. average output attributable to the last unit of an output.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

As long as marginal product is increasing, marginal product is:
less than average product.
B.greater than average product.
C. equal to average output.
D. equal to total product.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

As the usage of an input increases, marginal product:
initially increases then begins to decline.
B. initially decreases then begins to increase.
C. consistently decreases.
D. consistently increases.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

If a firm is operating on the production function, then workers:
must be putting forth maximal effort.
B. may not be putting forth maximal effort.
C. are usually putting forth average effort.
D. are usually putting forth minimal effort.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The manager institutes an incentive structure to ensure:
workers are in fact working at the expected potential.
B. workers are in fact working at their utility-maximizing effort level.
C.the firm produces on the production function.
D. the firm produces above the production function.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 03 Hard

The value of marginal product of an input is the value of the:
total output produced by total inputs.
B. average output produced by inputs.
C.output produced by the last unit of an input.
D. output produced by the first unit of an input.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

It is profitable to hire labor so long as the:
MP_L is greater than wage.
B. MP_L is less than wage.
C. VMP_L is less than wage.
D.VMP_L is greater than wage.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The demand for labor by a profit-maximizing firm is determined by:
MP_L = MC.
B. VMP_L = MC.
C. MP_L = W.
D.VMP_L = W.

Answer: D

Learning Objective: 05-02

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The demand for an input is:
sloping upward.
B.the VMP of the input.
C. determined by MP_L = W.
D. derived from input owner’s profit-maximizing condition.

Answer: B

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The Leontief production function:
implies inputs are used in variable proportions.
B.implies inputs are used in fixed proportions.
C. is Q = max {bK, cL}.
D. is Q = aK + bL.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

With a linear production function there is a:
perfect complementary relationship between all inputs.
B.perfect substitutable relationship between all inputs.
C. fixed-proportion relationship between all inputs.
D. variable-proportion relationship between all inputs.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The Cobb-Douglas production function is:
Q = aK + bL.
B. Q = min {bK, cL}.
C. Q = max {bK, cL}.
D.Q = K^aL^b.

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty 01 Easy

The average product of labor depends on how many units of:
labor are used.
B. capital are used.
C.labor and capital are used.
D. None of the preceding statements is correct.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The marginal product of capital for the Cobb-Douglas production function is given by:
bK^a L^b-1.
B.aK^a-1 L^b.
C. aK^a-1 L^b-1.
D. bK^a L^b.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

An isoquant defines the combination of inputs that yield the producer:
higher levels of output than the desired level of output.
B. lower levels of output than the desired level of output.
C.the same level of output.
D. None of the preceding statements is correct.

Answer: C

Learning Objective: 05-02

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The isoquants are normally drawn with a convex shape because inputs are:
not perfectly substitutable.
B. perfectly substitutable.
C. perfect complements.
D. normal goods.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The marginal rate of technical substitution:
determines the rate at which a producer can substitute between two inputs in order to increase one additional unit of output.
B.is the absolute value of the slope of the isoquant.
C. is the absolute value of marginal revenue.
D. is constant along the isoquant curve.

Answer: B

Learning Objective: 05-02

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 02 Medium

Whenever an isoquant exhibits a diminishing marginal rate of technical substitution, the corresponding isoquants are:
convex to the origin.
B. concave to the origin.
C. L-shaped.
D. linear.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

An isocost line:
represents the combinations of w and K that cost the firm the same amount of money.
B.represents the combinations of K and L that cost the firm the same amount of money.
C. represents the combinations of r and w that cost the firm the same amount of money.
D. has a convex shape.

Answer: B

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

For given input prices, isocosts farther from the origin are associated with:
lower costs.
B. the same costs.
C.higher costs.
D. initially lower, then higher costs.

Answer: C

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

If the marginal product per dollar spent on capital is less than the marginal product per dollar spent on labor, then in order to minimize costs the firm should use:
less capital and more labor.
B. less labor and more capital.
C. less labor and less capital.
D. more labor and more capital.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

If the price of labor increases, in order to minimize the costs of producing a given level of output, the firm manager should use:
less of labor and more of capital.
B. less of labor and less of capital.
C. more of labor and more of capital.
D. more of labor and less of capital.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Sunk costs are those costs that:
do not vary without output.
B.are forever lost after they have been paid.
C. can be collected even after they have been paid.
D. do vary with output.

Answer: B

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Average fixed cost:
initially declines, reaches a minimum, and then begins to increase as output increases.
B. increases continuously as output increases.
C.declines continuously as output is expanded.
D. keeps constant as output is expanded.

