ECO 110 – Introduction to Economics
Professor Mike Rizzo
Second COLLECTED Problem Set – SOLUTIONS This is an assignment that WILL be
collected and graded. Please feel free to talk about the assignment with your friends or
with your group and I strongly encourage you to submit your assignment as a group.
Assigned:
Due:
Monday, April 4th
Monday, April 11th
COMPLETE ANY 10 of the 15
1. Why do insurance policies with deductibles cost less? Give two reasons.
Recall that a deductible is how much money you have to spend of your own before you can
“reach into the bucket” and have access to the pool of insurance money. Since insurance
premiums depend on both the probability of a bad event happening AND the size of the
insurance payout when that event happens, the more money of your own that you put up
when an event happens, the less expensive the insurance premium will have to be. Second,
when there are deductibles, people have a larger incentive to avoid bad outcomes. For
example, if you have to pay $2,000 to repair your car before the insurance company will
begin to pick up the tab for cosmetic damages, then you will likely drive more carefully
when you are in crowded parking lots.
2. Suppose the laws against sale of marijuana are weakened (for example, by paroling
drug-dealers after only 3 years), while laws against use of marijuana are
strengthened (for example, by imposing a 3-year mandatory minimum sentence for
use). What happens to the market for marijuana?
The weakening of the laws on selling will certainly increase the supply of marijuana and
may cause the supply curve to be more elastic. The strengthening of laws on using will
tend to decrease the demand. Therefore, the price will definitely fall, but the overall drug
use in society is ambiguous.
3. Suppose that you can buy a baseball franchise for $100 million, and its annual net
revenues (revenues minus expenses) are $5 million. The interest rate is 10 percent
per year.
a. What are net revenues as a percent of the purchase price? This is the "rental
rate" for the baseball franchise.
Annual rent / purchase price = $5M / $100M = 5%
b. If the appreciation rate of the franchise is 8 percent per year, use the
profitability formula to calculate the profitability for the franchise. Should you
buy the franchise?
Profitability = Rental Rate + Appreciation Rate – Interest Rate
= 5% + 8% - 10%
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= 3% Æ this tells us that each year of owning the franchise generates $3
million more that if we would have had had we not purchased the franchise.
c. If your cash flow is equal to net revenues minus interest expense, calculate
the first year cash flow from owning the franchise.
Cash flow = $5 million - $10 million = MINUS $5 million. The interest expense is calculated
as 10% of the $100 million purchase price.
d. Explain the difference between rent-buy analysis and cash flow analysis for
this franchise.
The cash flow analysis does not take into account the cash value of the “capital gains” I
earn from holding onto the franchise. It is still profitable to buy the team even if I lose $5
million in cash each year, because I will be able to MORE than make up for these lost cash
flows at the time I sell the team.
4. You can buy a share of stock for $100. The stock pays a dividend of $1 per year.
The ratio of the dividend to the price is the "rental income" from the stock. If the
interest rate is 5 percent and the rate at which dividends and share prices appreciate
is 3 percent, is the stock a good buy?
Use the profitability formula. The rental rate in this case is $1 / $100 = 1%. The
appreciation in BOTH the dividend and share price does not affect the rental rate, but does
affect the profitability of holding the stock. The profitability formula = 1% +3% - 5%, so
this is -1%, the stock is NOT a good buy.
5. You deposit $3000 in the bank and earn 5 percent interest, compounded
continuously.
The formula for continuous compounding is Yn = Y0 x enr. Where n is the number of periods
and r is the interest rate per period.
a. How much will you have in the bank after one year? after four years?
Y1 = $3,000 x exp(1 x 0.05) = $3,153.81 after 1 year
Y4 = $3,000 x exp(4 x 0.05) = $3,664.21 after 4 years
b. How long will it take to have $10,000 in the bank?
We want to solve for n as we did in class by taking natural logs of both sides.
n = ln(Yn / Y0) / r = ln($10,000 / $3,000) / .05 = 24.1 years
6. If you deposit $C in the bank every year, for n years, at an interest rate of r
compounded annually, after you make your deposit at the start of the nth year you
will have: B = C[(1+r)n-1] /r in the bank.
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a.
Suppose that you deposit $1000 a year for 10 years at an interest rate of 6
percent (r = .06). How much will you have after you make your deposit at
the start of the tenth year?
$13,180.79
b. Suppose that you want to have $100,000 after 10 years, and the interest rate
is 6 percent. How much will you have to deposit each year?
$7,586.80
c. Suppose that you want to have $1 million after 30 years, and the interest
rate is 7 percent. How much will you have to deposit each year?
