Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-34 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
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
d. cannot use this rule to make the decision
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
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 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
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-36 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
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 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
d. not enough information to tell
15-37 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
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 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
d. not enough information to tell
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-38 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
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 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
d. not enough information to tell
15-39 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
unchanged
no new plants
1 new plant
2 new plants
$20 million
$30 million
$40 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
d. not enough information to tell
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
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
15-41 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 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.
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-42 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 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
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
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-44 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 variance of the distribution?
a. 136.4
b. 278.8
c. 18.6
d. 346.4
e. 162.3
15-45 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 coefficient of variation for this distribution?
a. 0.39
b. 2.34
c. 0.86
d. 1.02
e. 0.10
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
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
e. none of the above
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
e. none of the above
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
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
15-49 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 2 is _____________.
a. 2,500
b. 2,758
c. 2,800
d. 3,000
e. none of the above
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-50 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
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
15-51 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 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
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
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
15-53 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 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
15-54 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
$150,000
Which option is chosen using the coefficient of variation rule?
a. Option A
b. Option B
c. Both options have the same coefficient of variation (to two decimal places).
d. cannot calculate expected profit with the given information
15-55 The manager’s utility function for profit is U() = 50, where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
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. $5,000
e. none of the above
15-56 The manager’s utility function for profit is U() = 50, where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
0.20
−$15,000
0.30
−$5,000
0.30
$5,000
0.20
$25,000
What is the expected utility of profit?
a. −2,500
b. 5,000
c. 15,000
d. 30,000
e. 100,000
15-57 The manager’s utility function for profit is U() = 50, where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
0.20
−$15,000
0.30
−$5,000
0.30
$5,000
0.20
$25,000
The marginal utility of an extra dollar of profit is __________.
a. 0.20
b. 0.30
c. 1.0
d. 10
e. none of the above
15-58 The manager’s utility function for profit is U() = 10 ln(), where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
0.05
$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. $15,000
e. none of the above
15-59 The manager’s utility function for profit is U() = 10 ln(), where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
0.05
$5,000
0.10
$10,000
0.35
$15,000
0.50
$20,000
What is the expected utility of profit?
a. 97
b. 245
c. 462
d. 974
e. 1,033
15-60 The manager’s utility function for profit is U() = 10 ln(), where is the dollar amount of profit.
The manager is considering a risky decision with the four possible profit outcomes shown below.
The manager makes the following subjective assessments about the probability of each profit
outcome:
Probability
Profit outcome ($)
0.05
$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