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.
{ 13 comments }
This was posted by professor Klein over at O&M some time ago.
He didn’t seem to have a problem with it.
Sounds like the type of example many economists and policy academics like to use. Completely moronic! The biggest obvious hole is that this string of events is not realistically possible. It is a pure fiction which you clearly point out. What is rather frightening is that it is the type of conjecture that occurs all the time in the Keynesian world of government economic policy and justification. It may seem like fun but only serves to confuse those who are already confused!
It’s called a temporary inflation of the money supply. While the money was there there was a reduction in the purchasing power of everybody else in town.
Hah ha!
I am not worried about the debt problem at all. I am not sure how the town hereafter looks with optimism. Town has learnt nothing and would now like to create a new debt for pseudo-growth. A closed economy vulnerable to shocks I must say! Imagine what happens if someone falls ill.
I’m rather disappointed in this so-called economics blog, as none of you clearly understand the basic principles of economics!
The solvency of a community is equal to the integration of the nth derivative (where n is the number of debtors in the community in an arbitrary logarithmic scale) of sinc(x) over the real numbers divided by pi.
As we can plainly see, the solvency of a community with no debt is 1. When we add a single debtor, we get… 0?
Wait a minute. That’s not supposed to happen. This calculator must be broken.
I had seen this “Resort Town” example of stimulus a few times, and I wrote a post analyzing it last month. So, I’ll add that to the discussion here.
The Stimulus Resort Town
This story is a vivid and amazing example. I am afraid that it is actually used to illustrate and justify government “stimulus” spending. But, it is contrived and unreal, like finding five dominoes ready to fall by pushing just the first one.
The solvency of a community is measured by the government squandering multiplier and is equal to the total amount of government squandering plus the total amount of private spending to repair the damage caused by government squandering minus the total amount of savings. A good estimate for this is the 26-dimensional discrete fractional Fourier transform of the eigenfunctions to the nonlinear time-dependent stochastic Schrödinger wave operator generalized to hyperbolic pseudo-Riemannian manifolds with quaternionic-valued curvature tensors. The real part of the integral over all nontrivial roots of the Riemann zeta function gives the log of the government squandering multiplier.
If it’s valid to say that everyone in town is in debt to each other, it’s just as valid to say that everyone in town has money coming! Maybe their situation was quite good after all. (just illustrating the absurdity in yet another way).
Robert Blumen spent WAY too much time on this; his first observation (about offsetting creditor positions) was all that was needed to resolve the “paradox.”
BTW Fourier is an intellectual ass-bandit.
All that was needed was a clearing house to facilitate offsetting claims.
Mikey’s answer is short and correct.
But in it’s brevity, it misses the point of the puzzle.
Yes, if you look at the accounting balance sheet of each individual there is one A/P entry and one A/R entry of equal arithmetic magnitude. And so they perfectly offset one another.
However, for a clearing house system to work, it would have to keep records of all transactions. And it would mail reconciliation reports to every household. In which case one must wonder if the feed/fuel supplier wants his wife to see that A/P (accounts payable) entry for the town’s prostitute? Similarly does the hotel proprietor want his staff to accidentally see that A/R entry of $100 for the town’s prostitute?
What the circulating $100 bill did was to hide identities and hide transaction records.
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Still, there is the moral dilemma of the hotel proprietor owing the tourist for the time use of the “loaned” $100 bill.
In addition to making negative balance sheet items explicit and postive balance sheet items implicit, there is an unwarranted temporal assumption in the brain teaser. It assumes that every town member would rush to pay off his/her debt instead of spending it on something else, or just holding the cash.
There is more on the morel dilemma: the hotel proprietor could not know about the cancelling debt, thus he cannot expect the $100 bill to come back shortly, thus what he is doing is simply stealing.
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