978-1260152616 Chapter 11 Solution Manual Part 2

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Chapter 11 – Time and Uncertainty

1. Many individuals prefer to have insurance (health insurance, car

insurance, etc.) rather than not, even if the expected value of their wealth is

higher without insurance. What does this imply about their willingness to

take on risk? [LO 11.5]

Answer: Not having insurance can be very risky. There is a chance that

you might face very high costs if you have a car accident, need surgery,

2. Lenders tend to o&er lower interest rates to borrowers with high credit

scores and higher interest rates to borrowers with low credit scores. What

does this imply about lenders’ willingness to take on risk? [LO 11.5]

Answer: Just like individual people, businesses are also typically risk-

3. Alie is outraged when she hears that a company is o&ering insurance

against being attacked by zombies: “Zombies aren’t even real! This company

is just taking advantage of people.” Without acknowledging the possible

existence of zombies, provide an alternative perspective on the insurance

company’s ethics. [LO 11.6]

Answer: Some people are afraid of zombies and believe in the possibility

of a zombie attack. The insurance company may not be selling protection

4. Julia pays $1,200 for an insurance policy with an expected value of

$1,000. Explain why this is a rational choice for Julia. [LO 11.6]

Answer: Paying more for insurance than its expected value is a rational

5. Suppose that the crop yield of corn farmers in Iowa depends solely on

rainfall levels. Also suppose that every part of the state gets approximately

the same amount of rain as every other part in any given year. Will the corn

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Chapter 11 – Time and Uncertainty

farmers of Iowa be able to e&ectively use pooling to reduce their exposure to

risk? Why or why not? [LO 11.7]

Answer: The farmers will not be able to e&ectively pool their risk. Risk

pooling works only if everyone in the pool is paying premiums but not

6. An insurance company that faces 5erce competition from other providers

is considering a strategy to sell more policies by simplifying its portfolio and

becoming the expert in =ood insurance for the state. The company managers

reason, “Everyone buys =ood insurance in this state, so let’s focus our e&orts

on becoming the preferred provider.” Evaluate this strategy. [LO 11.7]

Answer: This strategy is risky for the insurance company. If everyone in

7. Suppose the economy is su&ering and many people are afraid they will be

laid o& from their jobs. Workers would like to protect against this risk with

insurance. Identify and explain two problems that prevent insurance

companies from o&ering layo& insurance. [LO 11.8]

Answer: Adverse selection: Individuals probably have more knowledge

about their own risk of layo& than does the insurance company. Those

8. BackPedal is a bike-rental shop that rents bicycles, helmets, and other

gear by the day. [LO 11.8]

a. BackPedal o&ers an optional helmet rental for $10/day with the rental of a

bicycle. To his surprise, the store manager has noticed that cycling accidents

are higher among customers who rent helmets than those who do not.

Explain this phenomenon using economic concepts. Assume that customers

who do not rent helmets also do not own helmets.

b. BackPedal is considering o&ering helmets for free with a bike rental.

Explain how this new policy will a&ect the issues you identified in part a.

Answer:

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Chapter 11 – Time and Uncertainty

a. Both moral hazard and adverse selection may be at play. In terms of

moral hazard, because cyclists feel safer when they are wearing a helmet,

b. Adverse selection will be reduced. O&ering helmets without charge will

cause many of the less-risky riders who may not have been willing to pay

Problems and Applications

1. Your bank o&ers 3 percent annual interest on savings deposits. If you

deposit $560 today, how much interest will you have earned at the end of

one year? [LO 11.1]

Answer: If you invest $560 for one year at 3 percent interest, you will

2. You have $350, which a friend would like to borrow. If you don’t lend it to

your friend, you could invest it in an opportunity that would pay out $392 at

the end of the year. What annual interest rate should your friend o&er you to

make you indi&erent between these two options? [LO 11.1]

Answer: In order to break even, you will need to receive $42 in interest.

This corresponds with a 12 percent interest rate.

