Question 1

For most people, as their income increases, their utility from that income ________ at a(n) ________ rate.
A) increases; increasing
B) decreases; decreasing
C) increases; decreasing
D) decreases; increasing

Accepted Answer

This is because of the principle of diminishing marginal utility, which states that as a person receives more of a good, the additional satisfaction (utility) from each additional unit of the good decreases.

Question 2

Mark has two job offers when he graduates from college. Mark views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $50,000. The second offer is at a fixed salary of $20,000 plus a possible bonus of $60,000. Mark believes that he has a 50-50 chance of earning the bonus. If Mark takes the offer that maximizes his expected utility and is risk neutral, which job offer will he choose?
A) Mark will take the first offer.
B) Mark will take the second offer.
C) Mark is indifferent between the offers-both yield the same expected utility.
D) Indeterminate from the given information.

Accepted Answer

The expected utility for the second offer is calculated as 0.5 * $20,000 (no bonus) + 0.5 * $80,000 (with bonus) = $10,000 + $40,000 = $50,000, which is the same as the fixed salary of the first offer. Since Mark is risk-neutral, he is indifferent between the two offers as they both yield the same expected utility.

Question 3

Refer to the data provided in Table 17.2 below to answer the following questions. The table shows the relationship between income and utility for Sue.
Table 17.2
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 20 \
\hline \$ 40,000 & 40 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 80\
\hline
\end{array}$$
-Refer to Table 17.2. From the table, we can see that Sue is ________.
A) risk averse
B) risk loving
C) risk neutral
D) We cannot determine Sue's attitude toward risk from the table.

Accepted Answer

Since the total utility increases linearly with income, Sue is exhibiting a constant marginal utility of income. This indicates she is risk-neutral.

Question 4

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. What is the expected value of the game?
A) -$6
B) $0
C) $6
D) $30

Accepted Answer

The expected value (EV) of the game can be calculated by multiplying each outcome by its probability and summing these products. The probability of rolling a 6 is 1/6, and the probability of rolling any other number (1-5) is 5/6. The expected value calculation is: EV = (1/6)*$30 + (5/6)*(-$6) = $5 - $5 = $0.

Question 5

Consider the following game. You pick a card from a deck and each time you select an ace, you get $260. For all other cards you must pay $13. What is the expected value of the game?
A) -$12
B) $0
C) $8
D) $32

Accepted Answer

First, we need to find the probabilities of selecting an ace and selecting a non-ace:

- Probability of selecting an ace: There are 4 aces in a deck of 52 cards, so the probability of selecting an ace is 4/52 = 1/13.
- Probability of selecting a non-ace: There are 48 non-aces in a deck of 52 cards, so the probability of selecting a non-ace is 48/52 = 12/13.

Now, we can find the expected value of the game:

Expected value = (probability of selecting an ace) x (amount won per ace) + (probability of selecting a non-ace) x (amount lost per non-ace)
Expected value = (1/13) x 260 + (12/13) x (-13)
Expected value = 20 - 12
Expected value = $8

Therefore, the best choice is C, as it has the highest expected value.

Question 6

Refer to the information provided in Figure 17.1 below to answer the questions that follow.  Figure 17.1
-Refer to Figure 17.1. John has two job offers when he graduates from college. John views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $50,000. The second offer is at a fixed salary of $20,000 plus a possible bonus of $60,000. John believes that he has a 50-50 chance of earning the bonus. What is the expected value of John's income for each job offer?
A) $50,000 for the first offer and $80,000 for the second offer
B) $50,000 for the first offer and $50,000 for the second offer
C) $50,000 for the first offer and $30,000 for the second offer
D) $25,000 for the first offer and $50,000 for the second offer

Accepted Answer

The expected value of the first offer is simply $50,000. For the second offer, the expected value is calculated as: (0.5 x $20,000) + (0.5 x ($20,000 + $60,000)) = $50,000. Therefore, both job offers have an expected value of $50,000, so John should choose based on other factors such as job responsibilities, company culture, etc.

