Microeconomics

Austan Goolsbee, Steven Levitt, Chad Syverson

Chapter 14 Investment, Time, and Insurance - all with Video Answers

Educators

Chapter Questions

01:49

Problem 1

Imagine that you have $\$ 100$ of ill-gotten gains stashed in an offshore bank account. Lest the IRS get too nosey, you
plan to leave that account idle until your retirement in 45 years.
a. If your bank pays you $3 \%$ annual interest, what will your account balance be upon retirement?
b. If your bank pays you $6 \%$ interest, what will your account balance be upon retirement?
c. Does doubling the interest rate double your accumulated balance at retirement? More than double it? Less?
Explain your answer.

Andrew Davis

Numerade Educator

02:38

Problem 2

Suppose that when you were one year old, your grandmother gave you a shiny silver dollar. Your parents put that silver dollar in a savings account with a guaranteed $9 \%$ interest rate, and then promptly forgot about it.
a. Use the Rule of 72 to estimate how much that account will grow to by the time you are $65 .$
b. Calculate exactly how much you will have in that account using the formula for compound interest.
c. How close are your answers to (a) and (b)?

Lourence Gonhovi

Numerade Educator

03:18

Problem 3

Evie is a 20 -year-old social media influencer who earns lots of income from her YouTube channel. She brags to her
friends, "I'm going to be a millionaire by the time I'm $40, "$ but seems to spend money as fast as it comes in.
a. If interest rates are currently $9 \%$, how much should Evie set aside today to guarantee her millionaire status by $40 ?$
b. How much should Evie set aside if she decides she wants to reach millionaire status by 30 instead of $40 ?$
c. Does the amount Evie must set aside double when she decides she needs to achieve millionaire status twice as
quickly?

Anand Jangid

Numerade Educator

00:30

Problem 4

You are writing the great American novel and have signed a contract with the world's most prestigious publisher. To keep you on schedule, the publisher promises you a $\$ 100,000$ bonus when the first draft is complete, and another $\$ 100,000$ following revisions. You believe that you can write the first draft in a year and have the revisions done at the end of the
second year. a. If interest rates are $5 \%,$ what is the value today of the publisher's future payments?
b. Suppose the publisher offers you $\$ 80,000$ after the first draft and $\$ 125,000$ following revisions. Is this a better deal
than the original offer?

Kimberly Waterbury

Numerade Educator

04:42

Problem 5

A state lottery makes the following announcement: "Frederick Carbuncle has just won $\$ 100$ million! We'll pay Frederick $\$ 10$ million each year for the next 10 years!"
a. Has Frederick really won $\$ 100$ million? Explain.
b. Many state lotteries allow winners to choose a single payment instead of a series of annual payments. "We'll offer you the present value of your annual payments, Frederick," the lottery commissioner says. "And because we're feeling generous, we'll use a really high interest rate when we calculate how much that prize will be. Congratulations, Fred!" Comment on the generosity of the lottery commissioner.

Charles Carter

Numerade Educator

06:26

Problem 6

You have just purchased a Kia with a $\$ 20,000$ price tag. The dealer offers to let you pay for your car in five equal
annual installments, with the first payment due in a year.
a. If the dealer finances your purchase at an interest rate of $10 \%$, how much will your annual payment be?
b. How much would your payment be if you had purchased a $\$ 40,000$ Camry instead of a $\$ 20,000$ Kia?
c. How much would your payment be if you arranged to pay in 10 annual installments instead of $5 ?$ Is your
payment cut in half? Why or why not?
d. How much would your payment fall if you paid $\$ 10,000$ down at the time of purchase?

Himanshu Kushwaha

Numerade Educator

04:36

Problem 7

Many college graduates feel as if their student loan payments drag on forever. Suppose that the government offers
the following arrangement: It will pay for your college in its entirety, and in return you will make annual payments
until the end of time.
a. Suppose the government asks for $\$ 6,000$ each year for all of eternity. If interest rates currently sit at $4 \%,$ what is
the present value of the payments you will make?
b. Your college charges $\$ 140,000$ for four years of quality education. Should you take the government up on its
offer to pay for your college? What if your college charges $\$ 160,000 ?$

Oluwadamilola Ameobi

Numerade Educator

08:38

Problem 8

As a New Year's gift to yourself, you buy your roommate's 1976 Ford Pinto. She has given you the option of two payment plans. Under Plan A, you pay $\$ 500$ now, plus $\$ 500$ at the beginning of each of the next two years. Under Plan $\mathrm{B}$, you would pay nothing down, but $\$ 800$ at the beginning of each of the next two years.
a. Calculate the present value of each plan's payments if interest rates are $10 \%$. Should you choose Plan A or Plan
$\mathrm{B} ?$
b. Recalculate the present value of each plan's payments using a $20 \%$ interest rate. Should you choose Plan $\mathrm{A}$ or
Plan B?
c. Explain why your answers to (a) and (b) differ.

