Question 1

(Table: Income and Total Utility for Naomi) Use Table: Income and Total Utility for Naomi. Naomi earns $50,000 per year but will be docked $20,000 of her pay if she is late with her work. Suppose there is a 25% probability that Naomi will be late with her work, reducing her income to $30,000. The premium for a fair insurance policy that would eliminate the uncertainty in her income would equal: $$\text { Table: Income and Total Utility for Naomi } \
\begin{array} { | l | l | } 
\hline \text { Income } & \text { Total Utility (in utils) } \
\hline \$ 30,000 & 1,000 \
\hline 32,500 & 1,800 \
\hline 35,000 & 2,500 \
\hline 37,500 & 3,100 \
\hline 38,200 & 3,267 \
\hline 40,000 & 3,620 \
\hline 40,500 & 3,700 \
\hline 42,500 & 4,000 \
\hline 43,750 & 4,175 \
\hline 45,000 & 4,300 \
\hline 47,500 & 4,500 \
\hline 50,000 & 4,600 \
\hline
\end{array}$$

Accepted Answer

The fair insurance premium is calculated as the expected loss due to the risk. The expected loss is 25% of $20,000, which is $5,000.

Question 2

(Table: Total Utility of Income After University Expenses and Scenario: University Expenses) Use Table: Total Utility of Income After University Expenses and Scenario: University Expenses. Mr. and Mrs. Perez would be willing to pay as much as _____ for insurance to pay their daughter's tuition and eliminate the uncertainty in the family's income after tuition.
Scenario: University Expenses
The Perez family would like to send their eldest daughter, Luciana, to university in the fall semester. There is a 25% chance that Luciana will earn a full scholarship to the Miller School of Medicine at the University of Miami, leaving the Perez family with $50,000 in income after tuition; a 50% chance that Luciana will earn a partial scholarship to the Florida State University College of Medicine and that the Perez family will have $40,000 in income after tuition; and a 25% chance that she will attend the Florida Institute of Technology, a private college, and that the Perez family will consequently have $30,000 in income after tuition.
 $${ \text { Table: Total Utility of Income after University Expenses} } \
\begin{array} { | l | l | } 
\hline
\text { Income } & \text { Total Utility (in utils) } \
\hline \$ 30,000 & 1,000 \
\hline 32,500 & 1,800 \
\hline 35,000 & 2,500 \
\hline 37,500 & 3,100 \
\hline 38,200 & 3,267 \
\hline 40,000 & 3,620 \
\hline 40,500 & 3,700 \
\hline 42,500 & 4,000 \
\hline 43,750 & 4,175 \
\hline 45,000 & 4,300 \
\hline 47,500 & 4,500 \
\hline 50,000 & 4,600 \
\hline
\end{array}$$

Accepted Answer

The expected utility of income after tuition is 0.25(4,600) + 0.50(3,620) + 0.25(1,000) = 3,050 utils. The expected utility of income after tuition with insurance is 4,600 utils. Therefore, the Perez family would be willing to pay as much as 4,600 - 3,050 = $1,550 for insurance to pay their daughter's tuition and eliminate the uncertainty in the family's income after tuition.

Question 3

(Table: Total Utility and Choices with Uncertainty and Scenario: A Novelist or a Teacher) Use Table: Total Utility and Choices with Uncertainty and Scenario: A Novelist or a Teacher. Suppose that the probability that a biography is not a success is 50%, that it is a success is 30%, and that it is a success and optioned for a movie is 20%. Given this information, Elizabeth's expected income is:
Scenario: A Novelist or a Teacher
Elizabeth is working as a high school English teacher and is considering leaving her teaching job to ghost write biographies for Hollywood actors. Her teaching job pays $40,000 per year. In contrast, the ghost writing will pay $25,000 for the first year whether the biography is a success or not, $50,000 if it is a success, and $100,000 if it is a success and is optioned for a movie deal. Elizabeth is a utility maximizer; her utility function is shown in the table.
 $$\text { Table: Total Utility and Choices with Uncertainty } \
\begin{array} { | l | l | } 
\hline \text { Income } & \text { Total Utility (utils) } \
\hline \$ 25,000 & 1,500 \
\hline 30,000 & 1,900 \
\hline 35,000 & 2,250 \
\hline 40,000 & 2,550 \
\hline 45,000 & 2,800 \
\hline 50,000 & 3,000 \
\hline 55,000 & 3,150 \
\hline 60,000 & 3,250 \
\hline 65,000 & 3,300 \
\hline 100,000 & 3,500 \
\hline
\end{array}$$

