chapter 18: decision making under risk and uncertainty · 2019-05-05 · 15-6 choosing the decision...

Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in

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Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY

Multiple Choice 15-1 A probability distribution

a. is a way of dealing with uncertainty.

b. lists all possible outcomes and the corresponding probabilities of occurrence.

c. shows only the most likely outcome in an uncertain situation.

d. both a and b

e. both a and c

Answer: b

Difficulty: 01 Easy

Topic: Distinctions Between Risk and Uncertainty

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 15-01

15-2 The variance of a probability distribution is used to measure risk because a higher variance is

associated with

a. a wider spread of values around the mean.

b. a more compact distribution.

c. a lower expected value.

d. both a and b

e. all of the above

Answer: a

Difficulty: 01 Easy

Topic: Measuring Risk with Probability Distributions


Blooms: Remember


15-3 Risk exists when

a. all possible outcomes are known but probabilities can't be assigned to the outcomes.

b. all possible outcomes are known and probabilities can be assigned to each.

c. all possible outcomes are known but only objective probabilities can be assigned to each.

d. future events can influence the payoffs but the decision maker has some control over their

probabilities.

e. c and d

Answer: b

Difficulty: 01 Easy



Blooms: Remember


15-4 When a manager can list all outcomes and assign probabilities to each

a. uncertainty exists.

b. both risk and uncertainty exist.

c. risk exists.

d. the manager should use the minimax rule for making a decision.

e. b and d



Answer: c

Difficulty: 01 Easy



Blooms: Remember


15-5 Subjective probabilities are

a. determined from actual data on part experiences.

b. used in the presence of uncertainty.

c. almost never used from decision making.

d. based on feelings or hunches.

e. c and d

Answer: d

Difficulty: 01 Easy



Blooms: Remember


15-6 Choosing the decision with the maximum possible payoff

a. is the maximax rule.

b. ignores possible bad outcomes.

c. is a guide for decision making under uncertainty.

d. all of the above

e. none of the above

Answer: d

Difficulty: 02 Medium

Topic: Decisions Under Uncertainty


Blooms: Understand


15-7 The maximin rule

a. ignores bad outcomes.

b. is used by optimistic managers.

c. minimizes the potential regret.

d. a and c


Answer: e




Blooms: Understand


15-8 Using the minimax regret rule the manager makes the decision

a. with the smallest worst−potential regret.

b. with the largest worst−potential regret.

c. knowing he will not regret it.

d. that has the highest expected value relative to the other decisions.

Answer: a



Difficulty: 01 Easy



Blooms: Remember


15-9 In making decisions under risk

a. maximizing expected value is always the best rule.

b. mean variance analysis is always the best rule.

c. the coefficient of variation rule is always best.

d. maximizing expected value is best for making repeated decisions with identical

probabilities.


Answer: d

Difficulty: 01 Easy



Blooms: Understand


15-10 A firm is considering two projects, A and B, with the following probability distributions for profit.

Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

80

100

10

15

50

15

10

10

15

25

40

10

Given the above, the expected value of project A (in $1,000s) is

a. $60

b. $65

c. $70

d. $75

e. $80

Answer: a

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

10

15

50

10

15

25



80

100

15

10

40

10

Given the above, the variance of project A is

a. 7.07

b. 50

c. 440

d. 4,000

e. 380

Answer: c



AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

80

100

10

15

50

15

10

10

15

25

40

10

Given the above, what is the expected value of project B (in $1,000s)?

a. $60

b. $65

c. $70

d. $75

e. $80

Answer: b

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

80

100

10

15

50

15

10

10

15

25

40

10



Given the above, what is the variance of project B?

a. 10

b. 21

c. 165

d. 440

e. 515

Answer: e



AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

80

100

10

15

50

15

10

10

15

25

40

10

Given the above, a decision maker using the coefficient of variation rule would

a. choose project A.

b. choose project A only if risk averse.

c. choose project B.

d. choose project B only if risk loving.

e. not be able to make a decision using that rule.