Jason Orozco

Numerade Educator

07:13

Problem 9

Ricardo is considering purchasing an ostrich, which he can graze for free in his backyard. Once the ostrich reaches maturity (in exactly three years), Ricardo will be able to sell it for $\$ 2,000$. The ostrich costs $\$ 1,500$.
a. Suppose that interest rates are $8 \% .$ Calculate the net present value of the ostrich investment. Does the NPV indicate that Ricardo should buy the ostrich?
b. Suppose that Ricardo passes on the ostrich deal and invests $\$ 1,500$ in his next-best opportunity: a safe
government bond yielding $8 \% .$ How much money will he have at the end of three years? Is this outcome better or
worse than buying the ostrich?
c. Calculate the net present value of the ostrich if interest rates are $11 \% .$ Does the NPV method indicate that
Ricardo should buy the ostrich?
d. If Ricardo passes on the ostrich deal and invests in a government bond yielding $11 \%,$ how much money will he have at the end of three years? Is this outcome better or worse than buying the ostrich?
e. Based on your answers to (b) and (d), how well does the NPV method capture the concept of opportunity cost?

Jesse Neumann

Numerade Educator

04:14

Problem 10

Marian currently makes $\$ 40,000$ a year as a tow truck driver. She is considering a career change: For a current expenditure of $\$ 30,000$, she can obtain her florist's license and become a flower arranger. If she makes that career change, her earnings will rise to $\$ 48,000$ per year. Marian has five years left to work before retirement (you may safely assume that
she gets paid once at the end of each year).
a. Calculate the net present value of Marian's investment in floriculture if interest rates are $10 \%$.
b. Assume that in terms of job satisfaction, floriculture and tow truck driving are identical. Should Marian change
careers?
c. Compare the present value of Marian's earnings as a tow truck driver to the present value of Marian's earnings as a florist. Is the difference large enough to justify spending $\$ 30,000 ?$
d. Does the method you used in part (a) give an identical answer to the method you used in part (c)? Explain.

Abby Kennedy

Numerade Educator

02:18

Problem 11

You are currently driving a gas-guzzling Oldsmobuick that you expect to be able to drive for the next five years. A recent spike in gas prices to $\$ 5$ per gallon has you considering a trade to a fuel-efficient hybrid Prius. Your Oldsmobuick has no resale value and gets 15 miles per gallon. A new Prius costs $\$ 25,000$ and gets 45 miles per gallon. You drive 10,000 miles each year.
a. Calculate your annual fuel expenditures for the Prius and the Oldsmobuick.
b. Assume that the interest rate is $7 \% .$ Calculate the present value of your costs if you continue to drive the Oldsmobuick for another five years. Assume that you purchase a new Prius at the end of the fifth year, and that a Prius still costs $\$ 25,000$. Also assume that fuel is paid for at the end of each year. (Carry out your cost calculations for only five years.)
c. Calculate the present value of your costs if you purchase a new Prius today. Again, carry out your cost calculations for only five years.
d. Based on your answers to (b) and (c), should you buy a Prius now, or should you wait for five years?
e. Would your answer change if your Oldsmobuick got 30 miles per gallon instead of $15 ?$

James Kiss

Numerade Educator

02:55

Problem 12

Whiskey makers have an unusual business model: They make a product today, and then let it sit in barrels in a
warehouse for 20 years before they sell it. Suppose that it takes $\$ 12$ of resources to produce a bottle of whiskey
today. How much will the whiskey maker have to charge for a bottle of whiskey in 20 years in order to make
spending that $\$ 12$ a wise investment? (Assume the whiskey maker faces market interest rates of $6 \% .)$

Karan Sood

Numerade Educator

01:07

Problem 13

You have $\$ 832.66$ in a savings account that offers a $5.25 \%$ interest rate.
a. If you leave your money in that account for 20 years, how much will you have in the account?
b. Suppose that inflation is expected to run at $3.25 \%$ for the next 20 years. Use the real interest rate to calculate the
inflation-adjusted amount your account will contain at the end of the 20 -year period.
c. The amount you calculated in (b) is smaller than the amount you calculated in (a). Explain exactly what the
amount you calculated in (b) tells you, and why the difference arises.

