Author: Lori Alden
Audience: High school
and college economics students
Is it possible for the price level to go up at the same time
inflation is going down?
Yes. Inflation measures the rate of growth of the price
level. When the rate of inflation falls (called
disinflation), the price level is still rising, but at a slower
rate. When prices fall, we experience deflation.
Which state boasts two Federal Reserve Banks?
with FRBs in
(Champ Clark of Missouri was Speaker of the House of
Representatives in 1913, when the Federal Reserve System was
Libby: "The unemployment rate went up between May and
June of 1991." Conrad: "the number of people
employed rose between May and June of 1991." Libby and
Conrad seem to be contradicting each other, but both of their
claims are correct. Can you explain why these statements
It's possible for both the unemployment rate and the number of
persons employed to increase if the labor force expands. The
unemployment rate is equal to the number of unemployed divided by
the labor force (number of unemployed plus employed). In May
of 1991, there were 125,232,000 people in the civilian labor
force, of which 116,591,000 were employed and 8,640,000 were
unemployed. The unemployment rate was 8,640,000/125,232,000
= 6.9%. In June, the civilian labor force had grown to
125,629,000, of which 116,884,000 were employed and 8,745,000 were
unemployed. While the number of employed persons increased
over that period, the unemployment rate rose to
8,745,000/125,629,000 = 7.0%.
A $100 sweater at Mendoza's
Department Store is on sale for 50% off. An identical $100
sweater at Hoffman's Department Store was originally market down
40%, but Hoffman's is having a clearance sale this week and is
subtracting an additional 15% from its sale prices. At which
store is the sweater cheapest?
the sweater is $100 - .5($100) = $50. At Hoffman's, the
sweater was originally marked down to $100 - .4($100) = $60.
With an additional 15% reduction, the new price is $60 - .15($60)= $51. It's cheaper at Mendoza's.
Your friends are planning to travel to South
this summer, but
you're down to your last dollar and can't go. While reading
the financial section of the paper, though, you discover that one
South African rand can be exchanged for 25 Japanese yen, that 150
Japanese yen can be exchanged for $1, and that $1 can be exchanged
for 5 rands. Is there a way you can earn travel money by
exploiting these exchange rates?
Buy 150 yen with $1, then use them to buy 6 rands. Pocket
one rand and buy your dollar back with the remaining five rands.
Repeat as needed.
Tom sells 1,000 light bulbs a day in the US
for $1 each. Since his total cost is $800 a day, he makes
$200 in profit per day. One day, he learns of an opportunity
to sell 1,000 additional light bulbs in France
for $.50 each. If he boosted production to 2,000 light bulbs
a day, his total cost would rise to $1,200, or $.60 per bulb.
Should he sell $.60 light bulbs to the French for only $.50?
(Assume that he can still sell 1,000 bulbs per day in the
for $1 each.)
Tom should produce the extra 1,000 light bulbs. His marginal
revenue from each of the extra bulbs is $.50. But his
marginal cost is ($1,200 - 800)/1,000, or $.40 per bulb.
He'll make $.10 on each of the 1,000 extra bulbs he produces.
His average total costs are high because of high sunk costs, but
these, of course, should be ignored.
You're waiting to take the bus home after school when your
neighbor drives up on his motorcycle and offers you a ride.
He doesn't have an extra helmet and you can smell whiskey on his
breath, so you figure there's a one in ten thousand chance that
you'll be killed if you accept the ride. On the other hand,
if you go with him, you'll save the $1 bus fare. You waver,
but decide to go with him. What's the most your life's
If you were indifferent between accepting the ride and not
accepting the ride, then the cost of the ride would be equal to
the benefit. Algebraically:
Chance of Death = $1
Chance of Death = $10,000
I.e., you're putting an
implicit value of, at most, $10,000 on your life if you accept the
Libby: "From 1977 to 1992, Americans in the top 1%
income group had their federal tax rates cut by more than
17%." Conrad: "In 1992, Americans in the top
1% income group paid a larger share of federal taxes than they did
in 1977." Libby and Conrad seem to be
contradicting each other, but both of their claims are correct.
Can you explain why these statements aren't contradictory?
From 1977 to 1992, the federal effective tax rate for families in
the top 1% income group fell from 35.5% to 29.3% -- a decrease of
more than 17%. Over this same period, the share of total
federal taxes paid by that group rose from 13.6% to 18.3%.
This happened because the share of
pretax income received by the top 1% grew substantially over this
period (from 8.7% in 1977 to 14.6% in 1992). With this
higher income, the richest 1% paid more taxes even though its tax
rates had fallen.