Answer: e


Topic: Decisions Under Risk

AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$ 20

40

60

80

100

10

15

50

15

10

10

15

25

40

10

Given the above, a decision maker who is risk neutral would

a. choose project A.

b. choose project B.



c. not be able to make a decision.

d. change probabilities because no decision maker is ever risk neutral.

Answer: b



AACSB: Analytic

Blooms: Apply



Profit

($1,000s)

Project A

Probability (%)

Project B

Probability (%)

$20406080100

se

10

15

50

15

10

10

15

25

40

10

Given the above, the coefficient of variation (to 2 decimal places) is

a. higher for A.

b. higher for B.

c. equal for the two.

d. unable to be used for this choice.

e. both c and d

Answer: e



AACSB: Analytic

Blooms: Apply


15-17 In the maximin strategy, a manager choosing between two options will choose the option that:

a. has the highest expected profit

b. provides the best of the worst possible outcomes

c. minimizes the maximum loss

d. both a and b

e. both b and c

Answer: e

Difficulty: 01 Easy



Blooms: Remember


15-18 In the maximax strategy a manager choosing between two options will choose the option that

a. has the highest expected profit.

b. provides the best of the worst possible outcomes.

c. provides the best of the highest possible outcomes.

d. has the lowest variance.

e. a and d



Answer: c

Difficulty: 01 Easy



Blooms: Remember


15-19 Refer to the following probability distribution for profit to answer the question below:

Profit Probability

$30

40

50

60

0.05

0.25

0.60

0.10

What is the expected profit for this distribution?

a. $11,875

b. $46

c. $47.50

d. $48.75


Answer: c

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply



Profit Probability

$30

40

50

60

0.05

0.25

0.60

0.10

What is the variance of this distribution?

a. 48.75

b. 2,376

c. 525

d. 70

e. 11.875

Answer: a



AACSB: Analytic

Blooms: Apply





Profit Probability

$30

40

50

60

0.05

0.25

0.60

0.10

What is the coefficient of variation for this distribution?

a. 1.67

b. 0.675

c. 18.6

d. 0.147

e. 1.03

Answer: d



AACSB: Analytic

Blooms: Apply


15-22 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under

2 possible states of nature: the product price is $10 or the product price is $20.

Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the maximax rule, the decision maker would choose

a. A.

b. B.

c. C.

d. impossible to say from the information given

Answer: c



AACSB: Analytic

Blooms: Apply




Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140



Using the maximin rule, the decision maker would choose

a. A.

b. B.

c. C.

d. either A or B because neither has negative profit

Answer: b




Blooms: Understand




Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the maximum expected value rule, the decision maker would choose

a. A.

b. B.

c. C.

d. impossible to tell from the information

Answer: d

Difficulty: 01 Easy



Blooms: Understand




Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the equal probability rule the decision maker would choose

a. A.

b. B.

c. C.

d. impossible to tell from information

Answer: c

Difficulty: 01 Easy


AACSB: Analytic



Blooms: Apply




Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the minimax regret rule the decision maker would choose

a. A.

b. B.

c. C.


Answer: a

Difficulty: 01 Easy



Blooms: Understand


15-27 The following payoff matrix shows the profit outcomes for three projects, A, B, and C, for each

of two possible product prices. There is a 60% probability the price will be $10 and a 40%

probability the price will be $20.

Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the maximum expected value rule a decision maker would choose

a. A.

b. B.

c. C.


Answer: b

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply




15-28 The following payoff matrix shows the profit outcomes for three projects, A, B, and C, for each

of two possible product prices. There is a 60% probability the price will be $10 and a 40%

probability the price will be $20.

Profit

Project P = $10 P = $20

A 20 80

B 40 60

C −26 140

Using the mean variance rule a decision maker would choose

a. A.

b. B.

c. C.

d. can't use this rule under these circumstances

Answer: b

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply


15-29 A firm making production plans believes there is a 30% probability the price will be $10, a 50%

probability the price will be $15, and a 20% probability the price will be $20. The manager must

decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The

following table shows 9 possible outcomes depending on the output chosen and the actual price.