3. If you deposit $500 in a savings account that o&ers 3 percent interest,

compounded annually, and you don’t withdraw any money, how much

money should you expect to have in the account at the end of three years?

[LO 11.2]

4. Suppose you run up a debt of $300 on a credit card that charges an

annual rate of 12 percent, compounded annually. How much will you owe at

the end of two years? Assume no additional charges or payments are made.

[LO 11.2]

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Chapter 11 – Time and Uncertainty

Answer: If you run up a debt of $300 on a credit card that charges 12

5. Your savings account currently has a balance of $32,300. You opened the

savings account two years ago and have not added to the initial amount you

deposited. If your savings have been earning an annual interest rate of 2

percent, compounded annually, what was the amount of your original

deposit? [LO 11.3]

Answer: If your savings account has a balance of $32,300 and has been

6. You run a business and are considering o&ering a new service. If you o&er

the new service, you expect it to generate $60,000 in pro5ts each year for

your business over the next two years. In order to o&er the new service, you

will need to take out a loan for new equipment. Assume a 5 percent annual

interest rate. [LO 11.3]

Answer: The present value of the pro5ts is: ($60,000 / 1.05) + ($60,000 /

7. You are driving home from work and get stuck in a traMc jam. You are

considering turning o& from your usual route home and taking a longer route

that might have less traMc. However, you know that there is some chance

that the traMc on your usual, shorter route will clear up. Based on Table 11P-

1, calculate the expected value (in minutes until you arrive home) of each

option. [LO 11.4]

Answer: The expected value of Route 1 is 39 minutes. The expected

value of Route 2 is 30 minutes. You should take route 2.

Route 1 Expected Value:

Route 2 Expected Value:

8. Books for Kids is a not-for-pro5t organization that runs after–school

reading programs in four school districts. Books for Kids is planning a fund-

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Chapter 11 – Time and Uncertainty

raiser to buy new books. Last time it held a fund-raiser, donors were allowed

to specify which district program they wanted to receive their donation. Table

11P-2 shows the average donations and the percent of all donations that

went to each district. Using the last fund-raiser as a projection, what is the

expected value of the average donation across all four programs? [LO 11.4]

Answer: The expected value of the average donation across all four

9. Cora had two options when buying car insurance. The expected value of

her wealth would be higher with Option A, but Cora chose option B. From the

list below, what can we assume about these policies and Cora’s willingness

to take on risk? Check all that apply. [LO 11.5]

a. Option B was riskier.

b. Option A was riskier.

c. Cora is risk-seeking.

d. Cora is risk-averse.

Answer: b and d. If option A had a higher expected value but Cora chose

10. Consider the following scenarios. For each scenario, determine whether

a risk averse person will definitely choose Option A, definitely choose Option

B, be indi&erent between Options A and B, or might choose either Option A

or B. [LO 11.5]

a. Option A: There is a 50% chance of winning $1,000 and a 50% chance of winning $0. Option

B: There is a 100% chance of receiving $500.

b. Option A: There is a 40% chance of winning $90 and a 60% chance of winning $110. Option

B: There is a 100% chance of winning $90.

c. Option A: There is a 50% chance of winning $0 and a 50% chance of winning $100. Option B:

There is a 50% chance of winning $20 and a 50% chance of winning $60.

Answer:

a. Though the two options have the same expected value, option B has no

b. Though option C involves risk, it will not yield a lower payo& than

c. Thought option E is riskier, it has a higher expected value. It’s unclear

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Chapter 11 – Time and Uncertainty

11. Suppose you own a beach house on a coast that has a small chance of

encountering a hurricane each year. There is a 1% chance that there will be a

hurricane this year that would completely destroy your $350,000 home.

(Assume that this home is the only store of wealth that you have.) An

insurance company has o&ered you insurance that would reimburse you the

entire value of your home in the event of a hurricane. The premium for this

insurance is $4,000. [LO 11.6]

a. What is the expected value of your wealth if you do not purchase

insurance?

b. What is the expected value of your wealth if you purchase the insurance at

a $4,000 premium?

c. Will a risk-averse person choose to purchase insurance?

d. Will a risk-seeking person choose to purchase insurance?

e. What would the premium have to be to make a risk-neutral person

indi&erent between buying the insurance and not buying the insurance?

f. If the insurance company o&ered the premium you found in part (e), would

a risk-averse person purchase insurance?