Answer: C

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The marginal cost curve:
lies always below the average total cost curve (ATC).
B. lies always above the average variable cost curve (AVC).
C. intersects the ATC and AVC at their maximum points.
D.intersects the ATC and AVC at their minimum points.

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

When marginal cost curve is below an average cost curve, average cost is:
increasing with output.
B.declining with output.
C. not varying with output.
D. None of the preceding statements is correct.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The difference between average total costs and average variable costs is:
marginal cost.
B.average fixed cost.
C. fixed cost.
D. None of the preceding statements is correct.

Answer: B

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Economies of scope exist when:
C(Q₁) + C(Q₂) < C(Q₁,Q₂).
B. C(Q₁) − C(Q₂) < C(Q₁,Q₂).
C.C(Q₁) + C(Q₂) > C(Q₁,Q₂).
D. C(Q₁) − C(Q₂) > C(Q₁,Q₂).

Answer: C

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Cost complementarity exists in a multiproduct cost function when:
the average cost of producing one output is reduced when the output of another product is increased.
B. the average cost of producing one output is increased when the output of another product is increased.
C. the marginal cost of producing one output is increased when the output of another product is decreased.
D.the marginal cost of producing one output is reduced when the output of another product is increased.

Answer: D

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. What are the fixed costs?
$50
B. $10
C. $1
D. $2

Answer: A

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. What is the total cost of producing 10 units?
$2,060
B.$1,060
C. $560
D. $1,010

Answer: B

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. What is the variable cost of producing 10 units?
$401
B. $1,060
C. $560
D.$1,010

Answer: D

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. What is the marginal cost of producing 10 units?
$401
B. $1,060
C. $560
D. $1,010

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. At 10 units of output, the average cost curve is:
in the increasing stage.
B. in the declining stage.
C. at the minimum level.
D. at the maximum level.

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

When there are economies of scope between two products which are separately produced by two firms, merging into a single firm can:
accomplish an increase in sales.
B.accomplish a reduction in costs.
C. lead to an increase in cost.
D. lead to a reduction in sales.

Answer: B

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

When there are economies of scope between products, selling off an unprofitable subsidiary could lead to:
a major reduction in costs.
B.only a minor reduction in costs.
C. only a minor reduction in sales.
D. a major reduction in sales.

Answer: B

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Economies of scale exist whenever long-run average costs:
increase as output is increased.
B.decrease as output is increased.
C. remain constant as output is increased.
D. None of the preceding statements is correct.

Answer: B

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The long-run average cost curve defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of:
fixed factors of production.
B. variable factors of production.
C.all factors of production.
D. sunk cost factors of production.

Answer: C

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The costs of production include:
the costs that appear on the income statements.
B. the opportunity costs foregone by producing a given product.
C. accounting costs.
D.accounting costs and opportunity costs.

Answer: D

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Suppose the long-run average cost curve is U-shaped. When LRAC is in the increasing stage, there exist:
economies of scope.
B. diseconomies of scope.
C. economies of scale.
D.diseconomies of scale.

Answer: D

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Constant returns to scale exist when long-run average costs:
increase as output is increased.
B. decrease as output is increased.
C.remain constant as output is increased.
D. None of the preceding statements is correct.

Answer: C

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Larger firms can produce a product at lower average cost than small firms when:
economies of scope exist.
B. diseconomies of scale exist.
C. economies of scale exist.
D. cost complementarities exist.

Answer: C

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Two firms producing identical products may merge due to the existence of:
economies of scope.
B.economies of scale.
C. cost complementarities.
D. All of the preceding statements are correct.

Answer: B

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the marginal product of labor is 10 and the marginal product of capital is 8. If the wage rate is $5 and the price of capital is $2, then in order to minimize costs the firm should use:
more capital and less labor.
B. more labor and less capital.
C. equal amounts of labor and capital.
D. None of the preceding statements is correct.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Suppose the production function is Q = min {3K, L}. How much output is produced when 6 units of labor and 3 units of capital are employed?
3
B.6
C. 9
D. None of the preceding statements is correct.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 01 Easy

Suppose the production function is given by Q = 2K + 5L. What is the marginal product of labor when 15 units of capital and 10 units of labor are employed?
2
B.5
C. 25
D. 50

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 01 Easy

Suppose the production function is given by Q = 4K + 6L. What is the average product of capital when 10 units of capital and 5 units of labor are employed?
14
B. 10
C.7
D. 5

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 01 Easy

For the cost function C(Q) = 75 + 4Q + 2Q², the marginal cost of producing 5 units of output is:
4.
B. 54.
C. 20.
D.24.

