Deck 15: Decisions Under Risk and Uncertainty

Question 1

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 1

a wider spread of values around the mean.

Question 2

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-A decision maker using the analysis of variance 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 2

not be able to make a decision using that rule.

Question 3

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-The expected value of project A (in $1,000s) is

A) $60
B) $65
C) $70
D) $75
E) $80

Answer 3

$60

Question 4

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

Question 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) are based on feelings or hunches.
E) c and d

Question 6

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-What is the variance of project B?

A) 10
B) 21
C) 165
D) 440
E) 515

Question 7

Refer to the following probability distribution for profit
$$\begin{array} { c c } \text { Prafit } & \text { Prabability } \\\hline \$ 30 & 0.05 \\40 & 0.25 \\50 & 0.60 \\60 & 0.10\end{array}$$

-What is the expected profit for this distribution?

A) $11,875
B) $46
C) $47.50
D) $48.75
E) none of the above

Question 8

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

Question 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 most reliable for making repeated decisions with identical probabilities.
E) none of the above

Question 10

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

Question 11

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.

Question 12

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-What is the expected value of project B (in $1,000s)?

A) $60
B) $65
C) $70
D) $75
E) $80

Question 13

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

Question 14

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-A decision maker who is risk neutral would

A) choose project A.
B) choose project B.
C) not be able to make a decision.

Question 15

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-The variance of project A is

A) 7.07
B) 50
C) 440
D) 4,000
E) 380

Question 16

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

Question 17

Refer to the following probability distribution for profit
$$\begin{array} { c c } \text { Prafit } & \text { Prabability } \\\hline \$ 30 & 0.05 \\40 & 0.25 \\50 & 0.60 \\60 & 0.10\end{array}$$

-What is the variance of this distribution?

A) 48.75
B) 2,376
C) 525
D) 70
E) 11.875

Question 18

The maximin rule

A) ignores bad outcomes.
B) is used by optimistic managers.
C) minimizes the potential regret.
D) a and c
E) none of the above

Question 19

Refer to the following:
A firm is considering two projects, A and B, with the following probability distributions for profit.
$$\begin{array} { c c c } \begin{array} { c } \text { Profit } \\\text { (\$1,000s) }\end{array} & \begin{array} { c } \text { Praject } A \\\text { Probability } ( \% )\end{array} & \begin{array} { c } \text { Project B} \\\text { Prabability (\%) }\end{array} \\\hline \$ 20 & 10 & 10 \\40 & 15 & 15 \\{ 5 0 } & 50 & { 2 5 } \\{ 8 0 } & 15 & 40 \\100 & 10 & 10\end{array}$$

-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

Question 20

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

Question 21

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

-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

Question 22

Refer to the following:
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.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands } & \text { contracts } & \text { unchanged } \\\hline \text { no new plants } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 4 \text { million } \\1 \text { new plant } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 6 \text { million } \\2 \text { new plants } & \$ 40 \text { million } & -\$ 12 \text { million } & \$ 8 \text { million }\end{array}$

-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

Question 23

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

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

A) 6,000
B) 8,000
C) 10,000
D) can't use this rule to make the decision

Question 24

Refer to the following:
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.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands } & \text { contracts } & \text { unchanged } \\\hline \text { no new plants } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 4 \text { million } \\1 \text { new plant } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 6 \text { million } \\2 \text { new plants } & \$ 40 \text { million } & -\$ 12 \text { million } & \$ 8 \text { million }\end{array}$

-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

Question 25

Refer to the following:
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.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands } & \text { contracts } & \text { unchanged } \\\hline \text { no new plants } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 4 \text { million } \\1 \text { new plant } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 6 \text { million } \\2 \text { new plants } & \$ 40 \text { million } & -\$ 12 \text { million } & \$ 8 \text { million }\end{array}$

