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A Misleading Brainteaser


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 provide $100 in order 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", but the origin of these hard times is never explained. It is hinted that the population is pessimistic because of the accumulated debts. The hard times are alleviated by canceling out all of the debt.

Could this be so?

From the detailed description of who owed money to whom, we can infer 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. The town is a closed economic system in which all necessary goods and services are produced and consumed locally. People can only borrow from other residents of the town.

Under these conditions, the accumulation of debt has no macro-economic consequences. For every debtor, there is an equal 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 become 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. Everything nets out. The total purchasing power within the town is shifted among residents.

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. Perhaps after binging, are having trouble servicing the debt?

This cannot be so. If the town is a closed economic system, then internal debt cannot enable the entire town to consume more than it produces -- that could only happen if the townspeople borrowed from non-residents. And while it need not be so, in this town, no one is a net debtor or a net creditor. Everyone has borrowed and loaned the same quantity of money. Everyone's net credit balance is zero. No one has increased their consumption by taking on debt.

If the business people in the town tend to run on credit, once in a while netting 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 debts is perfectly compatible with a booming economy. Because everyone's credit balance is zero, these debts could be canceled at any time; or the business people could carry the debts, paying the interest out of their income. Everyone's net interest payment is zero because the interest they receive is the same as the interest that they pay.

While the factors of the story do not support the hypothesis that the townspeople have borrowed from an external lender, let's go down that path briefly.

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. So even foreign debt does not necessarily imply any macro-economic problems.

The story concludes "the whole town is now without debt, and looks to the future with a lot of optimism." True, everyone has been relieved of debt, but everyone has also reduced their asset position by the exact same amount. The writer equally well could have concluded that the town can look to the future with pessimism because everyone has fewer assets; or, just as plausibly, that the town's mood was unchanged because everyone's net financial balance was the same as before.

In summary, if this is supposed to explain anything about the financial crisis or the US economy, I'm not sure what.

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