Answer: D

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 01 Easy

For the cost function C(Q) = 50 + 4Q + 2Q², the total variable cost of producing 7 units of output is:
32.
B. 102.
C.126.
D. None of the answers are correct.

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 01 Easy

If a firm’s production function is Leontief and the price of capital goes down, the:
firm must use less labor in order to minimize the cost of producing a given level of output.
B. firm must use more capital in order to minimize the cost of producing a given level of output.
C. firm must use less capital in order to minimize the cost of producing a given level of output.
D.cost-minimizing combination of capital and labor does not change.

Answer: D

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Which of the following “costs” could a firm that wants to remain in business avoid if it halted current production?
Fixed costs
B.Variable costs
C. Sunk costs
D. Opportunity costs

Answer: B

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

If the production function is Q = K^.5L^.5 and capital is fixed at 1 unit, then the average product of labor when L = 36 is:
1/3.
B.1/6.
C. 2/3.
D. None of the answers are correct.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Which of the following conditions is true when a producer minimizes the cost of producing a given level of output?
The marginal product per dollar spent on all inputs is equal.
B. The MRTS is equal to the ratio of the quantity of inputs.
C. The marginal products of all inputs are equal.
D. The marginal product per dollar spent on all inputs is equal and the MRTS is equal to the ratio of the quantity of inputs.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The inputs that a manager uses to alter production are referred to as:
variable factors.
B. long-run factors.
C. fixed factors.
D. All of the preceding statements are correct.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

The point where diminishing marginal returns has begun to affect production is best characterized by the point where the:
total product curve flattens out.
B. average product curve begins to be negatively sloped.
C.marginal product curve begins to be negatively sloped.
D. marginal product curve equals the average product curve.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Changes in the price of an input cause:
isoquants to become steeper.
B.slope changes in the isocost line.
C. parallel shifts of the isocost lines.
D. changes in both the isoquants and isocosts of equal magnitude.

Answer: B

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

In the short run, the marginal cost curve crosses the average total cost curve at:
a point just below the average fixed cost curve.
B.the minimum point of the average total cost curve.
C. the maximum point of the average total cost curve.
D. the point where the average total cost curve and average variable cost curve intersect.

Answer: B

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

Which of the following cost functions exhibits cost complementarity?
−3Q₂ + 4Q₁
B. 5Q₁Q₂ − Q₁
C. Q₂Q₁ + 2Q₁
D.−5Q₁Q₂ + 7Q₁

Answer: D

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 01 Easy

Which of the following cost functions exhibits economies of scope over the specified output range?
C(Q₁,Q₂) = 2 − 0.5Q₁Q₂ − (Q₁)² + (Q2)², for all Q₁ > 0 and Q₂ > 0
B. C(Q₁,Q₂) = 2 − 3Q₁Q₂ − (Q₁)² + (Q2)², for all Q₁ > 0 and Q₂ > 0
C.C(Q₁,Q₂) = 2 − 0.5Q₁Q₂ − (Q₁)² + (Q2)², for all Q₁ < 2 and Q₂ < 2
D. C(Q₁,Q₂) = 2 − 3Q₁Q₂ − (Q₁)² + (Q2)², for all Q₁ > 4 and Q₂ > 4

Answer: C

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The production function for good X exhibited in the table below is for the:


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

long run, since K is the fixed input.
B.short run, since L is the fixed input.
C. long run, since K is the variable input.
D. short run, since L is the variable input.

Answer: B

Learning Objective: 05-06

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

The marginal product of capital of producing 2,991 units of output (find point A) in the table below is:


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

26.7.
B. 19.5.
C. 5.7.
D. 2.4.

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The production function for good X in the table below exhibits increasing marginal returns to capital over what output range?


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

Between 0 and 1,524
B. Between 0 and 2,991
C. Between 2,391 and 3,048
D. Between 3,016 and 2,945

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The production function in the table below exhibits negative marginal returns to capital over what output range?


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

Between 0 and 1,524
B. Between 0 and 2,991
C. Between 2,391 and 3,048
D.Between 3,016 and 2,945

Answer: D

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The production function in the table below exhibits decreasing marginal returns to capital over what output range?