-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

Question 26

Refer to the following:
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.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands } & \text { contracts } & \text { unchanged } \\\hline \text { no new plants } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 4 \text { million } \\1 \text { new plant } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 6 \text { million } \\2 \text { new plants } & \$ 40 \text { million } & -\$ 12 \text { million } & \$ 8 \text { million }\end{array}$

-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

Question 27

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

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

A) $171
B) $840
C) $640
D) $340
E) $260

Question 28

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-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

Question 29

Refer to the following probability distribution for profit
$$\begin{array} { c c } \text { Prafit } & \text { Prabability } \\\hline \$ 30 & 0.05 \\40 & 0.25 \\50 & 0.60 \\60 & 0.10\end{array}$$

-What is the coefficient of variation for this distribution?

A) 1.67
B) 0.675
C) 18.6
D) 0.147
E) 1.03

Question 30

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

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

A) A.
B) B.
C) C.
D) impossible to tell from the information

Question 31

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

-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) can't use this rule to make the decision

Question 32

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-Using the equal probability rule the decision maker would choose

A) A.
B) B.
C) C.
D) impossible to tell from information

Question 33

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

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

A) $500
B) $700
C) $625
D) $1,000
E) $1,754

Question 34

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-Using the minimax regret rule the decision maker would choose

A) A.
B) B.
C) C.
D) impossible to tell from the information

Question 35

Refer to the following:
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.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands } & \text { contracts } & \text { unchanged } \\\hline \text { no new plants } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 4 \text { million } \\1 \text { new plant } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 6 \text { million } \\2 \text { new plants } & \$ 40 \text { million } & -\$ 12 \text { million } & \$ 8 \text { million }\end{array}$

-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

Question 36

Refer to the following:
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%.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands }(0.20) & \text { contracts }(0.40) & \text { unchanged }(0.40) \\\hline \text { no new plants } & \$ 10 \text { million } & -\$ 2 \text { million } & \$ 3 \text { million } \\1 \text { new plant } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 7 \text { million } \\2 \text { new plants } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 5 \text { million }\end{array}$

-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

Question 37

Refer to the following:
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 4 possible outcomes depending on the output chosen and the actual price.
$$\begin{array} { c c c c } & { \text { Prodi } ( \text { Loss } ) \text { when price is } } \\\hline \text { Prodiction } & \$ 10 & \$ 15 & \$ 20 \\\hline \text { G,000 } ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \\\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \\10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000\end{array}$$

-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
D) can't use this rule to make the decision

Question 38

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-Using the maximum expected value rule a decision maker would choose

A) A.
B) B.
C) C.
D) impossible to tell from the information

Question 39

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-Using the maximin rule, the decision maker would choose

A) A.
B) B.
C) C.
D) impossible to tell from the information given

Question 40

Refer to the following:
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.
$\begin{array}{l}\text { Profit }\\\begin{array}{l|c|c|}\hline \text { Project }&P=\$ 10 & P=\$ 20 \\\hline A&20 & 80 \\\hline B&40 & 60 \\\hline C&-26 & 140 \\\hline\end{array}\end{array}$

-Using the maximax rule, the decision maker would choose

A) A.
B) B.
C) C.
D) impossible to say from the information given

Question 41

Use the following two probability distributions for sales of a firm to answer Questions :
$$\begin{array} { c c c } \text { Sales } & \begin{array} { c } \text { Distribution1} \\\text { Probability }\end{array} & \begin{array} { c } \text { Distribution2} \\\text { Probability }\end{array} \\\hline 2,000 & 0.05 & 0.05 \\3,000 & 0.20 & 0.15 \\4,000 & 0.50 & 0.20 \\5,000 & 0.20 & 0.35 \\6,000 & 0.05 & 0.25\end{array}$$

-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

Question 42

Refer to the following:
The following table shows the expected value and variance for 5 projects a firm can undertake.
$$\begin{array} { c c c } \text { Praiecl } & \text { Expeted Value } & \text { Variance } \\\hline A & \$ 100 & \$ 124 \\B & \$ 220 & \$ 110 \\C & \$ 100 & \$ 138 \\D & \$ 180 & \$ 138 \\E & \$ 200 & \$ 124\end{array}$$