Question 7

Refer to the information provided in Figure 17.2 below to answer the questions that follow.  Figure 17.2
-Refer to Figure 17.2. Sam has two job offers when he graduates from college. Sam views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $60,000. The second offer is at a fixed salary of $30,000 plus a possible bonus of $60,000. Sam believes that he has a 50-50 chance of earning the bonus. If Sam takes the offer that maximizes his expected utility and is risk neutral, which job offer will he choose?
A) Sam will take the first offer.
B) Sam will take the second offer.
C) Sam is indifferent between the offers-both yield the same expected utility.
D) Indeterminate from the given information.

Accepted Answer

Since Sam is risk-neutral, he will base his decision on the expected value of each offer. The first offer has an expected value of $60,000. The second offer has an expected value of $30,000 (fixed salary) plus 0.5 * $60,000 (50% chance of earning the bonus), totaling $60,000. Therefore, both offers have the same expected value, making Sam indifferent between the two.

Question 8

Mark has two job offers when he graduates from college. Mark views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $40,000. The second offer is at a fixed salary of $20,000 plus a possible bonus of $40,000. Mark believes that he has a 50-50 chance of earning the bonus. If Mark takes the offer that maximizes his expected utility and is risk loving, which job offer will he choose?
A) Mark will take the first offer.
B) Mark will take the second offer.
C) Mark is indifferent between the offers-both yield the same expected utility.
D) Indeterminate from the given information.

Accepted Answer

Mark is risk-loving, which means he prefers more risky options with higher expected payoffs. To compare the two job offers, we need to calculate the expected value of the second offer.
Expected value of the second offer = (Probability of earning the bonus * Bonus amount) + (Probability of not earning the bonus * Fixed salary)
= (0.5 * 40,000) + (0.5 * 20,000)
= 30,000
Compared to the first offer of a fixed annual salary of $40,000, the expected value of the second offer is higher. Therefore, Mark will choose the second offer.

Question 9

Refer to the data provided in Table 17.1 below to answer the following questions. The table shows the relationship between income and utility for Jane.
Table 17.1
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 25 \
\hline \$ 40,000 & 45 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 70\
\hline
\end{array}$$
-Refer to Table 17.1. Suppose Jane has a 1/3 chance of becoming disabled in any given year. If she does become disabled, she will earn $0. If Jane does not become disabled, she will earn her usual salary of $60,000. Jane has the opportunity to purchase disability insurance which will pay her her full salary in the event she becomes disabled. On average, how much would such a contract cost the insurance company (per person)?
A) $20,000
B) $30,000
C) $40,000
D) $60,000

Accepted Answer

The average cost to the insurance company per person can be calculated by considering the probability of Jane becoming disabled and the amount the insurance would have to pay out in that event. Since there's a 1/3 chance of Jane becoming disabled, and the insurance would have to pay her full salary of $60,000 in that event, the average cost per person is $1/3 \times \$60,000 = \$20,000$.

Question 10

Refer to the data provided in Table 17.1 below to answer the following questions. The table shows the relationship between income and utility for Jane.
Table 17.1
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 25 \
\hline \$ 40,000 & 45 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 70\
\hline
\end{array}$$
-Refer to Table 17.1. Suppose Jane has a 1/3 chance of becoming disabled in any given year. If she does become disabled, she will earn $0. If Jane does not become disabled, she will earn her usual salary of $60,000. Jane has the opportunity to purchase disability insurance which will pay her her full salary in the event she becomes disabled. How much would such an insurance policy be worth to Jane?
A) $0
B) $20,000 or less
C) more than $20,000 but less than $40,000
D) $40,000 or more

Accepted Answer

Without the insurance, Jane's expected utility is:
$$ E(U) = \frac{2}{3} U(60000) + \frac{1}{3} U(0) = \frac{2}{3} U(60000) $$
With the insurance, her expected utility is:
$$ E(U) = U(20000) \times \frac{1}{3} + (U(60000) \times \frac{2}{3}) = 31.67 $$
Therefore, the insurance policy is worth the difference in utility, which is:
$$ 31.67 - \frac{2}{3} U(60000) = 31.67 - 40 = -8.33 $$
Since the policy is worth negative value (i.e. it reduces her utility), Jane wouldn't purchase the insurance.