Profit (Loss) when price is

Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

What is the expected profit if 6,000 units are produced?

a. $171

b. $840

c. $640

d. $340

e. $260

Answer: d



AACSB: Analytic

Blooms: Apply









Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

What is the expected profit if 10,000 units are produced?

a. $500

b. $700

c. $625

d. $1,000

e. $1,754

Answer: b



AACSB: Analytic

Blooms: Apply







Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

If the mean-variance rule is used, how much should the firm produce?

a. 6,000

b. 8,000

c. 10,000

d. cannot use this rule to make the decision

Answer: d



AACSB: Analytic

Blooms: Apply









Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

What is the variance if 6,000 units are produced?

a. 490,000

b. 176,400

c. 100,000

d. 68,200

e. 76,460

Answer: b



AACSB: Analytic

Blooms: Apply







Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

For the above payoff matrix, suppose the manager has no idea about the probability of any of the

three prices occurring. If the maximax rule is used how much will the firm produce?

a. 6,000

b. 8,000

c. 10,000


Answer: c




Blooms: Understand









Production

6,000 (A)

8,000 (B)

10,000 (C)

$10

−$200

−$400

−$1,000

$15

$400

$600

$800

$20

$1,000

$1,600

$3,000

For the above payoff matrix, suppose the manager has no idea about the probability of any of the

three prices occurring. If the maximin rule is used how much will the firm produce?

a. 6,000

b. 8,000

c. 10,000


Answer: a




Blooms: Understand


15-35 A firm is considering the decision of investing in new plants. The following is the profit payoff

matrix under three conditions: it does not expand, it builds two new plants, or it builds one new

plant. Three possible states of nature can exist--no change in the economy, the economy contracts

and the economy grows. The firm has no idea of the probability of each state.

The economy

expands contracts unchanged

no new plants

1 new plant

2 new plants

$20 million

$30 million

$40 million

−$ 3 million

−$ 6 million

−$12 million

$4 million

$6 million

$8 million

What decision would be made using the maximax rule?

a. no new plants

b. one new plant

c. two new plants

d. not enough information to tell

Answer: c

Difficulty: 01 Easy



Blooms: Understand








The economy


no new plants

1 new plant

2 new plants

$20 million

$30 million

$40 million

−$ 3 million

−$ 6 million

−$12 million

$4 million

$6 million

$8 million

What decision would be made using the maximin rule?

a. no new plants

b. one new plant

c. two new plants


Answer: a




Blooms: Understand






The economy


no new plants

1 new plant

2 new plants

$20 million

$30 million

$40 million

−$ 3 million

−$ 6 million

−$12 million

$4 million

$6 million

$8 million

What decision would be made using the maximum expected value rule?

a. no new plants

b. one new plant

c. two new plants


Answer: d

Difficulty: 01 Easy



Blooms: Understand






plant. Three possible states of nature can exist--no change in the economy, the economy

contracts and the economy grows. The firm has no idea of the probability of each state.

The economy


no new plants

1 new plant

2 new plants

$20 million

$30 million

$40 million

−$ 3 million

−$ 6 million

−$12 million

$4 million

$6 million

$8 million

What decision would be made using the minimax regret rule?

a. no new plants

b. one new plant

c. two new plants


Answer: c




Blooms: Understand






The economy


no new plants

1 new plant

2 new plants

$20 million

$30 million

$40 million

−$ 3 million

−$ 6 million

−$12 million

$4 million

$6 million

$8 million

What decision would be made using the equal probability rule?

a. no new plants

b. one new plant

c. two new plants


Answer: c



AACSB: Analytic

Blooms: Apply




15-40 A firm is considering the decision of investing in new plants. It can choose no new plants, one

new plant, or two new plants. The following table gives the profits for each choice under three

states of the economy. The manager assigns the following probabilities to each state of the

economy: the economy expands, 20%, the economy contracts, 40%, or the economy is unchanged

40%.

The economy

expands (0.20) contracts (0.40) unchanged (0.40)

no new plants

1 new plant

2 new plants

$10 million

$20 million

$30 million

−$2 million

−$3 million

−$6 million

$3 million

$7 million

$5 million

Using the expected value rule which is correct? Building

a. no new plants is better than one.

b. one new plant is better than two.

c. one new plant is equivalent to building two.

d. one new plant is better than none.

e. c and d

Answer: e



AACSB: Analytic

Blooms: Apply






40%.