$10,586.40
7. Remember that the formula for an annuity is: C = rB/[1-(1+r)-n]; where C is the
annuity payment, B is the initial balance, r is the interest rate, and n is the number
of years that the annuity will run. Suppose that you have $500,000 and the interest
rate is 6 percent, and the annuity runs for 20 years.
a. What is the annuity payment?
$43,592.28
b. Suppose that the inflation rate is 2 percent per year. What is the real
interest rate that would be used to calculate a real annuity payment?
It’s the nominal rate (6%) minus the inflation rate (2%) = 4%.
c. Calculate the real annuity payment assuming that inflation is 2 percent per
year.
$36,790.88
d. The annuity payment in the first year is equal to the real annuity payment.
In the second year, the annuity payment is the real annuity payment times (1
+ .02). In the third year, the annuity payment is the real annuity payment
times (1 + .02)2. Calculate the annuity payment for the second year and for
the third year.
The second year payment is just $36,790.88 x (1.02) = $37,526.70 and the third year
payment is then $38,277.23.
8. Suppose that you have $100,000, the interest rate is 8 percent, and the annuity runs
for 4 years. If the inflation rate is 5 percent, calculate the real annuity. Calculate
the actual annuity payments for each of the four years.
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Using the annuity formula, C = rB/[1-(1+r)-n], the first year annuity withdrawal amount
would be $26,903. The payment should increase by the rate of inflation each (5%) year so
that your purchasing power is unchanged from year to year. So, year two payment is
$28,248, year 3 is $29,660 and the final year withdrawal is $31,143.
Show that the annuity works. That is, for each year, fill out a table with the
beginning balance, interest earned, annuity paid, and ending balance. Show that
after four years the ending balance is exactly zero.
It is easy to show that this works in the absence of inflation. For example, if the rate of
interest was 3% and there was no inflation you would have:
Year
1
2
3
4
Beginning
Balance
$100,000
$76,097
$51,478
$26,119
Interest Earned
$3,000
$2,283
$1,544
$784
Annuity Paid
$26,903
$26,903
$26,903
$26,903
Ending Balance
$76,097
$51,478
$26,119
$0
It is somewhat more difficult when dealing with inflation because the real value of your
principle and interest falls over time. If we take this into account we would have a result
that looks something like:
Year
1
2
3
4
Beginning
Balance
$100,000
$81,097
$55,167
$27,912
Interest Earned
$8,000
$6,488
$4,413
$2,233
Annuity Paid
$26,903
$28,248
$28,831
$28,749
Ending Balance
$81,097
$55,167
$27,912
($40)
9. The formula for finding the monthly payment on a mortgage or an auto loan is the
same as the formula for an annuity. However, the interest rate is the annual
interest rate divided by 12, and the number of periods, n, is the number of years
times 12.
a. Find the monthly payment on a 30-year mortgage with a $100,000 initial
balance and an interest rate of 12 percent.
$1,028.61
b. Find the monthly payment on a 5-year auto loan with a $20,000 initial
balance and an interest rate of 5 percent.
$377.42
10. Daniel Kahneman, Jack L. Knetsch and Richard Thaler have done research on the
notions of fairness that people apply to market transactions. One of their articles,
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titled, “Fairness as a Constraint on Profit Seeking: Entitlements in the Market,”
reports the results of a public opinion survey designed to determine the rules of
fairness people use in evaluating actions by business firms. Here is one hypothetical
situation that was described in the survey:
A grocery store has several months’ supply of peanut butter in stock which it has
on the shelves and in the storeroom. The owner hears that the wholesale price
of peanut butter has increased and immediately raises the price on his current
stock of peanut butter.
Of the 147 respondents surveyed, only 21% thought this was acceptable behavior
while 79% deemed it unfair.
a. The wholesale price of peanut butter in stock is a sunk cost. Is it relevant to
pricing decisions for a seller who shares the majority view on fairness in
pricing?
It is. The seller is going to include something like a loss of self-respect in his estimate of
the cost of raising his price on old stock. It will cost him more in self-respect to raise the
price than he will gain in money by doing so.
b. How could it be relevant to a seller who personally holds the minority view
but also knows that his customers will find out what he has done if he raises
the price on “old” stock?
Even a seller who finds nothing wrong with raising the price on old stock will consider the
marginal cost of angering his customers.
c. The economic way of thinking does not usually distinguish a sum of money
paid out from a sum of money not received: both are equally costs. The
majority of the public apparently does distinguish, because it holds that
sellers may raise their prices to cover higher wholesale cost payments but
may not do so merely because consumers are willing to pay the higher
prices. Can you defend the popular distinction, or do you think it is simply
the product of failure to understand what’s going on?