Accepted Answer

To calculate Elizabeth's expected income from ghostwriting, we multiply each income by its respective probability and sum these products: $$ (0.5 \times \$25,000) + (0.3 \times \$50,000) + (0.2 \times \$100,000) = \$12,500 + \$15,000 + \$20,000 = \$47,500. $$

Question 4

(Table: Total Utility and Choices with Uncertainty and Scenario: A Novelist or a Teacher) Use Table: Total Utility and Choices with Uncertainty and Scenario: A Novelist or a Teacher. Suppose that the probability that a biography is not a success is 30%, that it is a success is 50%, and that it is a success and optioned for a movie is 20%. Given this information, Elizabeth's expected income is:
Scenario: A Novelist or a Teacher
Elizabeth is working as a high school English teacher and is considering leaving her teaching job to ghost write biographies for Hollywood actors. Her teaching job pays $40,000 per year. In contrast, the ghost writing will pay $25,000 for the first year whether the biography is a success or not, $50,000 if it is a success, and $100,000 if it is a success and is optioned for a movie deal. Elizabeth is a utility maximizer; her utility function is shown in the table.
 $$\text { Table: Total Utility and Choices with Uncertainty } \
\begin{array} { | l | l | } 
\hline \text { Income } & \text { Total Utility (utils) } \
\hline \$ 25,000 & 1,500 \
\hline 30,000 & 1,900 \
\hline 35,000 & 2,250 \
\hline 40,000 & 2,550 \
\hline 45,000 & 2,800 \
\hline 50,000 & 3,000 \
\hline 55,000 & 3,150 \
\hline 60,000 & 3,250 \
\hline 65,000 & 3,300 \
\hline 100,000 & 3,500 \
\hline
\end{array}$$

Accepted Answer

Elizabeth's expected income is calculated as follows: (0.3 * $25,000) + (0.5 * $50,000) + (0.2 * $100,000) = $7,500 + $25,000 + $20,000 = $52,500.

Question 5

(Scenario: Deciding on Insurance Type under Uncertainty) Use Scenario: Deciding on Insurance Type under Uncertainty. For $900, the Garcia family can buy insurance that will cover the full cost of accidents. If family members are risk averse and maximize their expected utility, they will:
Scenario: Deciding on Insurance Type under Uncertainty
The Garcia family owns three cars and is considering buying insurance to cover the cost of repairs made necessary by accidents. They face two possible states: state 1, in which their cars require no repairs, and their income available for purchasing other goods and services is $50,000; and state 2, in which their cars require $10,000 worth of repairs, and their income available for purchasing other goods and services is reduced to $40,000. The probability that their cars will require repairs is 10%; the probability that they will not is 90%.

Accepted Answer

The Garcia family is risk averse and will want to maximize their expected utility. Given the probabilities and costs of the two states, the expected cost of repairs without insurance is $1,000 ($10,000 x 10%) and the expected income available for purchasing other goods and services is $49,100 (($50,000 x 90%) + ($40,000 x 10%)). With insurance, the total cost is $900, regardless of whether repairs are needed or not, and the expected income available for purchasing other goods and services is still $49,100. Therefore, buying insurance will reduce their expected cost and help them maximize their expected utility.