The economy


no new plants

1 new plant

2 new plants

$10 million

$20 million

$30 million

−$2 million

−$3 million

−$6 million

$3 million

$7 million

$5 million

Using the mean variance rules, which decision is correct?

a. The firm should build no new plants.

b. The firm should build one new plant.

c. The firm should build two new plants.

d. If deciding only between one or two new plants, the firm should build one.

e. If deciding only between one or two new plants, the firm should build two.

Answer: d



AACSB: Analytic

Blooms: Apply








40%.

The economy


no new plants

1 new plant

2 new plants

$10 million

$20 million

$30 million

−$2 million

−$3 million

−$6 million

$3 million

$7 million

$5 million

Using the coefficient of variation rule, the firm should build

a. no new plants.

b. one new plant.

c. two new plants.

d. cannot tell with this information

Answer: b



AACSB: Analytic

Blooms: Apply


15-43 Refer to the following table showing the probability distribution of payoffs from an activity to

answer the question below:

Units Payoff Probability

1

2

3

4

5

$30

40

60

50

10

10%

25%

30%

20%

15%

What is the expected value?

a. 16.5

b. 28

c. 36.5

d. 42.5

e. 49

Answer: d

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply







1

2

3

4

5

$30

40

60

50

10

10%

25%

30%

20%

15%

What is the variance of the distribution?

a. 136.4

b. 278.8

c. 18.6

d. 346.4

e. 162.3

Answer: b



AACSB: Analytic

Blooms: Apply





1

2

3

4

5

$30

40

60

50

10

10%

25%

30%

20%

15%

What is the coefficient of variation for this distribution?

a. 0.39

b. 2.34

c. 0.86

d. 1.02

e. 0.10

Answer: a



AACSB: Analytic

Blooms: Apply




15-46 The following table shows the expected value and variance for 5 projects a firm can undertake.

Project Expected Value Variance

A

B

C

D

E

$100

$220

$100

$180

$200

$124

$110

$138

$138

$124

Which of the following is (are) correct?

a. Project B dominates all others

b. Project E dominates all others

c. Project C is the least preferable

d. a and c


Answer: d

Difficulty: 03 Hard


AACSB: Analytic

Blooms: Apply


15-47 The following table shows the expected value and variance for 5 projects a firm can undertake.

Project Expected Value Variance

A

B

C

D

E

$100

$220

$100

$180

$200

$124

$110

$138

$138

$124

Which of the following is (are) correct if the mean−variance rule is used for the decision?

a. Project C is preferable to A.

b. Project E is preferable to B.

c. Project D is preferable to C.

d. all of the above


Answer: c



AACSB: Analytic

Blooms: Apply




15-48 Use the following two probability distributions for sales of a firm to answer the following

question:

Sales

Distribution 1

Probability

Distribution 2

Probability

2,000 0.05 0.05

3,000 0.20 0.15

4,000 0.50 0.20

5,000 0.20 0.35

6,000 0.05 0.25

The expect value of sales for Distribution 1 is _____________.

a. 2,500

b. 2,758

c. 2,800

d. 3,000

e. 4,000

Answer: e

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply



question:

Sales

Distribution 1

Probability

Distribution 2

Probability

2,000 0.05 0.05

3,000 0.20 0.15

4,000 0.50 0.20

5,000 0.20 0.35

6,000 0.05 0.25

The expect value of sales for Distribution 2 is _____________.

a. 2,500

b. 2,758

c. 2,800

d. 3,000


Answer: e

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply





question:

Sales

Distribution 1

Probability

Distribution 2

Probability

2,000 0.05 0.05

3,000 0.20 0.15

4,000 0.50 0.20

5,000 0.20 0.35

6,000 0.05 0.25

Which distribution is more risky?

a. Distribution 1 has a higher variance than Distribution 2, so Distribution 1 is more risky.

b. Distribution 2 has a higher variance than Distribution 1, so Distribution 2 is more risky.

c. Distribution 2 has a larger standard deviation than Distribution 1, so Distribution 2 is

more risky.