Which is more valuable: a 2' X 2' X 2' box filled with
1-ounce Gold Eagle coins (worth about $430 each) or a 3' X 3' X 3'
box filled with 1/4-ounce Gold Eagles (worth about $110 each)?
The larger box holds far more gold, so it's more valuable.
(It doesn't matter that a 1-ounce coin is more valuable than a
1/4-ounce coin. The 1/4-ounce coin is smaller so there are
more of them per cubic foot.)
A professor asked her research assistant to find out if the
average wage for females rose or fell over a ten-year period.
That afternoon, the assistant returned and said, "I wasn't
able to find anything on females, but I found out that the average
wage for all workers fell during that period while the average
wage for males rose. It must be therefore be true that the
average wage for females fell." "Not
necessarily," sniffed the professor. "It's
possible that the average wage for females rose during that
period, too." How could that happen?
As an example, suppose that 70% of the labor force was male and
30% was female and that their average wage rates were $10 and $7
respectively. The average wage for all workers would be (70%
X $10 + 30% X $7) = $9.10. Now suppose that over the
ten-year period the composition of the labor force changed so that
30% was male and 70% was female, and that their average wage rates
rose to $11 and $8 respectively. The average wage for all
workers would fall to (30% X $11 + 70% X $8) = $8.90.
If the government reduced the budget deficit, would the national
debt rise or fall?
It would rise as long as there's a budget deficit. The
federal budget deficit measures how much the government borrows
per year. The national debt is the sum of all the deficits
less all the surpluses the government has run since the 1789.
The budget deficit, then, tells us by how much the national debt
increased in any given year. We decrease the national debt
only when we run budget surpluses.
Trucks with triple trailers have 35% more accidents as those with
double trailers, but two triple-trailered trucks can deliver as
much freight as three double-trailered trucks. Would there
be more or fewer accidents if we allowed triple trailers in all
There'd be fewer accidents. If we switched to triple-trailered
trucks, each truck would have 135% as many accidents, but we'd
need only 67% as many trucks. This means we'd have 1.35 ×
.67 = 90.45% as many accidents with triple-trailered trucks as
with double-trailered trucks.
Suppose that you read in the paper that the price of gasoline had
gone up from $1.90 in April to $2.00 in June, and that gasoline
sales had also gone up, from 120 million gallons a day in April to
140 million gallons a day in June. Does this violate the Law
Solution: No. This could be explained by a rightward shift of the
When a woman working for a consumer polling firm asked three
shoppers about their favorite ice cream flavors, two said they
prefer chocolate to vanilla and two said they prefer vanilla to
strawberry. After answering the woman's questions, the
shoppers were treated to a free serving of ice cream, but they
could choose between only two flavors: chocolate and
strawberry. To the woman's surprise, two of the shoppers
picked strawberry. Had they lied to the woman about their
Not necessarily. The shoppers could have ranked the flavors
One prefers chocolate to
vanilla and vanilla to strawberry.
One prefers vanilla to
strawberry and strawberry to chocolate.
One prefers strawberry to
chocolate and chocolate to vanilla.
While two of the shoppers
prefer chocolate to vanilla and two prefer vanilla to strawberry,
it's also true that two prefer strawberry to chocolate.
(Economist Kenneth Arrow used this sort of paradox to demonstrate
that voting can sometimes lead to arbitrary results.)
Teaser #15: The tickets to a concert are sold out, but you go anyway and
hope to find a scalper. There is, alas, but one scalper, and
she has but one ticket to sell. Since there are about 25
people trying to buy the ticket, she announces that she will
auction it by sealed bid, and that she will award the ticket to
the highest bidder--but the winner need only pay the second
highest amount bid. As you prepare to write down your bid,
you decide that the most the ticket is worth to you is $56.
How much should you bid--$56, more than $56, or less than $56?
Bid exactly $56. Suppose that you bid more than $56 (say,
$60), and that yours was the winning bid. If the second
highest bid was $58, you'll end up paying more for the ticket than
it's worth to you. On the other hand, if you bid less than
$56, (say, $50), then you risk losing the ticket to someone else
who bids more than $50 but less than $56.
Teaser #16: A professor asked her research assistant to find out the
average hourly wage of librarians in 2002. The research
assistant looked for the information in Occupational Outlook,
and found that the annual salary for librarians was about $43,000
a year. To calculate the hourly wage from that, he reasoned
as follows: Out of 365 days, librarians don't work 16
hours a day, which comes to 243 days a year. They also have
weekends off, which comes to 104 days a year. They also get
10 days of vacation, and they're off on New Year's Day, Memorial
Day, Independence Day, Labor Day, Thanksgiving, and Christmas, or
6 days a year. This means that librarians work only
365-243-104-10-6 = 2 days or 16 hours a year, so their hourly wage
must be $20,000/16 hours = $1,250/hour. When he showed
that result to the professor, she said that he must be wrong.
