Who Paid
for the Beer?
ANSWER
Here are the alternatives mentioned in the puzzle, with an explanation
for each of why it is right or wrong. The text of the original puzzle is
reprinted at the end.
-
The logger. WRONG. The logger ends his day with as much money as
he started and loses nothing else (except maybe consciousness and/or his
lunch).
-
The bartenders, or the bars. WRONG. The bartenders/bars get value
for each beer they sell. It doesn't matter that they are dealing in U.S.
and Canadian dollars; they could be exchanging beaver pelts or cowrie shells;
the fact remains that for each beer they sell, they take in something with
a certain value to them and give back something of lesser value. Some people
say that the bartenders pay for the beers in that they let the logger do
what they could do: take the foreign currency across the border and get
more value for it. This is an opportunity cost, however, not a real
cost. If I walk past a hundred dollar bill on the street and decline to
pick it up, am I $100 poorer? No, I'm $100 poorer than I might have
been. I'm ignoring the opportunity to get richer, but it doesn't make
me poorer. Think of it as if there were two stacks of dimes sitting on
the two barrooms' floors, dimes left by some previous, absent-minded patrons.
The logger walks into one bar, picks up a dime, pays for the beer, crosses
over to the other bar, picks up a dime there, pays for the beer, crosses
back, etc. The bartender has lost an opportunity to get the dimes for himself,
but the fact remains that s/he got value for the beer.
-
The townspeople. WRONG. If the bartenders/bars aren't paying for
the beer, then how can the townspeople be? An even stronger argument is
that there need not be any townspeople at all; we could just have two bars
facing each other across the border.
-
The United States and Canada; the federal treasuries of each country. WRONG.
The decisive argument is that the two bars need not be operating within
an established government at all; they could each be issuing scrip that
the other bar accepts (albeit at a discounted rate). Let me note that answers
like this are simple lazy, hazy thinking. "If it isn't anything obvious,
then it must be the government." As if there were only two alternatives.
-
The banks. WRONG. What banks? None of this involves banks or requires
banks to work. More lazy thinking.
-
The exchange rate, or the difference in currency rates. WRONG. Still
more lazy thinking. The exchange rates? Even if the beer purchases did
affect the exchange rates, this doesn't specify who therefore lost money
(so that the loss pays for the beer).
-
Everyone. WRONG. Everyone equally? Some but not others? - and if
so, who and how?
-
No one. WRONG. The beers didn't materialize by magic; someone had
to make them, and they had to either get paid for them or take the loss
themselves.
-
Someone or something else. RIGHT, namely: the people who brought
the foreign currency into the country in the first place. Say I'm a U.S.
citizen with U.S. $1 in my pocket. I could buy ten beers with that. If
I go to Canada, the same dollar will buy me only nine beers. For each dollar
I take across the border, I lose a beer. When the logger takes that dollar
back to its country of origin, he is drinking that beer I lost.
-
A MORE GENERAL ANSWER is that the beer was paid for by whoever was
holding the dollars when they were devalued from $1.00 to $.90. If
the bills are devalued by crossing the border, then the above answer is
certainly correct. But this second, more general formulation also
covers the case where the dollars were simply devalued suddenly, creating
a loss for each person holding the "wrong" country's dollar. [I am
indebted to Saul Wax for this answer -- the first substantive improvement
on the puzzle I've encountered.]
THE ORIGINAL
PUZZLE
Around 1900, back when you could still buy a ten-cent beer, a small
logging town on the U.S.-Canadian border was experiencing a strange currency
exchange situation. On the Canadian side of the border, a U.S. dollar was
only worth ninety Canadian cents, while on the U.S. side, a Canadian dollar
was only worth ninety U.S. cents. (In other words, the citizens of both
countries discounted the other country's currency by ten percent.)
In this particular town, the international border ran right down the
center of the main street, and there were bars on both sides catering to
loggers from the surrounding area. One Saturday, an American logger rolled
into town with little money (only U.S. $1.00) but lots of financial cunning.
He stopped at the first bar he found on the U.S. side of the street, ordered
himself a ten-cent beer, paid with his U.S. dollar, and asked for a Canadian
dollar in change (worth only U.S. $.90, remember). After finishing his
beer, he walked across the street to a Canadian bar, ordered another ten-cent
beer, paid with the Canadian dollar, and asked for a U.S. dollar in change
(there, worth only Canadian $.90). Back he went to the American side for
another beer, then back across to the Canadian side -- and so on all afternoon
and evening, finally staggering back to his camp after a final drink from
a Canadian bar and a U.S. one-dollar bill in change -- just as he had started
out with.
But what his fellow loggers could never figure out was, who paid for
the beer?
Page URL: http://www.d.umn.edu/~schilton/Courses/Beer.html
Page Author: Stephen Chilton
Link to Home Page: www.d.umn.edu/~schilton/index.html
Last Modified: September 28, 2001
Mail suggestions and comments, especially re. typos and other errors,
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