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

Between 0 and 1,524
B. Between 0 and 2,991
C.Between 2,391 and 3,048
D. Between 3,016 and 2,945

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The average product of capital of producing 2,991 units of output (find point B) in the table below is:


Production Function for Good X

L*	K	Q	MP_K=(∆Q/∆K)	AP_K = (Q/K)
Labor	Capital	Output	Marginal Product of Capital	Average Product of Capital
9	0	0	—	—
9	10	57	5.7	5.70
9	20	324	26.7	16.20
9	30	657	33.3	B
9	40	1,072	41.5	26.80
9	50	1,524	45.2	30.48
9	60	1,976	45.2	32.93
9	70	2,391	41.5	34.16
9	80	2,724	33.3	34.05
9	90	2,991	A	33.23
9	100	3,048	5.7	30.48
9	110	3,016	-3.2	27.42
9	120	2,945	-7.1	24.54

11.1.
B.21.9.
C. 37.
D. 73.

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the fixed cost of using 81 units of capital and 9 units of labor is:
$2,160.
B.$2,025.
C. $135.
D. There is insufficient information to determine the fixed costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the variable cost of using 81 units of capital and 9 units of labor is:
$2,160.
B. $2,025.
C.$135.
D. There is insufficient information to determine the variable costs.

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the average total cost of using 81 units of capital and 9 units of labor is:
$5.
B. $75.
C.$80.
D. There is insufficient information to determine the average total costs.

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the average variable cost of using 81 units of capital and 9 units of labor is:
$5.
B. $75.
C. $80.
D. There is insufficient information to determine the average variable costs.

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the average fixed cost of using 81 units of capital and 9 units of labor is:
$5.
B.$75.
C. $80.
D. There is insufficient information to determine the average fixed costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The derivative, dAC(Q)/dQ = (1/Q₂) {Q(dC/dQ) − C(Q)}, illustrates that when:
MC(Q) < AC(Q), average costs increase as output increases.
B.MC(Q) < AC(Q), average costs decrease as output increases.
C. MC(Q) > AC(Q), average costs decrease as output increases.
D. None of the answers are correct.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

The first-order conditions for maximizing profits, p = P × F(K, L) – wL − rK, are:
P × {¶F(K, L) / ¶K} − r = 0 and P × {¶F(K, L) / ¶L} − w = 0.
B. P × MP_K − r = 0 and P × MP_L − w = 0.
C. VMP_K = r and VMP_L = w.
D.All of the answers are correct.

Answer: D

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Which of the following profit functions exhibits a Leontief production function?
p = P × K^0.75L^0.50 − 20L − 35K
B.p = P × min (2L, 5K) − 20L − 35K
C. p = P × (3K + 4L) − 20L − 35K
D. p = P × (3K^0.5 + 4L^0.5)^1/0.2 − 20L − 35K

Answer: B

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Which of the following profit functions exhibits a linear production function?
p = P × K^0.75L^0.50 − 20L − 35K
B. p = P × min (2L, 5K) − 20L − 35K
C.p = P × (3K + 4L) − 20L − 35K
D. p = P × (3K^0.5 + 4L^0.5)^1/0.2 − 20L − 35K

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Which of the following profit functions exhibits a Cobb-Douglas production function?
p = P × K^0.75L^0.50 − 20L − 35K
B. p = P × min (2L, 5K) − 20L − 35K
C. p = P × (3K + 4L) − 20L − 35K
D. p = P × (3K^0.5 + 4L^0.5) ^1/0.2 − 20L − 35K

Answer: A

Learning Objective: 05-01

Topic: The Production Function

Blooms: Understand

AACSB: Knowledge Application

Difficulty: 02 Medium

Which of the following relations is the slope along a given isoquant?
dQ = {¶F(K, L)/¶K} dK + {¶F(K, L)/¶L} dL, where dQ > 0
B. 0 = {¶F(K, L)/¶L} dK + {¶F(K, L)/¶K} dL
C.0 = {¶F(K, L)/¶K} dK + {¶F(K, L)/¶L} dL
D. dQ = {¶F(K, L)/¶K} dL + {¶F(K, L)/¶L} dK, where dQ > 0

Answer: C

Learning Objective: 05-02

Topic: The Production Function

Blooms: Understand

AACSB: Analytical Thinking
Difficulty: 2 Medium

Suppose the w = $20 and r = $30. The isocost line for a firm in this industry is:
C = 20K + 30L.
B.K = 0.033C − 0.66L.
C. 1.5L + K = 0.5C.
D. Depends entirely on the functional form of the production function.

Answer: B

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose the production function is given by Q = 2K + L. If w = $4 and r = $4, how many units of K and L will be utilized in the production process?
All K and no L.
B. All L and no K.
C. Equal amounts of K and L.
D. A combination of K and L not represented above.

Answer: A

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

For given input prices, isocosts closer to the origin are associated with:
lower costs.
B. the same costs.
C. higher costs.
D. initially lower, then higher costs.