What was his mistake?
The 16 hours a day that librarians shouldn't have been taken off a
second time for the 104 weekend days and the 10 vacation days and
6 holidays. Librarians work 365-104 - 10 - 6 = 245 days a
year. On these days, they don't work 16 hours, which is the
equivalent of 16/24 (245) = 163.33 24-hour days. This means
that they work an equivalent of 245 - 163.33 days, or 81.67
24-hour days, or 1,960 hours a year. The salary, then, would
be $43,000/1960 hours = $21.94/hour. This isn't a
conventional way of calculating hourly salaries, though, since
salaried workers are normally paid for vacations and holidays.
Mary and Gary are counterfeiters. One day, they make a
perfect copy of a $10 bill. They use it to pay their
gardener. The gardener uses the $10 to buy pizza. The
pizza maker uses the $10 to rent video tapes. The $10 bill
keeps circulating in the economy, and no one ever discovers that
it is counterfeit. Who was harmed by Mary and Gary
counterfeiting a $10 bill?
Solution: The government--and its citizens--lose. The Federal
Reserve Board usually increases the money supply by buying
government securities--the stuff that the U.S. Treasury issues to
finance budget deficits. This process is called monetizing
the deficit. Most of the new money that's created eventually
assumes the form of demand deposits (a.k.a. checking accounts),
but some of it is in the form of vault cash and currency in
circulation. By issuing their own $10 bill, the
counterfeiters prevented the Fed from taking a piece of paper that
only cost the Bureau of Engraving and Printing about 2½¢ to
produce and exchanging it for $10 worth of government securities.
The Food Barn sells candy bars at a price of 5 for $1.
Margaret bought $12 worth of candy bars there and resold half of
them at a price of 3 for $1 and half at a price of 2 for $1.
How much profit did she make (assuming her labor costs are zero)?
Solution: $13. She bought 60 candy bars for $12. Her
revenue on the 30 candy bars she sold at 3/$1 is $10; her revenue
on the 30 she sold at 2/$1 is $15. Total revenue less total
cost is $25 - $12, or $13.
the ratio of the black unemployment rate to the white unemployment
rate rises, will the ratio of the black employment rate to the
white employment rate rise or fall?
Solution: It could rise or fall, but it often rises. For
example, here's the ratio of the two unemployment rates in 1980:
unemployment rate/White unemployment rate = 14.3%/6.3% = 2.27
This ratio rose in 1990:
unemployment rate/White unemployment rate = 11.3%/4.7% = 2.40
Given that the employment rate equals one minus the
unemployment rate, here's the ratio of the two employment rates in
employment rate/White employment rate = 85.7%/93.7% = .91
This ratio also rose in 1990:
employment rate/White employment rate = 88.7%/95.3% = .93
Both ratios rise because blacks have a higher unemployment rate (and
therefore a lower employment rate) than whites. This means
that an improving economy often changes the black unemployment
rate by a smaller percentage than the white unemployment rate, but
changes the black employment rate by a larger percentage than the
white employment rate. When this happens, the ratio of black
to white unemployment rates increases since the numerator goes
down by a smaller proportion than the denominator. The ratio
of black to white employment rates also increases since the
numerator in that ratio rises by a larger proportion than the
Andrew bought some shares of ABC Corporation and XYZ Corporation.
A year later, he sold the ABC shares for $3,000 and the XYZ shares
for $3,000. When he asked his broker if he’d made money on
the stocks, she told his that the ABC shares had gone up by 50%
and the XYZ shares had gone down by 50%. “Oh well,”
sighed Andrew. “I guess I broke even.” Did he?
No. Andrew must have bought the ABC stock for $2,000 and the
XYZ stock for $6,000. This means that the value of his
portfolio dropped from $8,000 to $6,000 over the year.
If two people are splitting a piece of cake, then the “I divide,
you decide” rule ensures that the cake cutter will try to cut
equal portions (since the other person chooses first).
But what do you do if three people are splitting a piece of
cake? Also, how do you
flip a coin if three people are trying to decide who gets to do
The “I divide, you decide” rule works on three-way splits, too.
Just have one person cut the cake into three equal slices,
but let the other two choose first.
Since the cake cutter gets the third largest slice, he or
she will take pains to cut the cake into exactly equal portions.
If you flip a coin twice, there are four possible outcomes:
HH, HT, TT, and TH. If
you’re flipping a coin to pick a winner among three people, have
each of them pick one of these outcomes (one will be left over).
Then flip twice. If
nobody wins, then flip twice more.
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