David R. Henderson  

An Answer to a Monetary Riddle

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Last quarter, I received the following "riddle" from a student in my class:

It's a slow day in some little town........
The sun is hot....the streets are deserted.
Times are tough, everybody is in debt, and everybody lives on credit.

On this particular day a rich tourist from back west is driving thru town.
He stops at the motel and lays a $100 bill on the desk saying he wants to inspect the rooms upstairs in order to pick one to spend the night.
As soon as the man walks upstairs, the owner grabs the bill and runs next door to pay his debt to the butcher.
The butcher takes the $100 and runs down the street to retire his debt to the pig farmer.
The pig farmer takes the $100 and heads off to pay his bill at the feed store.

The guy at the Farmer's Co-op takes the $100 and runs to pay his debt to the local prostitute, who has also been facing hard times and has had to offer her services on credit.
She, in a flash rushes to the motel and pays off her room bill with the motel owner.
The motel proprietor now places the $100 back on the counter so the rich traveler will not suspect anything.

At that moment the traveler comes down the stairs, picks up the $100 bill, states that the rooms are not satisfactory, pockets the money & leaves.

NOW,... no one produced anything...and no one earned anything...however the whole town is out of debt and is looking to the future with much optimism.

Here's monetary economist Jeffrey Rogers Hummel's answer:

There are several ways to think about this intriguing example. But they all must recognize that these transactions have made no change in any of the parties' NET wealth. True, at the beginning each resident has a $100 liability. But each also has an offsetting financial asset of $100. At the end, they all have neither. So the $100 bill acts as a clearing mechanism.

If you want to think of the town as a distinct economy, then the rich tourist has temporarily increased the town's money stock by $100. In effect, he has made a short-term loan of a new $100 bill, increasing liquidity. The $100 provides the residents with a medium of exchange that allows them to clear their offsetting debts.

Or if you broaden the economy to include the rich tourist, his short-term loan has provided liquidity through increasing the transactions velocity of money. If the rich tourist hadn't provided the loan, any of the residents could have accomplished the same result by borrowing $100 cash from someone else. No new final goods and services were produced (they had been produced already). But borrowing from the tourist may have cost less interest (zero percent) than otherwise. (I'm ignoring the possible complication that the hotel owner only gets a zero-percent loan by embezzling: using the tourist's deposit without permission.)

Either way, the $100 cash would have been unnecessary if the residents had a central clearinghouse. The fact that the hotel owner seems to know that the $100 bill will come back quickly suggests they already had everything necessary for an informal clearing, and didn't need the bill in the first place. The hotel owner could have gone to each party in succession, offering to take on their debt if they cancelled his.

Nonetheless, the example illustrates Mises's point that increases in the efficiency of the clearing system reduce the demand for (increase the velocity of) money. A clearing system is an alternative way of providing medium of exchange services. In fact, in my classes I use a similar example with fewer parties to illustrate the nature and benefits of a clearing system. At the limit, a perfectly efficient clearing system would be an all-encompassing network of computerized barter making money completely unnecessary. So your student's intuition is partly right. What the tourist's short-term loan has produced is monetary services.

Comments and Sharing


COMMENTS (14 to date)
D. F. Linton writes:

Just before the clearing system became all-encompassing and perfect, the velocity of money would approach infinity.

Mises made a similar point about the absurdity of general equilibrium: Since the schedule and amounts of all of one's future obligations is by definition perfectly known, the need for cash balances is eliminated by careful arrangement of the timing of receipts. Since this is true and most efficient for all actors, there are no money balances in general equilibrium and hence no money at all.

HH writes:

Just one question: no one in this town is actually in debt, are they? Their net worth (at least as described) is zero.

mark writes:

It also illustrates a point I made somewhere in the blogosphere related to the Krugman argument that we don't have to repay debt because "we owe it all to ourselves". The point I made, which this example illustrates, is that, if we owe it all to ourselves, then it equally follows that we could pay it all back in full immediately. If you have a closed loop, it doesn't matter whether you stand still or run all the way around it, you wind up in the same place.

As economically that doesn't make sense, it suggests that the "we owe it all to ourselves" premise is false. There is a difference between "we" who owe and the "ourselves" who are owed to.

David R. Henderson writes:

The riddle does not give us enough information to tell us each person’s net worth. Some could be millionaires. But each owes $100.

Rick Hull writes:


Great point. While seemingly trivial, it's one that should be (at least) acknowledged before delving into any aspect of the "we owe it to ourselves" argument, lest readers get the wrong idea (i.e. that a simple clearing mechanism wipes out the debt).

OneEyedMan writes:

Linton, if you have even small transaction costs you can get money in GE. See for example, Commodity money equilibrium in a convex trading
post economy with transaction costs by Starr (2008)

david writes:

The moment you have sticky debt and rational actors, you get a broadly New Keynesian dynamic. If debt is furthermore sticky in a stable way to the total money supply, then you get an outright Monetarist dynamic.

Invoking Mises here is at best misleading. Invoking Mises in the same breath as demanding a central clearinghouse is outright disingenuous, given what the likes of Oskar Lange advocated and what side Mises picked in that fight.

Russtovich writes:

Everyone may have made out ok from this... except the motel owner. He is basically out $100 now as he took the $100 from the prostitute and gave it back to the rich traveler. In a sense he just wrote off some of his debt (the cost of the room the prostitute owed him). What I get from this is that the banks should be happy to write off lots of debt then and everything will be ok? :)

steve writes:

I think there was a change to net wealth. Basically, cash in hand is worth more then a lean. Without the embezlement, a more realistic result would be for the wealthy stranger to buy one or all the loans at a modest discount. Everyone could then "almost" pay off their debts.

MG writes:

OMG I can't believe that it took so many posts for someone (Russtovich) to actually see the mathematical flaw in the argument. That this is not an obvious and cardinal flaw in the whole scheme shows the usefulness of aggregates in economics in hiding micro flaws.

Jeff Hummel writes:

Linton and OneEyed Man: Even in a world of zero transaction costs with an all-encompassing clearing system, where the demand for a medium of exchange has fallen to zero, the velocity of money and price level only soar to infinity under fiat money. With commodity money, the commodity still has a non-monetary demand. Its commodity value thus anchors the price level as it provides the unit of account (i.e., becomes the numeraire) in a Walrasian world without ever being used as a medium of exchange.

David: why do you automatically assume that a highly developed clearing network has to be centrally planned, when in the world today, credit cards, electronic funds transfers, and other financial innovations are increasing the efficiency of a decentralized clearing system? Nor was I demanding or advocating such a development, as you state, but was merely engaging in a thought experiment similar to one you can find in Rothbard's discussion of money in MAN, ECONOMY, AND STATE.

Ritwik writes:


The central clearing system would have to bear counterparty risk. In general, a medium of exchange is required due to transaction demand which in turn is required due to credit risk. An issuer of fiat currency that also has the power to tax is exactly the clearing house that you are looking for.

Kevin writes:

Russtovich & MG, the hotel owner started with a $100 payable to the butcher and a $100 receivable from the hooker. Now he has neither. He's not out anything unless you want to say he should have just stolen the money from the traveler (recall that the traveler didn't actually rent a room so there was no $100 transaction there, just the posting and redemption of the $100 deposit for the right to inspect the rooms).

Russtovich writes:

Kevin, thanks. How did I miss that? (sigh)

That makes the riddle pretty useless as an example of debt, since everything balances out. I doubt the world debt situation is that easy. :)



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