Question 6

(Table: The Utility from Income for Alexandra) Use Table: The Utility from Income for Alexandra. Alexandra runs her own business, which generates an annual income of $40,000. Alexandra is considering developing a new product. The probability that the new product will increase Alexandra's income by $30,000 is 0.5, and the probability that it will reduce Alexandra's income by $10,000 is 0.5. Suppose Alexandra can buy a fair insurance policy that will compensate her for any losses. Alexandra's premium will be _____, her guaranteed income will be _____, and her expected utility will be _____ utils. $$\text { Table: The Utility from Income for Alexandra } \
\begin{array} { | l | l | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline 10,000 & 200 \
\hline 20,000 & 360 \
\hline 30,000 & 500 \
\hline 40,000 & 620 \
\hline 50,000 & 720 \
\hline 60,000 & 800 \
\hline 70,000 & 860 \
\hline
\end{array}$$

Accepted Answer

The fair insurance premium would be calculated based on the expected loss, which is the average of the potential outcomes. With a 0.5 probability of losing $10,000, the expected loss is $5,000. Therefore, to guarantee her current income of $40,000, Alexandra would need to pay a premium of $5,000, not $10,000 as any option suggests directly. However, the correct understanding of the insurance premium in this context is that it ensures her income does not decrease, thus maintaining her utility at 620 utils, which corresponds to her current income without considering the insurance premium directly in the options provided. The misunderstanding in the question's phrasing about the premium's direct impact on guaranteed income and expected utility leads to selecting the option that correctly identifies her utility at her current income level, despite the confusion about the premium's calculation.

Question 7

Suppose that the probability of a theft at a museum is 1%, while the probability of an earthquake hitting the museum is 2.3%. The probability that both would occur on the same day is therefore:

Accepted Answer

To find the probability of both events happening, you multiply the probabilities of each event: 1% * 2.3% = 0.01 * 0.023 = 0.00023, which is 0.023%.

Question 8

Aisha is considering turning pro before her senior year basketball season. It has always been her dream to join the WNBA. If she turns pro, Aisha expects a rookie contract worth $2 million. If she does not turn pro, there is a 10% chance an injury will prevent her from playing professionally and a 90% chance she will get a rookie contract worth $4 million in present value. What is the expected present value of Aisha's rookie contract if she stays in college for her senior year?

Accepted Answer

The expected present value of Aisha's rookie contract if she stays in college for her senior year is calculated as follows: 90% chance of a $4 million contract = 0.9 * $4 million = $3.6 million. The 10% chance of not playing professionally due to injury results in $0, which does not affect the calculation since it's multiplied by 0. Therefore, the expected value is $3.6 million.

Question 9

Chloe recently graduated from the University of Chicago with a doctorate in economics. She has been offered a job in finance on Wall Street in New York with an uncertain income. There is an 80% probability that she will earn $100,000 and a 20% probability that she will earn $200,000. Suppose Chloe is offered another job at the Federal Reserve Bank of New York with a certain income. All else equal, if she has a constant marginal utility of income, she will accept the second job offer if it pays more than:

Accepted Answer

Chloe has a constant marginal utility of income, meaning that she values each additional dollar of income equally regardless of her overall income level. Therefore, her decision between the two job offers depends solely on the expected income from each job. The first job has an expected income of:

(0.8 x $100,000) + (0.2 x $200,000) = $120,000

The second job has a certain income that must be at least $120,000 to be preferred to the first job. Therefore, Chloe will accept the second job if it pays more than $120,000. The only option that meets this requirement is choice B, $140,000.

Question 10

The probability that it will hail in Denver on any given day in February is 2.5%, and the probability that you, living in Los Angeles, will have a car accident on any given day in February is 1%. The probability of both events occurring on the same day is _____.

Accepted Answer

To find the probability of both events occurring on the same day, we multiply their probabilities: 0.025 x 0.01 = 0.00025, which is 0.025% in percentage form. Therefore, the answer is (C) 0.025%.

Question 11

Casinos, such as those in Las Vegas or Atlantic City, tend to attract:

Accepted Answer

Casinos tend to attract people who have an irrational belief in their ability to beat the odds or who are seeking immediate gratification, despite the risks involved. These individuals may have a preference for risk-averse behavior in other areas of their lives, but are drawn to the thrill of gambling. Professional gamblers are a small minority of casino patrons.

Question 12

In shopping for a new LED television at Best Buy, Davina finds one that she likes and that is in her price range. A warranty offered by Best Buy that would cover the cost of repair or replacement of the television would:

Accepted Answer

The warranty offered by Best Buy would increase Davina's expected utility from consuming the good because it provides her with additional protection and security in case her television needs repair or replacement. This would give her peace of mind and increase her satisfaction with the purchase, thus improving her overall expected utility.

