Author:  Lori Alden

Audience:  High school and college economics students

Teaser #1Is it possible for the price level to go up at the same time inflation is going down?

Solution:  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.

Teaser #2Which state boasts two Federal Reserve Banks?

Solution Missouri , with FRBs in St. Louis and Kansas City .  (Champ Clark of Missouri was Speaker of the House of Representatives in 1913, when the Federal Reserve System was established.)

Teaser #3Libby:  "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 aren't contradictory?

SolutionIt'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%.

Teaser #4A $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?

SolutionAt Mendoza's, 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.

Teaser #5Your friends are planning to travel to South Africa 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?

Solution:  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.

Teaser #6Tom 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 US for $1 each.)

SolutionTom 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.

Teaser #7You'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 worth?

SolutionIf 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:

Cost = Benefit

1/10,000 Chance of Death = $1

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 motorcycle ride.

Teaser #8Libby:  "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?

SolutionFrom 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 U.S. 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.

Teaser #9Which 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)?

SolutionThe 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.)

Teaser #10A 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?

SolutionAs 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.

Teaser #11If the government reduced the budget deficit, would the national debt rise or fall?

SolutionIt 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. 

Teaser #12:  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 states? 

SolutionThere'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.

Teaser #13Suppose 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 of Demand?

Solution:  No.  This could be explained by a rightward shift of the demand curve.

Teaser #14When 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 preferences?

SolutionNot necessarily.  The shoppers could have ranked the flavors this way:

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 #15The 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?

SolutionBid 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 #16A 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?

Solution:   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.

Teaser #17Mary 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?

SolutionThe 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 2 to produce and exchanging it for $10 worth of government securities.

Teaser #18The 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.

Teaser #19If 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?

SolutionIt could rise or fall, but it often rises.  For example, here's the ratio of the two unemployment rates in 1980:

Black unemployment rate/White unemployment rate = 14.3%/6.3% = 2.27

This ratio rose in 1990:

Black 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 1980:

Black employment rate/White employment rate = 85.7%/93.7% = .91

This ratio also rose in 1990:

Black 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 denominator.

Teaser #20:  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?

Solution:   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. 

Teaser #21:  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 something?

Solution:  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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