Question 11

Refer to the information provided in Figure 17.1 below to answer the questions that follow.  Figure 17.1
-Refer to Figure 17.1. John has two job offers when he graduates from college. John views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $50,000. The second offer is at a fixed salary of $20,000 plus a possible bonus of $60,000. John believes that he has a 50-50 chance of earning the bonus. What is John's expected utility for each job offer?
A) expected utility of 200 for the first offer and expected utility of 218 for the second offer
B) expected utility of 200 for the first offer and expected utility of 110 for the second offer
C) expected utility of 200 for the first offer and expected utility of 164 for the second offer
D) expected utility of 100 for the first offer and expected utility of 164 for the second offer

Accepted Answer

The expected utility for the first offer is straightforward since it's a fixed amount, so its utility is directly calculated from that amount. For the second offer, the expected utility is calculated by taking the average of the utility of the $20,000 salary and the utility of the $80,000 total ($20,000 salary + $60,000 bonus), assuming a 50% chance of receiving the bonus. The correct answer must accurately reflect this calculation.

Question 12

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. Since the expected value of this game is $0, the game is called a(n) ________.
A) gamble
B) fair bet
C) even game
D) zero sum game

Accepted Answer

A fair bet is defined as a bet where the expected value of the outcomes is zero, meaning that over time, you neither gain nor lose money on average. In this game, the probability of rolling a 6 is 1/6, so the expected earnings are $30*(1/6) = $5. The probability of rolling any other number is 5/6, so the expected loss is $6*(5/6) = $5. Since the expected earnings equal the expected loss, the expected value of the game is $0, making it a fair bet.

Question 13

Refer to the data provided in Table 17.1 below to answer the following questions. The table shows the relationship between income and utility for Jane.
Table 17.1
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 25 \
\hline \$ 40,000 & 45 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 70\
\hline
\end{array}$$
-Refer to Table 17.1. Suppose Jane has a 1/3 chance of becoming disabled in any given year. If she does become disabled, she will earn $0. If Jane does not become disabled, she will earn her usual salary of $60,000. Jane has the opportunity to purchase disability insurance for $20,000 which will pay her her full salary in the event she becomes disabled. Jane's utility per year with the policy is ________ and her expected utility without the policy is ________.
A) 45; 40
B) 45; 45
C) 60; 40
D) 20; 45

Accepted Answer

The answer of Refer to the data provided in Table...

Question 14

Refer to the data provided in Table 17.1 below to answer the following questions. The table shows the relationship between income and utility for Jane.
Table 17.1
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 25 \
\hline \$ 40,000 & 45 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 70\
\hline
\end{array}$$
-Refer to Table 17.1. From the table, we can see that Jane is ________.
A) risk averse
B) risk loving
C) risk neutral
D) We cannot determine Jane's attitude toward risk from the table.

Accepted Answer

The answer of Refer to the data provided in Table...

Question 15

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. The $30 when you "win" and the -$6 when you "lose" are called ________.
A) payoffs
B) tradeoffs
C) incentives
D) expected values

Accepted Answer

The amounts of money you either win or lose in this game are referred to as "payoffs," which are the outcomes associated with different actions or events in decision-making situations, such as games.

Question 16

Refer to the information provided in Figure 17.1 below to answer the questions that follow.  Figure 17.1
-Refer to Figure 17.1. Suppose John's utility from income is given in the figure. From this we would say that John is ________.
A) risk neutral
B) risk averse
C) risk loving
D) a risk taker

Accepted Answer

Since John's utility function is concave (i.e. diminishing marginal utility), he is risk averse. Therefore, he would prefer a certain income of $50,000 over a gamble with an expected value of $50,000 and a 50% chance of $100,000 and a 50% chance of $0. So, the best choice for John would be the certain income of $50,000.

