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Jason Rosenhouse
over at Evolution Blog
provides the following "breain teaser":
It is the month
of August; a resort town sits next to the shores of a lake. It is raining,
and the little town looks totally deserted. It is tough times, everybody is
in debt, and everybody lives on credit. Suddenly, a rich tourist comes to
town. He enters the only hotel, lays a 100 dollar bill on the reception
counter, and goes to inspect the rooms upstairs in order to pick one.
The hotel
proprietor takes the 100 dollar bill and runs to pay his debt to the butcher.
The Butcher takes the 100 dollar bill and runs to pay his debt to the pig
raiser. The pig raiser takes the 100 dollar bill and runs to pay his debt to
the supplier of his feed and fuel. The supplier of feed and fuel takes the
100 dollar bill and runs to pay his debt to the town's prostitute that, in
these hard times, gave her "services" on credit. The hooker runs to
the hotel, and pays off her debt with the 100 dollar bill to the hotel
proprietor to pay for the rooms that she rented when she brought her clients
there.
The hotel
proprietor then lays the 100 dollar bill back on the counter so that the rich
tourist will not suspect anything. At that moment, the rich tourist comes
down after inspecting the rooms, and takes his 100 dollar bill, after saying
he did not like any of the rooms, and leaves town.
No one earned
anything. However, the whole town is now without debt, and looks to the future
with a lot of optimism.
Wow, where to
start.
The brain teaser
combines a rather silly and obvious paradox with some bad macro-economics.
The solution to
the paradox is that, when credit claims run in a circle, the residents of the
town don't need an external party to settle. They could simply get together
and net out all of their credit positions. Because everyone has an equal
asset and liability, everyone could net their position to zero. The
introduction of the $100 bill by the rich tourist does nothing that the
townspeople could not do by themselves. Suppose you and a friend owed each
other $100. You could agree to cancel your obligations to each other without
any cash changing hands.
Now let's look at
the bad macro-economics. The town is said to be experiencing "hard
times". It is implied that the downturn is somehow related to the
accumulation of debt. The hard times are alleviated canceling out all of the
debt. Could this be so?
The town is a
resort. This suggests a town that exports tourism services to the external
world and imports goods. Suppose that such a town imports more goods than it
exports, i.e. the town has a trade deficit. Does this portend any economic
problems? Not necessarily. The residents of the town may be voluntarily
choosing to spend down accumulated savings. There are many examples of
pleasant resort towns where wealthy people go to retire and live off their
lifetime savings. Another possible explanation for a trade deficit is an
inflow of savings from the rest of the world. Real estate developers in other
cities, for example, could investing in the construction of new hotels. The
town's trade deficit in goods would be offset by foreign direct investment.
Assuming that the entrepreneurs building the new facilities were correct in
their forecast, the increase in the capital stock of the town would raise
real wages and increase the volume of employment. After the hotels were
complete, the town would be able to accommodate more tourists and increase
its export of tourism services.
But this is
probably not the explanation. Based on the second paragraph, we can assume
that the debt is all internal to the town. The hotel owner has borrowed from
the butcher who has borrowed from the pig farmer, etc.
So let's look at
a different model. Consider a town that is a closed economic system in which
all necessary goods and services are produced and consumed locally. People
can borrow from each other. Under these conditions, the accumulation of debt
has no macro-economic consequences. For every debtor, there is a creditor.
When a loan is made, the increase in the immediate purchasing power of the
borrower is offset by a decrease in the purchasing power of the lender. The
interest payments made by the borrower becomes the income of the lender. If someone
takes on too much debt and cannot service it, the lender may foreclose on the
collateral, in which case the borrower's forfeit of asset becomes the
lender's accumulation of the same asset.
It is implied,
but not stated, that everyone has gotten into debt because their desired
consumption levels exceeded their income, so they have borrowed in order to
maintain their standard of living. It is implied that the economy of the town
is in bad shape because everyone is burdened by excessive debt. This cannot
be so. If the town is a closed economic system, then the entire town cannot
consume more than it produces through accumulating debt. In a closed system,
all that debt can do is to shift purchasing power around. An gross increase
in consumption can only happen in a town that trades with the external world.
In paragraph two, we learn that each person's debt is exactly offset by a
credit from someone else. This means that everyone's net balance is zero. No
one has been able to increase their consumption (or decrease their
consumption) by taking on debt.
If the business
people in the town have extended each other credit, and then, net everything
out to avoid the inconvenience of unnecessary cash transfers, this tells us
exactly nothing about the macro-economic situation of the town. The presence
of a chain of interlocking debts is perfectly compatible with a booming
economy. As stated above, everyone's net debt position is zero. These debts
could be canceled at any time that they wanted to, or the business people
could service their debts out of income.
The final
paragraph states that "the whole town is now without debt, and looks to
the future with a lot of optimism." It is true that everyone has been
relieved of their debt, but everyone has reduced their asset position by the
exact same amount. The writer could have equally well reached the opinion
that the town can look to the future with pessimism because everyone has
fewer assets. Or, more likely, that the mood is unchanged because everyone's
net financial balance is unchanged.
In summary, if
this is supposed to explain anything about the financial crisis or the US
economy, I'm not sure what.
Robert Blumen
Also
by Robert Blumen
Robert Blumen is
an independent software developer based in San Francisco, California
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