Question 13

(Scenario: Hurricane Coverage in Southern Florida) Use Scenario: Hurricane Coverage in Southern Florida. Your expected loss from a hurricane is:
Scenario: Hurricane Coverage in Southern Florida
Suppose that you own a home, estimated to be worth $250,000, that is located in the hurricane belt of southern Florida. The probability that you will lose your home to a hurricane is 30%.

Accepted Answer

The expected loss from a hurricane can be calculated by multiplying the value of the asset ($250,000) by the probability of losing it (30%). Therefore, the expected loss is $75,000. Choice B is the best option.

Question 14

(Scenario: Hurricane Coverage in Southern Florida) Use Scenario: Hurricane Coverage in Southern Florida. Suppose that an insurance company offers you hurricane insurance. MOST likely, this insurance would require a premium payment:
Scenario: Hurricane Coverage in Southern Florida
Suppose that you own a home, estimated to be worth $250,000, that is located in the hurricane belt of southern Florida. The probability that you will lose your home to a hurricane is 30%.

Accepted Answer

Since the probability of losing your home to a hurricane is 30%, the amount of insurance coverage for hurricane insurance should be greater than the potential loss of $75,000 (30% of $250,000). Therefore, the best choice is B, which is greater than $75,000. The other choices are either too low or unnecessarily high.

Question 15

As a result of frequent hurricanes, the insurance market has noted a positive correlation between hurricane damages and the amount of insurance monies paid out for such events. Holding the demand for insurance constant, if hurricanes are expected to continue to be a problem, hurricane insurance premiums will most likely:

Accepted Answer

The positive correlation between hurricane damages and insurance payouts means that insurance companies will have to pay out more for damages resulting from hurricanes. To compensate for this, they will likely raise premiums for hurricane insurance to maintain their profitability.

Question 16

Hilary and Larissa make up the auto insurance market. Hilary has a 10% probability of having an accident this year, while Larissa has a 5% probability of having an accident. What is the probability that Hilary and Larissa will both have accidents this year?

Accepted Answer

The answer of Hilary and Larissa make up the auto...

Question 17

Solange and Brittany make up the auto insurance market. Solange has a 5% probability of having an accident this year, while Brittany has a 2.5% probability of having an accident. What is the probability that Solange and Brittany will both have accidents this year?

Accepted Answer

The probability that Solange and Brittany will both have accidents this year is the product of their individual probabilities, which is 0.05 * 0.025 = 0.00125, or 0.125%.

Question 18

Earthquakes have become more frequent, forcing earthquake insurers to make larger payments to satisfy earthquake insurance claims. As a result, homeowners in earthquake-prone areas will find that earthquake insurance:

Accepted Answer

With the increase in frequency of earthquakes, earthquake insurance has become more costly and difficult to find as insurers have to make larger payments to satisfy the claims.

Question 19

Omar has just landed a great job and plans to buy a fancy car worth $100,000. Although Omar is generally risk averse, he likes to drive fast. Assume that the probability that he will wreck the car (a total loss of $100,000) is 0.1 and that the probability that he will have no accidents is 0.9. How much would Omar pay for a fair insurance policy that would completely replace his car in the event of a wreck? What is the most he would pay for an insurance policy that would completely replace his car if he totaled it?

Accepted Answer

The answer of Omar has just landed a great job...

Question 20

(Table: Avocado Crop Income for Evan's Farm) Use Table: Avocado Crop Income for Evan's Farm. Evan is a farmer, whose income depends on the weather.
​
 $${ \text { Table: Avocado Crop Income for Evan's Farm } } \
\begin{array} { | l | l | l | l | } 
\hline \text { Crop Conditions } & \text { Income } & \text { Utility } & \text { Probability } \
\hline \text { Very Poor } & \$ 0 & 0 & .25 \
\hline \text { Normal } & 1,000 & 200 & .50 \
\hline \text { Good } & 2,000 & 300 & .15 \
\hline \text { Outstanding } & 3,000 & 375 & .10 \
\hline
\end{array}$$

Accepted Answer

The answer of (Table: Avocado Crop Income for Evan's Farm)...

Quiz 19: Decisions Involving Uncertainty