d. both b and c

Answer: d




Blooms: Understand



question:

Sales

Distribution 1

Probability

Distribution 2

Probability

2,000 0.05 0.05

3,000 0.20 0.15

4,000 0.50 0.20

5,000 0.20 0.35

6,000 0.05 0.25

The coefficients of variation for Distributions 1 and 2 are, respectively, ___________ and

___________, so Distribution ______ has MORE risk relative to its mean.

a. 0.22; 0.25; 2

b. 0.22; 0.25; 1

c. 0.31; 0.44; 1

d. 0.31; 0.44; 2

Answer: a



AACSB: Analytic

Blooms: Apply




15-52 A firm is making production plans for next quarter, but the manager does not know what the price

of the product will be next month. She believes there is a 30 percent chance price will be $500

and a 70 percent chance price will be $750. The four possible profit outcomes are:

Profit (loss) when price is:

$500 $750

Option A: produce 1,000 units −$12,000 $80,000

Option B: produce 2,000 units −$20,000 $150,000

Which option has the higher expected profit?

a. Option A

b. Option B

c. Both Options have the same expected profit

d. cannot calculate expected profit with the given information

Answer: b

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply






$500 $750



Which option has the highest (absolute) risk?

a. Option A is riskier than Option B.

b. Option B is riskier than Option A.

c. Both options have the level of risk if the manager is risk averse.

d. cannot calculate risk with the given information

Answer: b

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply






$500 $750





Which option is chosen using the coefficient of variation rule?

a. Option A

b. Option B

c. Both options have the same coefficient of variation (to two decimal places).

d. cannot calculate expected profit with the given information

Answer: c



AACSB: Analytic

Blooms: Apply


15-55 The manager’s utility function for profit is U() = 50, where is the dollar amount of profit.

The manager is considering a risky decision with the four possible profit outcomes shown below.

The manager makes the following subjective assessments about the probability of each profit

outcome: Probability Profit outcome ($)

0.20 −$15,000

0.30 −$5,000

0.30 $5,000

0.20 $25,000

What is the expected profit?

a. $2,000

b. $3,000

c. $4,000

d. $5,000


Answer: a

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply





outcome:

Probability Profit outcome ($)

0.20 −$15,000

0.30 −$5,000

0.30 $5,000

0.20 $25,000

What is the expected utility of profit?

a. −2,500

b. 5,000

c. 15,000

d. 30,000

e. 100,000

Answer: e



Difficulty: 01 Easy

Expected Utility: A Theory of Decision Making Under Risk

AACSB: Analytic

Blooms: Apply





outcome:


0.20 −$15,000

0.30 −$5,000

0.30 $5,000

0.20 $25,000

The marginal utility of an extra dollar of profit is __________.

a. 0.20

b. 0.30

c. 1.0

d. 10


Answer: e



AACSB: Analytic

Blooms: Apply


15-58 The manager’s utility function for profit is U() = 10 ln(), where is the dollar amount of profit.



outcome: Probability Profit outcome ($)

0.05 $5,000

0.10 $10,000

0.35 $15,000

0.50 $20,000

What is the expected profit?

a. $12,000

b. $13,000

c. $14,000

d. $15,000


Answer: e

Difficulty: 01 Easy


AACSB: Analytic

Blooms: Apply







outcome:


0.05 $5,000

0.10 $10,000

0.35 $15,000

0.50 $20,000

What is the expected utility of profit?

a. 97

b. 245

c. 462

d. 974

e. 1,033

Answer: a



AACSB: Analytic

Blooms: Apply





outcome:


0.05 $5,000

0.10 $10,000

0.35 $15,000

0.50 $20,000

Given this utility function for profit, the utility of profit is

a. equal to 198 for $20,000.

b. increasing as profit gets larger, so the manager is risk-loving.

c. decreasing as profit gets larger, so the manager is risk-averse.

d. both a and b

e. both a and c

Answer: d

Difficulty: 03 Hard


AACSB: Analytic

Blooms: Apply


chapter 18: decision making under risk and uncertainty · 2019-05-05 · 15-6 choosing the decision...

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