Question 17

Refer to the information provided in Figure 17.2 below to answer the questions that follow.  Figure 17.2
-Refer to Figure 17.2. Suppose Sam's utility from income is given in the diagram. From this we would say that Sam is ________.
A) risk neutral
B) risk loving
C) risk averse
D) a risk taker

Accepted Answer

The answer of Refer to the information provided in Figure...

Question 18

The sum of the utilities from each possible outcome of a situation weighted by the probability of that outcome is known as ________.
A) expected utility
B) total utility
C) marginal utility
D) expected value

Accepted Answer

Expected utility is the sum of utilities from each possible outcome of a situation weighted by the probability of that outcome. It helps in making the best decision by considering the probabilities of each outcome and their respective utilities.

Question 19

Refer to the information provided in Figure 17.1 below to answer the questions that follow.  Figure 17.1
-Refer to Figure 17.1. John has two job offers when he graduates from college. John views the offers as identical, except for the salary terms. The first offer is at a fixed annual salary of $50,000. The second offer is at a fixed salary of $20,000 plus a possible bonus of $60,000. John believes that he has a 50-50 chance of earning the bonus. If John takes the offer that maximizes his expected utility and is risk averse, which job offer will he choose?
A) John will take the first offer.
B) John will take the second offer.
C) John is indifferent between the offers-both yield the same expected utility.
D) Indeterminate from the given information.

Accepted Answer

Risk-averse individuals prefer a certain outcome over a gamble with the same expected value. The first offer guarantees $50,000, while the second has an expected value of $50,000 ($20,000 guaranteed plus a 50% chance of an additional $60,000) but with risk involved. Therefore, a risk-averse individual like John would choose the first offer.

Question 20

Refer to the data provided in Table 17.2 below to answer the following questions. The table shows the relationship between income and utility for Sue.
Table 17.2
 $$\begin{array} { | c | c | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 20,000 & 20 \
\hline \$ 40,000 & 40 \
\hline \$ 60,000 & 60 \
\hline \$ 80,000 & 80\
\hline
\end{array}$$
-Refer to Table 17.2. Sue earns $40,000 annually. She has the opportunity to bet her entire salary on the upcoming super bowl. If Sue takes the bet, she will pick the Patriots. She believes that the Patriots have a 50-50 chance of winning the game. If the Patriots win, Sue will double her money ($80,000) but if they lose she loses her entire salary ($0). This bet can be characterized as ________.
A) risk neutral
B) an unfair bet
C) a fair bet
D) risk loving

Accepted Answer

The bet is characterized as a fair bet because the expected value of the bet is equal to the current value of her salary. With a 50-50 chance of either doubling her money to $80,000 or losing it all ($0), the expected value is the average of these two outcomes, which is $40,000, the same as her current salary.

Quiz 17: Uncertainty and Asymmetric Information

For most people, as their income increases, their utility from that income at a(n) rate.

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. What is the expected value of the game?

Consider the following game. You pick a card from a deck and each time you select an ace, you get $260. For all other cards you must pay $13. What is the expected value of the game?

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. Since the expected value of this game is $0, the game is called a(n) ________.

Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. The $30 when you "win" and the -$6 when you "lose" are called ________.

Refer to the information provided in Figure 17.1 below to answer the questions that follow. Figure 17.1 -Refer to Figure 17.1. Suppose John's utility from income is given in the figure. From this we would say that John is ________.

Refer to the information provided in Figure 17.2 below to answer the questions that follow. Figure 17.2 -Refer to Figure 17.2. Suppose Sam's utility from income is given in the diagram. From this we would say that Sam is ________.

The sum of the utilities from each possible outcome of a situation weighted by the probability of that outcome is known as ________.