Answer:

12. You are considering buying one of two types of health insurance. You

guess that in the next year there is a 1 percent chance of serious illness that

will cost you $67,500 in health care; a 9 percent chance of a moderate illness

that will cost you $2,500; and a 90 percent chance of regular health care

needs that will cost you $500. One type of health insurance is emergency–

only coverage; it will cover your expenses for serious illness but not

moderate illness or regular care. The other type covers moderate illness and

regular expenses, but its payout is capped, so it will not cover the cost of a

serious illness. [LO 11.6]

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Chapter 11 – Time and Uncertainty

a. What is the expected value of payouts from the emergency-only

insurance?

b. What is the expected value of payouts from the capped-coverage

insurance?

c. Which option is a more risk-averse person likely to choose?

Answer:

a. EV = 0.01(67,500) = $675.

b. EV = 0.09(2,500) + 0.9(500) = $675.

13. For each of the following scenarios, say whether pooling or

diversication is a more promising risk-mitigation strategy. [LO 11.7]

a. Employees of a company who invest their savings in that company’s

stocks.

b. Families who are worried about losing their possessions if their houses

burn down.

c. Neighboring farmers who grow the same crop, which is prone to failure in

dry years.

Answer: Risk pooling organizes people into a group to collectively absorb

the risk faced by each individual. Risk diversi5cation means avoiding large

risks by replacing them with smaller ones that are unrelated.

14. You have two possessions you would like to insure against theft or

damage: your new bicycle, which cost you $800, and a painting you

inherited, which has been appraised at $55,000. The painting is more

valuable, but your bicycle must be kept outdoors and is in much greater

danger of being stolen or damaged. You can a&ord to insure only one item.

Which should you choose? Why? [LO 11.7]

Answer: If you have to choose, you should insure the painting. Even

15. Farmer Tom is trying to decide what to produce on his farm in the

upcoming season. In the past, he has usually grown Crop A. If he grows Crop

A, there is a 70% chance that his crop will yield $15,000 in pro5t and a 30%

chance that he will earn zero pro5t. [LO 11.7]

a. What is the expected value of his pro5t if he grows only Crop A?

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Chapter 11 – Time and Uncertainty

b. Now Farmer Tom considers dividing his land between two crops: Crop A

and Crop B. There is a 5% chance that both crops will fail, and Tom will earn

zero pro5t. There is a 25% chance that only one crop will grow, and Tom will

earn $6,000 in pro5t. There is a 60% chance that both crops will grow, and

Tom will earn $15,000 in pro5t. What is the expected value of his pro5t if he

grows both crops?

c. Which option would a risk-averse farmer choose?

d. Which option would a risk-seeking farmer choose?

e. Which option would a risk-neutral farmer choose?

Answer:

16. Say whether each of the following scenarios describes an insurance

problem caused by adverse selection or by moral hazard. [LO 11.8]

a. People who have homeowners insurance are less likely than others to

replace the batteries in their smoke detectors.

b. People who enjoy dangerous hobbies are more likely than others to buy

life insurance.

c. People whose parents died young are more likely than others to seek out

health insurance with better coverage.

d. People who have liability coverage on their car insurance take less care

than others to avoid accidents.

Answer: Adverse selection occurs when buyers and sellers have di&erent

information about the quality of a good or the riskiness of a situation. With

moral hazard, people engage in behavior that is considered undesirable

by the person who bears the cost of the behavior.

17. As part of the A&ordable Care Act of 2010, all individuals in the U.S. are

now required to have health insurance. Do economists expect mandatory

health insurance to reduce adverse selection, moral hazard, both, or neither?

[LO 11.8]

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Answer: This policy would reduce adverse selection by removing the opt-

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