Answer: A

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Remember

AACSB: Knowledge Application
Difficulty: 01 Easy

For the cost function C(Q) = 500 + 12Q + 4Q² + Q³, what is the marginal cost of producing the eighth unit of output?
$184
B.$268
C. $524
D. $852

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

If the production function is Q = K^.5L^.5 and capital is fixed at 9 units, then the marginal product of labor when L = 49 is:
3.
B. 9/98.
C.3/14.
D. None of the answers are correct.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose the production function is given by Q = 4K + 3L. What is the average product of labor when 10 units of capital and 5 units of labor are employed?
3
B. 4
C.11
D. 45

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

The production function is Q = K^.4 L^.6. The marginal rate of technical substitution is:
3/2 K^-1 L.
B. K^-1 L^-1.
C.3/2 K L^-1.
D. K^.6 L^-.4.

Answer: C

Learning Objective: 05-01

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

For the cost function C(Q) = 100 + 4Q + 19Q² + 2Q³, what is the marginal cost of producing the fourth unit of output?
$42
B. $295
C.$252
D. $116

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose the cost function is C(Q) = 50 + Q − 10Q² + 2Q³. At 3 units of output, the marginal cost curve is:
in the increasing stage.
B. in the declining stage.
C. at the minimum level.
D. at the maximum level.

Answer: A

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $86.80 and the per-unit wage, w, is $20, then the average total cost of using 25 units of capital and 49 units of labor is:
$5.
B. $75.
C.$90.
D. There is insufficient information to determine the average total costs.

Answer: C

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = 4K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $86.80 and the per-unit wage, w, is $20, then the average total cost of using 25 units of capital and 49 units of labor is:
$5.25.
B. $22.50.
C.$31.00.
D. There is insufficient information to determine the average total costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = 4K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $12 and the per-unit wage, w, is $20, then the average total cost of using 25 units of capital and 49 units of labor is:
$6.25.
B. $9.14.
C.$10.07.
D. There is insufficient information to determine the average total costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking

Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $25, then the average fixed cost of using 9 units of capital and 81 units of labor is:
$5.
B.$75.
C. $80.
D. There is insufficient information to determine the average fixed costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $125, then the average fixed cost of using 16 units of capital and 25 units of labor is:
$9.
B.$12.
C. $56.
D. There is insufficient information to determine the average fixed costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $5, then the average fixed cost of using 16 units of capital and 25 units of labor is:
$9.
B.$12.
C. $56.
D. There is insufficient information to determine the average fixed costs.

Answer: B

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Essay Questions

Congress is considering legislation that will provide additional investment tax credits to businesses. Effectively, an investment tax credit reduces the cost to firms of using capital in production. Would you expect labor unions to lobby for or against such a bill? (Hint: What impact would such a plan have on the capital-to-labor ratio at the typical firm?)

Answer:

An investment tax credit would reduce the price of capital relative to labor. Other things equal, this would increase w/r, thereby making the isocost line steeper. This means that the cost-minimizing input mix will now involve more capital and less labor, as firms substitute toward capital. If labor unions are concerned that this higher capital/labor ratio will translate into lost jobs, they will likely oppose the investment tax credit. On the other hand, the marginal product of labor will likely rise as a result of the greater use of capital, so those workers employed might receive higher wages. If the union values higher wages, they might favor the legislation.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Evaluate

AACSB: Analytical Thinking
Difficulty: 02 Medium

You have been hired to replace the manager of a firm that used only two inputs, capital and labor, to produce output. The firm can hire as much labor as it wants at a wage of $5 per hour and can rent as much capital as it wants at a price of $50 per hour. After you look at the company books, you learn that the company has been using capital and labor in amounts that imply a marginal product of labor of 50 and a marginal product of capital of 100. Do you know why the firm hired you? Explain.

Answer:

Before the manager is hired, the marginal rate of technical substitution is 1/2. However, the relative input price is 1/10. This means that either more workers or less physical capital should be used. Hence, you are hired to change this input ratio in order to minimize costs.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The manager of a meat-packing plant can use either butchers (labor) or meat saws (capital) to prepare packages of sirloin steak. Based on estimates provided by an efficiency expert, the firm’s production function for sirloin steak is given by Q = K + L
a. Graph the isoquant corresponding to 5 units of output.
b. What is the marginal product of capital and labor? Does the answer depend on how much labor and capital are used?
c. If the price of labor is $2 per hour and the rental price of capital is $3 per hour, how much capital and labor should be used to minimize the cost of producing 5 units of output?