-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

Question 43

Use the following two probability distributions for sales of a firm to answer Questions :
$$\begin{array} { c c c } \text { Sales } & \begin{array} { c } \text { Distribution1} \\\text { Probability }\end{array} & \begin{array} { c } \text { Distribution2} \\\text { Probability }\end{array} \\\hline 2,000 & 0.05 & 0.05 \\3,000 & 0.20 & 0.15 \\4,000 & 0.50 & 0.20 \\5,000 & 0.20 & 0.35 \\6,000 & 0.05 & 0.25\end{array}$$

-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

Question 44

Using the following:
The manager's utility function for profit is U $\pi$ = 50 $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Probability } & \text { Profit outcome (\$) } \\\hline 0.20 & - \$ 15,000 \\0.30 & - \$ 5,000 \\0.30 & \$ 5,000 \\0.20 & \$ 25,000\end{array}$$

-What is the expected profit?

A) $2,000
B) $3,000
C) $4,000
D) $5,000
E) none of the above

Question 45

Refer to the following situation:
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:
$$\begin{array} { l c c } & \text { Prod (toss) when pice is: } \\\hline & \$ 500 & \$ 750 \\\hline\text { Option } A \text { produce } 1,000 \text { unids } & - \$ 12,000 & \$ 80,000 \\\text { Oplion } B \text { produce } 2,000 \text { unids } & \$ 20,000 & \$ 150,000\end{array}$$

-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

Question 46

Refer to the following:
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%.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands }(0.20) & \text { contracts }(0.40) & \text { unchanged }(0.40) \\\hline \text { no new plants } & \$ 10 \text { million } & -\$ 2 \text { million } & \$ 3 \text { million } \\1 \text { new plant } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 7 \text { million } \\2 \text { new plants } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 5 \text { million }\end{array}$

-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

Question 47

Using the following:
The manager's utility function for profit is U $\pi$ = 10 ln $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Prabability } & \text { Profit outcome (\$) } \\\hline 0.05 & \$ 5,000 \\0.10 & \$ 10,000 \\0.35 & \$ 15,000 \\0.50 & \$ 20,000\end{array}$$

-What is the expected profit?

A) $12,000
B) $13,000
C) $14,000
D) $15,000
E) none of the above

Question 48

Using the following:
The manager's utility function for profit is U $\pi$ = 50 $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Probability } & \text { Profit outcome (\$) } \\\hline 0.20 & - \$ 15,000 \\0.30 & - \$ 5,000 \\0.30 & \$ 5,000 \\0.20 & \$ 25,000\end{array}$$

-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

Question 49

Using the following:
The manager's utility function for profit is U $\pi$ = 50 $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Probability } & \text { Profit outcome (\$) } \\\hline 0.20 & - \$ 15,000 \\0.30 & - \$ 5,000 \\0.30 & \$ 5,000 \\0.20 & \$ 25,000\end{array}$$

-What is the expected utility of profit?

A) -2,500
B) 5,000
C) 15,000
D) 30,000
E) 100,000

Question 50

Refer to the following:
The following table shows the expected value and variance for 5 projects a firm can undertake.
$$\begin{array} { c c c } \text { Praiecl } & \text { Expeted Value } & \text { Variance } \\\hline A & \$ 100 & \$ 124 \\B & \$ 220 & \$ 110 \\C & \$ 100 & \$ 138 \\D & \$ 180 & \$ 138 \\E & \$ 200 & \$ 124\end{array}$$

-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

Question 51

Refer to the following table showing the probability distribution of payoffs from an activity.
$$\begin{array} { c c c } \text { Units } & \text { Payaff } & \text { Prabability } \\\hline 1 & \$ 30 & 10 \% \\2 & 40 & 25 \% \\3 & 60 & 30 \% \\4 & 50 & 20 \% \\5 & 10 & 15 \%\end{array}$$

-What is the expected value?

