Musical Chairs
In September, 1982, railroad engineers across the United
States went on strike for several days until the President
signed a bill ordering them back to work. The strike created
transportation difficulties in several major cities,
including Chicago, as suburbanites who normally rode the
train sought alternative ways to get to work. Many found
that highway congestion was not as serious a problem as was
parking-lot congestion. When they finally got downtown,
there were no parking spaces left. After reporting the
problem, one television newscaster in Chicago advised all
commuters to start driving earlier the next day so they
would find a spot to park.
If all commuters had followed this advice, the situation
would have been worse rather than better. The parking lots
would have filled up earlier and the same number of people
would have been unsuccessful in finding spots. Everyone
would have wasted time by starting earlier. The situation
here is not unlike the proverbial fire in the theater. If
everyone calmly walks to the exits, the theater will be
emptied as fast as, if not faster than, if everyone runs to
the exits. What may be a solution for one is not a solution
for all if everyone tries it.
As another example of a matching problem, consider
this excerpt from a letter that many thousands of people
have received:
"You too will be making easy money in three to
four weeks...My method is simple. I sell thousands of
people a product for $5.00 that costs me pennies to
produce and mail. Everyone involved in the program makes
money from everyone else in the program. If anyone makes
money, everyone makes money...This plan has the effect
and appeal of a chain letter, but it is legal since you
are offering a legitimate product to your people."
The product being sold is a copy of instructions that the
buyer then can sell to others.
Is it possible for everyone involved to make money from
this scheme? To see that it is not, you must first realize
that because the "product" being sold is worthless, the
scheme is simply a way of redistributing money. It works
with the same logic as a chain letter. All the money that
people make in the scheme must come from others involved in
the scheme. The sum of money received must equal the sum of
money sent. The redistribution is the same as that which
takes place in a poker game: the sum of winnings must equal
the sum of losings. If anyone involved in the game ends up
with more than he started with, someone else must end up
with less. (These are zero-sum games--the sum of all
winnings and all losses equals zero.)
In matching problems, there is no need for any
assumptions of how people act; the results are determined
regardless of how people behave. Economists do use matching
formulas, but never alone as a complete theory. Economic
theories always contain assumptions about how people act.
But within the theories, matching formulas in the form of
identities can play important roles. An identity is a
statement true by definition. An example of an identity is
the statement, "The amount bought must equal the amount
sold." Because whatever is bought must have been sold and
vice versa, this statement must always be true. Another
example of an identity is the statement "Net worth equals
assets minus liabilities." This statement underlies the
balance sheet, a basic tool of accounting.
Next we discuss contingent
behavior.
Copyright
Robert Schenk
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