Answer:

See below:
MP_K = 1; MP_L = 1. These marginal products do not depend on how much labor and capital are used.
c. Five hours of labor and zero hours of capital should be used to minimize the cost of producing five units of output.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The manager of a national retailing outlet recently hired an economist to estimate the firm’s production function. Based on the economist’s report, the manager now knows that the firm’s production function is given by and that capital is fixed at 1 unit.
Calculate the average product of labor when 9 units of labor are utilized.
b. Calculate the marginal product of labor when 9 units of labor are utilized.
c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output.
d. What is the maximum price of capital at which the firm will still make nonnegative profits?

Answer:

Q = (1)^1/2(9)^1/2 = 3. The average product of labor is thus Q/L = 3/9.
b. MP_L = .5K^1/2L^-1/2 = .5(1)^1/2 (9)^-1/2 = 1/6
c. The profit-maximizing level of labor and output is achieved where VMP_L = w, where VMP_L = .5($100)(L^-1/2) and w = $10. Solving for L yields L = 25. The corresponding level of output is Q = (25)^1/2 = 5.
d. The firm’s variable costs are (25)($10) = $250, while its total revenues are 5 × $100 = $500. The maximum price of capital, hence, cannot be greater than $250 per unit.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 03 Hard

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 , where costs are measured in thousands of dollars and output is measured in thousands of hours rented.
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?
e. What is the relation between the answers to (a), (b), and (c) above? Is this a general property of average cost curves?

Answer:

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.

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

There are over 5,000 banks in the United States—more than 10 times more per person than in other industrialized countries. A recent study suggests that the long-run average cost curve for an individual bank is relatively flat. If Congress took steps to consolidate banks, thereby reducing the total number to 2,500, what would you expect to happen to costs within the banking industry? Explain.

Answer:

With a flat long-run average cost curve, there are neither economies nor diseconomies of scale in banking services. Consolidation would mean that 2,500 banks would each have to double their output in order to service the consumers initially served by 5,000 banks. But the corresponding average cost per firm, as well as total costs for the industry, would be unchanged.

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

A production function exhibits constant returns to scale if a twofold (threefold, etc.) increase in all inputs leads to a twofold (threefold, etc.) increase in output. For example, by doubling the use of capital and labor, the firm would exactly double its output.
What would the average and marginal cost curves look like under constant returns to scale? Explain.
b. Give an example of a production function that exhibits constant returns to scale.

Answer:

Average and marginal cost curves coincide and are flat (constant).
b. Q = K + L

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Create

AACSB: Analytical Thinking
Difficulty: 03 Hard

A production function exhibits decreasing returns to scale if a twofold (threefold, etc.) increase in all inputs increases output by less than twofold (less than threefold, etc.). For example, by doubling the use of capital and labor, the firm would less than double its output.
What would the average and marginal cost curves look like under decreasing returns to scale? Explain.
b. Give an example of a production function that exhibits decreasing returns to scale.

Answer:

Average and marginal cost curves are increasing, since doubling the inputs means doubling the total cost but less than doubling the output. Hence, average cost is increasing with output. A similar argument holds for marginal cost.
b. Q = L^1/2

Learning Objective: 05-06

Topic: The Cost Function

Blooms: Create

AACSB: Analytical Thinking
Difficulty: 03 Hard

The total costs for Morris Industries are summarized in the following table. Based on this information, fill in the missing entries in the table for fixed cost, variable cost, average fixed cost, average variable cost, average total cost, and marginal cost.

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Q	FC	VC	TC	AFC	AVC	ATC	MC
0			1,000
10			2,000
20			2,500
30			4,000
40			6,000
50			10,000
60			15,000

Answer:

Q	FC	VC	TC	AFC	AVC	ATC	MC
0	1,000	0	1,000	–	–	–	–
10	1,000	1,000	2,000	100	100	200	100
20	1,000	1,500	2,500	50	75	125	50
30	1,000	3,000	4,000	33.33	100	133	150
40	1,000	5,000	6,000	25	125	150	200
50	1,000	9,000	10,000	20	180	200	400
60	1,000	14,000	15,000	16.7	233.3	250	500

Learning Objective: 05-05

Topic: The Cost Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

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)	(2)	(3)	(4)	(5)	(6)	(7)
K	L	Q	MP_K	AP_K	AP_L	VMP_K
0	5	0
1	5	10
2	5	30
3	5	60
4	5	80
5	5	90
6	5	95
7	5	95
8	5	90
9	5	80
10	5	60
11	5	30

Which inputs are fixed inputs? Which are the variable inputs?
b. How much are your fixed costs?
c. What is the variable cost of producing 20 units of output?
d. How many units of the variable input should be used to maximize profits?
e. What are your maximum profits?
f. Over what range of variable input usage do increasing marginal returns exist?
g. Over what range of variable input usage do decreasing marginal returns exist?
h. Over what range of variable input usage do negative marginal returns exist?