A) 16.5
B) 28
C) 36.5
D) 42.5
E) 49

Question 52

Refer to the following table showing the probability distribution of payoffs from an activity.
$$\begin{array} { c c c } \text { Units } & \text { Payaff } & \text { Prabability } \\\hline 1 & \$ 30 & 10 \% \\2 & 40 & 25 \% \\3 & 60 & 30 \% \\4 & 50 & 20 \% \\5 & 10 & 15 \%\end{array}$$

-What is the coefficient of variation for this distribution?

A) 0.39
B) 2.34
C) 0.86
D) 1.02
E) 0.10

Question 53

Using the following:
The manager's utility function for profit is U $\pi$ = 10 ln $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Prabability } & \text { Profit outcome (\$) } \\\hline 0.05 & \$ 5,000 \\0.10 & \$ 10,000 \\0.35 & \$ 15,000 \\0.50 & \$ 20,000\end{array}$$

-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

Question 54

Use the following two probability distributions for sales of a firm to answer Questions :
$$\begin{array} { c c c } \text { Sales } & \begin{array} { c } \text { Distribution1} \\\text { Probability }\end{array} & \begin{array} { c } \text { Distribution2} \\\text { Probability }\end{array} \\\hline 2,000 & 0.05 & 0.05 \\3,000 & 0.20 & 0.15 \\4,000 & 0.50 & 0.20 \\5,000 & 0.20 & 0.35 \\6,000 & 0.05 & 0.25\end{array}$$

-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 a and c
E)non of the bove

Question 55

Refer to the following situation:
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:
$$\begin{array} { l c c } & \text { Prod (toss) when pice is: } \\\hline & \$ 500 & \$ 750 \\\hline\text { Option } A \text { produce } 1,000 \text { unids } & - \$ 12,000 & \$ 80,000 \\\text { Oplion } B \text { produce } 2,000 \text { unids } & \$ 20,000 & \$ 150,000\end{array}$$

-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

Question 56

Refer to the following table showing the probability distribution of payoffs from an activity.
$$\begin{array} { c c c } \text { Units } & \text { Payaff } & \text { Prabability } \\\hline 1 & \$ 30 & 10 \% \\2 & 40 & 25 \% \\3 & 60 & 30 \% \\4 & 50 & 20 \% \\5 & 10 & 15 \%\end{array}$$

-What is the variance of the distribution?

A) 136.4
B) 278.8
C) 18.6
D) 346.4
E) 162.3

Question 57

Refer to the following situation:
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:
$$\begin{array} { l c c } & \text { Prod (toss) when pice is: } \\\hline & \$ 500 & \$ 750 \\\hline\text { Option } A \text { produce } 1,000 \text { unids } & - \$ 12,000 & \$ 80,000 \\\text { Oplion } B \text { produce } 2,000 \text { unids } & \$ 20,000 & \$ 150,000\end{array}$$

-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

Question 58

Using the following:
The manager's utility function for profit is U $\pi$ = 10 ln $\pi$ , where $\pi$ 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:
$$\begin{array} { c c } \text { Prabability } & \text { Profit outcome (\$) } \\\hline 0.05 & \$ 5,000 \\0.10 & \$ 10,000 \\0.35 & \$ 15,000 \\0.50 & \$ 20,000\end{array}$$

-What is the expected utility of profit?

A) 97
B) 245
C) 462
D) 974
E) 1,033

Question 59

Refer to the following:
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%.
$\text { The economy }$
$\begin{array}{lccc} & \text { expands }(0.20) & \text { contracts }(0.40) & \text { unchanged }(0.40) \\\hline \text { no new plants } & \$ 10 \text { million } & -\$ 2 \text { million } & \$ 3 \text { million } \\1 \text { new plant } & \$ 20 \text { million } & -\$ 3 \text { million } & \$ 7 \text { million } \\2 \text { new plants } & \$ 30 \text { million } & -\$ 6 \text { million } & \$ 5 \text { million }\end{array}$

-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.