Carson Merrill

Numerade Educator

07:13

Problem 14

Mariq really likes M\&Ms. Currently, he has $\$ 100$, which, at the market price of $\$ 1$ per bag of M\&Ms, translates to
100 bags. He's considering putting that money in the bank so next year he can afford even more M\&Ms.
a. Suppose that Mariq can earn $7 \%$ interest on any money he saves. In one year, how many dollars will he have?
How many M\&Ms will he be able to afford?
b. The real rate of return is calculated by using goods and services rather than dollars. Calculate Mariq's real rate of return by dividing next year's possible M\&M count by this year's. In percentage terms, how many more M\&Ms
can Mariq enjoy?
c. Suppose Mariq can save at $7 \%$, but that over the course of the year, the price of a bag of M\&Ms increases by $3 \%$,
to $\$ 1.03 .$ If Mariq saves his money today, how many bags of M\&Ms will Mariq be able to afford next year? What
is his real rate of return?
d. What happens to Mariq's real rate of return if the price of a bag of M\&Ms increases by $10 \%$, to $\$ 1.10$, over the
next year?
e. Using your results from (b), (c), and (d), develop a formula that relates the nominal interest rate, the real interest rate, and the inflation rate (percentage increase in prices). Your formula may be an approximation.

Jesse Neumann

Numerade Educator

02:49

Problem 15

Mel is a risk-neutral investor concerned about the future availability of gas. He is considering purchasing a gallon of
gas today and placing it in storage for 10 years as a hedge against future gas price increases.
a. If today's price of gas is $\$ 4.00$ per gallon, and the future price of gas is $\$ 6.00$ per gallon, is placing a gallon of gas in storage a good idea? Assume that the market interest rate is $4 \%$.
b. Suppose that Mel is uncertain of the future price of gas. He estimates that there is a 0.1 probability that gas will continue to sell for $\$ 4.00$ per gallon, a 0.4 probability that gas will sell for $\$ 5$ per gallon, and a 0.5 probability that gas will sell for $\$ 6.80$ per gallon. Should Mel place a gallon of gas in storage today? Will your answer be the same if Mel is risk-averse?

Nick Johnson

Numerade Educator

05:50

Problem 16

You are romantically interested in Chris, but have always wanted to date the president of the Economics Club. As it turns out, Chris is battling Pat for control of the Econ Club. That battle should be decided in a year, and you estimate
the odds of Chris winning at $60 \%$. Attracting Chris and kindling a relationship will involve $\$ 1,000$ of effort on your part; if Chris wins the presidency, you will receive benefits worth $\$ 2,200$ (assume you receive these benefits one
year after beginning the relationship). If Chris loses the election, you receive nothing.
a. Assume an interest rate of $10 \% .$ Calculate the net present value of building a relationship with Chris today.
Notice that the costs of kindling a relationship today are certain, but the benefits are uncertain.
b. Considering only your answer to (a), should you initiate a relationship with Chris at this time? Assume you are
risk-neutral in formulating your answer.
c. Calculate the net present value of waiting until the presidency is decided to build a relationship with Chris. Note that both the costs and benefits of kindling a relationship are uncertain at this point, but that two will be
certain in one year.
d. Based on your answers to both (a) and (c), should you initiate a relationship with Chris today, or should you wait
to initiate the relationship until the presidency is determined?

Jesse Neumann

Numerade Educator

04:02

Problem 17

You are considering the purchase of an old fire station, which you plan to convert to an indoor playground. The fire
station can be purchased for $\$ 200,000$, and the playground will generate lifetime profits (excluding the cost of the building)
of $\$ 700,000$. (Assume that those profits are all realized one year after opening.) However, there is a $20 \%$ chance that the city
council will rezone the district to exclude establishments such as yours; a hearing is scheduled for the coming year, and if your building is rezoned, your profit will be zero. Assume that there is no other building currently under consideration.
a. Assume an interest rate of $10 \% .$ Calculate the net present value of opening the playground today. Note that the cost of purchasing the building today is certain, but the benefits are uncertain.
b. Calculate the net present value today of opening the playground in one year, after the zoning issues have been decided. Note that the benefits of opening the playground are uncertain today, but will be certain in one year.
c. Based on your answers to (a) and (b), should you open the playground today, or should you wait until the zoning commission reaches its decision?