Answer:

K	L	Q	MP_K	AP_K	AP_L	VMP_K
0	5	0	—	—	—	—
1	5	10	10	10	2	50
2	5	30	20	15	6	100
3	5	60	30	20	12	150
4	5	80	20	20	16	100
5	5	90	10	18	18	50
6	5	95	5	15.8	19	25
7	5	95	0	13.6	19	0
8	5	90	−5	11.3	18	−25
9	5	80	−10	8.9	16	−50
10	5	60	−20	6	12	−100
11	5	30	−30	2.7	6	−150

Labor is the fixed input while capital is the variable input.
b. Fixed costs are (5)($5) = $25.
c. Assume that capital is indivisible, (that is, it must be rented in an integer number of units). Then the required variable cost is (2)($20), which equals $40.
d. Using the VMP_K = r rule, six units of capital should be used to maximize profits.
e. The maximum profits are ($5)(95) − ($20)(6) − ($5)(5) = $330.
f. There are increasing marginal returns when K is less than or equal to 3.
g. There are decreasing marginal returns when K is greater than 3.
h. There are negative marginal returns when K is greater than 7.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Your firm produces two products, Q₁ and Q₂. An economic consulting firm has estimated your cost function to be .
a. Are there economies of scope?
Are there cost complementarities?
Your market for Q₁ is not very good, and an overseas firm has offered to buy the division of your company that produces Q₁. What will happen to your marginal cost of producing Q₂ if you sell the division?

Answer:

For a quadratic multiproduct cost function, economies of scope exist if . Here, f = 100 and a = 1, so economies of scope exist whenever .
Since a = 1 > 0, there are no cost complementarities.
c. Since a = 1 > 0, the marginal cost of producing product 2 will fall if the division producing product 1 is sold.

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

In the text, we showed that the multiproduct cost function exhibits cost complementarity whenever and economies of scope whenever .
Can cost complementarity exist without economies of scope?
b. Can there be economies of scope when cost complementarities exist?

Answer:

Cost complementarities cannot exist without economies of scope. This is because when a is negative, f − aQ₁Q₂ is necessarily positive (remember, f is fixed cost, which is nonnegative).
b. Suppose f is positive and a is negative. Then f − aQ₁Q₂ must be positive. Hence, there are both economies of scope and cost complementarities.

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

Standard Enterprises produces an output that it sells in a highly competitive market at a price of $100 per unit. Its inputs include two machines (which cost the firm $50 each) and workers, who can be hired on an as-needed basis in a labor market at a cost of $2,800 per worker. Based on the following production data, how many workers should the firm employ to maximize its profits?

Machines	Workers	Output
2	0	0
2	1	60
2	2	100
2	3	129
2	4	148
2	5	160
2	6	168

Answer:

The relevant production data is as follows:

Machines	Workers		Output		Marginal Product of Labor		Average Product of Labor		VMP Labor		Wage
2	0	0		_–		_–
2	1	60		60		60		$6,000		$2,800
2	2	100		40		50		$4,000		$2,800
2	3	129		29		43		$2,900		$2,800
2	4	148		19		37		$1,900		$2,800
2	5	160		12		32		$1,200		$2,800
2	6	168		8		28		$800		$2,800

To maximize profits, the firm should continue adding workers so long as the value marginal product exceeds the wage. The value marginal product is defined as the marginal product times the price of output. Here, output sells for $100 per unit, so the value marginal product of the third worker is $100(29) = $2,900. The table above summarizes the VMP_L for each possibility. Since the wage is $2,800, the profit-maximizing number of workers is 3.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Evaluate

AACSB: Analytical Thinking
Difficulty: 02 Medium

You are the manager of Telecall Inc., a small telemarketing company. Your company pays $10,000 per month for office space. A real estate agent has noticed that you are only using 75 percent of your available space and tells you that Telecall could add $800 per month to its bottom line by renting out the space it does not use. Telecall has been asked to do a new telemarketing campaign for a large credit card company, but this would require it to use the remaining office space. What is the opportunity cost of using the extra office space to handle the credit card company’s promotion?

Answer:

The $800 per month that could be earned by renting out the excess office space.

Learning Objective: 05-03

Topic: The Cost Function

Blooms: Understand

AACSB: Knowledge Application
Difficulty: 02 Medium

Suppose the production function of automobiles is given by .
Show that the marginal product of any given quantity of labor increases as capital is increased.
b. Suppose Japanese and U.S. automakers produce on identical isoquants with this Cobb-Douglas production function and that labor costs are higher in Japan than in the United States. Do autoworkers in Japan have a higher marginal product than American autoworkers? Explain carefully.
c. Now suppose Japanese automakers produce on a different isoquant from U.S. firms, but the prices of Japanese and American cars are identical. Do Japanese or American autoworkers have a higher marginal product? Why?