I can understand it, and understanding it is at least a partial defense. I think many people
would reason in this fashion: A sum of money paid out makes one poorer, and no one is
under a normal obligation to become poorer. A sum of money not received keeps one from
becoming wealthier, and people may often be under a moral obligation to refrain from
actions that would make them wealthier (at someone else’s presumed expense).
11. “When lenders extend credit to high-risk borrowers, they must raise the interest rate
that may be charged low-risk borrowers in order to cover their losses from defaults.”
Does this claim make any sense?
How can they succeed in charging low-risk borrowers more than they’re willing to pay, or
more than they have to pay some other lender? Our analysis in class should have made
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clear that sellers can’t raise their prices simply because they have incurred losses. Buyers
don’t usually increase their demand for a good out of sympathy for the seller’s plight.
Furthermore, lenders charge a higher price to high risk borrowers PRECISELY to account for
the fact that they are less likely to receive payments. Therefore, the higher price to high
risk lenders already takes this risk into account, so it would be unnecessary to charge a
higher rate to a low risk lender.
12. About half of all new restaurants fail within a year, and 85% close within five years.
What do these figures indicate about the profitability of the restaurant business?
Why do so many entrepreneurs nonetheless start up new restaurants every year?
The restaurant business, considered as a whole, is highly unprofitable. Aggregate losses
exceed aggregate profits. Why do people nonetheless continue to open new restaurants?
Adam Smith spoke about the extraordinary confidence most people have in both their own
abilities and their own good luck.
13. Before 1980, the Interstate Commerce Commission rarely granted new permits to
trucking firms to haul goods interstate, and operating rights were often extremely
valuable. They were listed as assets on the books of trucking companies and made
up a significant portion of the purchase price whenever such companies were sold.
a. What factors established the market value of such operating rights?
The market value became the discounted present value of the stream of additional net
revenue that could be anticipated as a result of owning operating rights in a situation of
government-restricted entry.
b. When the Motor Carrier Act of 1980 took effect, allowing much easier entry
into interstate trucking, the market value of operating rights fell. Why?
The restrictions on competition had made the expected net revenue from trucking (with
operating rights) larger than it would otherwise be.
c. Was this fall a loss?
Yes. Notice that if the owner of the operating right had anticipated its loss soon enough, he
could have sold it to someone less skilled at divining the future. He would thereby have
avoided the loss, but only by shifting it to someone else.
d. Losses as well as profits are the consequences of uncertainty. What was the
uncertainty that produced this loss for trucking companies in 1980?
Uncertainty about the continuance of the regulation and privilege of operating rights under
a regime of restricted entry.
e. What would have happened to the value of operating rights in the 1970s if
everyone had known 10 years in advance that Congress was going to ease
restrictions on entry into interstate trucking after 1980?
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The value of those rights would have declined steadily as 1980 drew closer.
f.
The Motor Carrier Act of 1980 was a change in the rules of the game. Which
were the principal property rights affected, and with what consequences?
Owners lost a valuable legal right to sell shipping services at high prices. Their employees,
such as the truck drivers, also lost something: the tight to bargain for high wages from firms
that had the government helping them keep up prices and prevent competitors from
entering the business.
14. “Everybody knows” that laborers receive wages and only owners receive profits. But
is this true?
a. If employees agree to continue working for an employer who is currently
unable to pay them, because they don’t want the firm to fail, are they
working for wages or profits?
They are working for the possibility of a profit.
b. If you agree to loan your lawn-mower to someone who wants to start a
lawn-care business, on condition that he pay you $2 each time he borrows it,
are you a capitalist? Is your $2 properly called profit? Would your answers
differ if he agreed to pay you 20% of his gross receipts?
You would be a capitalist if a capitalist is someone who owns capital and lets other people
work with it for a price. That isn’t everyone’s definition of a capitalist, however. It
certainly wasn’t Marx’s. If you agreed to content yourself with 20% of the gross, you would
be taking on an entrepreneurial function and yes that would be a profit. However, if you
receive $2 each time your friend uses the lawn-mower, that would properly be called “rent”
because there is no uncertainty inherent in this contractual arrangement.
15. Take a look at the yellow pages of your local phone book, or surf the web for a little
while. Can you provide a list of three entrepreneurial firms in each of the categories
below, and provide reasons for your placement? Do some of the firms fall into more
than one category?
a. Firms that primarily engage in arbitrage activity
b. Firms that primarily engage in innovative activity
c. Firms that primarily engage in entrepreneurial imitation
I suspect that you guys can do this on your own!
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