Jerrah Biggerstaff

Numerade Educator

05:53

Problem 18

Speedy Steve is a traveling salesman. His utility function is given by $$U=I^{0.5}$$, where $U$ is his utility and $I$ is his income. Steve's income is $\$ 900$ each week, but if Steve is caught speeding while making his rounds, he will receive a hefty fine. There is a $50 \%$ chance he will be caught speeding in any given week and pay a fine of $\$ 500$.
a. Calculate Steve's expected income and expected utility.
b. Suppose that Steve's boss offers him a position in online sales that eliminates the risk of being caught speeding. What salary would provide Steve with the same utility he expected to receive as a traveling salesman?
c. Suppose instead that Steve was given the opportunity to purchase speeding ticket insurance that would pay all of his fines. What is the most Steve would be willing to pay to obtain this insurance? Explain how you arrived at this
number.
d. If the company issuing the insurance referred to in (c) convinces Steve to pay the amount you indicated, will the insurer earn a profit? If so, how much profit will it eam?

Oluwadamilola Ameobi

Numerade Educator

02:33

Problem 19

Danielle is a farmer with a utility function of $$U=I^{0.5}$$ , where $U$ is Danielle's utility and $I$ is her income. If the weather is good, she will earn $\$ 100,000$. If there is a hailstorm, she will earn only $\$ 50,000$. The
probability of a hailstorm in any given year is $30 \%$.
a. What is Danielle's expected income if she is uninsured? Her expected utility?
b. Suppose a crop insurer makes the following offer to Danielle: In years when there is no hailstorm, Danielle pays the insurer $\$ 16,000 .$ In years when there is a hailstorm, the insurer pays Danielle $\$ 34,000 .$ What is Danielle's expected income? Her expected utility?
c. Comment on the following statement, referring to your answers to parts (a) and (b): "The insurance agreement in
(b) reduces Danielle's expected income. Therefore, it must make her worse off."
d. Suppose instead the insurer offers Danielle the following: In years when there is no hailstorm, Danielle pays the insurer $\$ 10,000 ;$ in years when there is a hailstorm, the insurer pays Danielle $\$ 20,000 .$ How does Danielle's expected income and expected utility compare to the uninsured outcome in (a) and the insured outcome in (b)?

Bryan Meares

Numerade Educator

03:31

Problem 20

Perry the picker has stumbled across a piece of pottery in an antique shop. Because of its style, he believes it might
be by Frog Woman, a famous Hopi artist. If he buys the pot for $\$ 3,000$, he will be able to resell it for $\$ 4,500$,
provided it is a genuine Frog Woman pot. If it is not genuine, he will be forced to unload it for only $\$ 1,000$. Perry estimates that there is a $$2 / 3$$ chance the pot is genuine. a. If Pemy bases his decision on expected monetary value, should he buy the pot?
b. Perry's utility depends on his wealth: Specifically, $U=W^{1 / 4}$ Compute Perry's utility at the possible levels of final wealth he might experience.
c. If Perry bases his decision to buy on expected utility, what should he do?
d. Suppose Perry spends a little bit too much time in the hotel bar, and buys the pot without doing the math first. At breakfast the next moming, Penny, another picker, notices the pot and decides to make an offer for it. What is the
minimum Penny would have to offer to convince Perry to sell. (Remember - Perry still doesn't know whether
the pot is genuine; an offer from Penny removes all risk.)
e. What is Perry's risk premium?

Akash M

Numerade Educator

00:48

Problem 21

A classmate offers to play the following game: He will roll a 10 -sided die; if it comes up between 1 and $9,$ he will
pay you $\$ 10 ;$ if it comes up a $10,$ he will pay you $\$ 110 .$
a. If you are risk-neutral, and base all decisions on expected monetary value, what is the most you will pay to play
this game?
b. Your classmate Risa has a utility function that depends on wealth. Specifically, $U=W^{2}$ If Risa bases her decisions on expected utility, what is the most she would pay to play this game? What can you
ascertain about Risa's attitude toward risk?

Ernest Castorena

Numerade Educator