Answer:

Notice that MP_L can be written as.75(K/L)^1/4, which increases as K increases.
b. Since the higher labor costs in Japan induce a higher K/L ratio, the result in part (a) implies that the marginal product of Japanese workers is higher than that of American workers.
c. Since the prices of American and Japanese cars are assumed to be identical, the ratio of the value marginal product of American workers to Japanese workers is simply the ratio of the marginal products. Since this ratio equals the ratio of the wages—which is higher in Japan—our conclusion in part (b) is obtained again. Japanese workers have higher marginal products than do American workers.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 03 Hard

Show that the Cobb-Douglas production function exhibits the law of diminishing marginal rate of technical substitution.

Answer:

MP_L/MP_K = 3(K/L). This clearly decreases as L increases.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

You are the manager of a firm that sells output at a price of $40 per unit. You are interested in hiring a new worker who will increase your firm’s output by 2,000 units per year. Several other firms also are interested in hiring this worker.
What is the highest annual salary you should be willing to pay this worker to come to your firm?
b. What will determine whether or not you actually have to offer this much to the worker to induce him to join your firm?

Answer:

The extra revenue you will earn by hiring the worker is 2,000 × $40 = $80,000 per year. The most you should pay the worker is an annual salary of $80,000.
b. It depends on how much the worker can get from other firms. For instance, if his opportunity cost is $60,000, you will only have to pay $60,000.01 to get him.

Learning Objective: 05-01

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

To open a new business, a manager must obtain a license from the city for $20,000. The license is transferable, but only $3,000 is refundable in the event the firm does not use the license.
What are the firm’s fixed costs? Sunk costs?
b. Suppose the manager obtains a license but then decides against opening the business. If another firm offers the manager $2,000 for the license, should the manager accept the offer?

Answer:

Fixed costs are $20,000. Sunk costs are $17,000.
b. No. The manager can get a refund of $3,000 from the city, and this exceeds the $2,000 that it would have earned by selling the license to another firm.

Learning Objective: 05-04

Topic: The Cost Function

Blooms: Apply

AACSB: Analytical Thinking
Difficulty: 02 Medium

The maker of Turbotax produces software that prepares federal income tax returns. In addition, it produces software that prepares various state income tax returns. Why doesn’t it pay for the firm to specialize in federal software?

Answer: There are cost complementarities and economies of scope in producing software for federal returns (Q_F) and state returns (Q_S). When the multiproduct cost function, C(Q_F,Q_S), for producing federal and state tax preparation software exhibits economies of scope, it will be cheaper to produce both types of software jointly than to produce them separately. When there are cost complementarities in production, the marginal cost of producing state software (Q_S) will be lower when federal software is produced (Q_F). The economies of scope and cost complementarities are due to similarities in the programs and user interfaces that comprise federal and state income tax preparation software. Once a basic program and interface is written to compute federal taxes, the marginal cost of producing software for state purposes is much lower (effectively, it is the cost of entering details about each particular state’s tax code). If the maker of Turbotax specialized, then another firm that produced both types of software could do so at lower cost and undermine Turbotax’s position in the market.

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

The management of Morris Industries is considering a plan to terminate a new employee. The action stemmed from documented evidence supplied by the firm’s accounting department that this new employee did not add as much to the firm’s overall output as did a worker hired two weeks earlier. Based on this evidence, do you agree that the latest worker hired should be fired? Explain.

Answer:

No. In order to maximize profits, firms should hire workers up to the point where the value marginal product equals the wage rate in the range of diminishing marginal returns. The data suggests that the last worker added less to total output than the previous worker, which means that the firm is indeed operating in the range of diminishing marginal returns, as it should. The worker should be fired if his or her value marginal product is less than the wage. Unfortunately, management is not considering this information.

Learning Objective: 05-02

Topic: The Production Function

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

In 1995 the U.S. Justice Department sued to block a merger between Microsoft and Intuit, the producer of the nation’s best-selling business software. The Justice Department argued that the merger would lessen competition and raise prices of business software. Is there an economic argument that the merger might actually result in lower prices? Explain.

Answer:

If there are economies of scope or cost complementarities in producing operating systems like DOS and Windows in conjunction with business software, then the merger might lower costs and therefore prices to consumers.

Learning Objective: 05-07

Topic: Multiple-Output Cost Functions

Blooms: Analyze

AACSB: Analytical Thinking
Difficulty: 02 Medium

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