Economix paradox: the "circle of debt"

[Maes]

It's about a sort of "economic problem/paradox", like the one with the waiter and the change that apparently doesn't add up, but of a more philosophical nature

I don't know what's the proper enunciation or even the proper name for this particular "economic paradox" problem, I called it a "circle of debt" because that's what it appears to be, at least on the surface. I first saw it in a greek comedy show as a dramatization, which I will illustrate here:

A Japanese businessman of sorts walks into a hotel in Greece and asks to personally inspect the best suite of the hotel before booking it for the night or something to that effect. The (somewhat shifty) receptionist tells him "why yes, of course you can inspect it yourself, sir, but I'll have to ask you for a cautionary 5000 drachmas deposit" (that's about 14 Euros).

The businessman agrees, gives the receptionist the 5000 drs bill, and he in turn hands him the key to the suite and sends him on his way. As the receptionist is grinning upon the easily earned money (it's made clear at this point that he had no intention of returning the bill), the bellboy comes along and tells him "Hey, remember that 5000 drs debt you had with me? Time to settle it" and before the receptionist can reply, the bellboy grabs the bill from his hand.

The bellboy however, goes to the kitchen to snatch a bite to eat, and stumbles upon the waiter, to whom he also owed 5000 drs. So the bill changes hands once more. Then the waiter happens upon the cook to whom the waiter owed 5000 drs...and the bill changes hands again.

To make a long story short, the bill changes hands many times (the maid, the gardener, the barman etc.) until, by some final debt, the receptionist gets his hands on the bill again and the circle closes.

At that point however, the Japanese businessman walks out casually, says "Sorry, I won't be booking that suite", grabs his 5000 drs "cautionary deposit" from the hands of the receptionist and disappears.

The paradox is that apparently the debts between the persons involved were all solved without anyone of them actually getting any richer or poorer, because there was a debt circle between them of which, however, none was fully aware.

The circle started closing once some external resource (the "cautionary deposit") was introduced in the circle, but at the end it was removed, and none of the participants actually got any richer.

IMHO, this rises an interesting question: if those persons were all made fully aware of their mutual debts, could they have called it even on those grounds, without even an external factor triggering the events? Are there real-world examples of such a situation?

Please discuss.

[Dr. Zin]

Stuff like this is what underpinned the whole financial idiocy that has caused today's recession. Except instead of debt, it was interest. You know, like someone investing $1000 at a 8% rate to someone who invests with someone else at 10%, etc. etc. down the line. Everyone in this circle of interest says they are making profits, yet at the end you only have the original $1000.

When one person is doing it (like Madoff) it is a Ponzi scheme. When dozens of organizations are engaging in this regulators turn a blind eye.

[Maes]

There's a significant difference compared to Ponzi schemes, MLM etc: those schemes are actually engineered to have a source (the victims) and a sink (the schemers) of real money, and the money flow is solely from the victims to the schemers, which at some point just "stop the merry-go-round" and beat it. In other words, someone must actually lose money to power those schemes.

What appears in the problem/story/whatever is a different situation: a series of identical debts, created at different times, but ending up forming a closed chain. There's no deliberate attempt at deception or manipulation here.

TO put it in simpler terms, imagine just you and two of your friends, having some mutual debts. You have a debt of $100 with Friend 1, and Friend 1 has an identical debt with Friend 2, who also happens to have a similar dept with you, but you are unaware of the circularity of the debt, because they occurred at different times and circumstances.

The question is: if you and your buddies happened to meet and by discussing about your debts you discovered that you have such a "circle" between you, could you just say "OK boys, then I guess we're even. No more debts between us, they are settled kthxbye" and walk away?

Would it be any different if you symbolically gave a $100 bill to friend 1, who gave it to friend 2 who gave it back to you?

Update: apparently there is a real-world concept of "circular debt": there's a software for decentralized payment networks called Ripple that aims (among others) at detecting and eliminating circular debt.

[Bank]

There ain't enough room for two incredibly long argument writers in this town, partner.

Oh and boo debt.

[Technician]

Yah, you’re cutting into Utahraptors territory.

[Maes]

As long as he loves economic paradoxes ;-)

[Ichor]

Starting around 1:30...

[Gokuma]

What people don't take into account is that all our unneccesarily and defective junk has lost value, so what it costs to produce or buy it is a loss. More and people are seeing junk and BS for what is, so it just loses more value. Things slow down and stop. To try to keep shit going, people or government are trying to make new bubbles and the Federal Reserve is just making up more money. Actually only %2 of the currency is in physical form, so that goes to show how even more made up BS it is.

[Maes]

Ichor said:

comedy stuff with circular payment

Heh, that rather reminds of a Pulcinella and Arlecchino sketch (they are Italian "commedia dell'arte" characters):

Pulcinella and Arlecchino were carrying around a demijohn of wine to deliver it to their master, Pantalone. At some point Arlecchino asks to have a sip of the wine.

"I can't do that" said Pulcinella, "this wine is for our master, and if any is found missing, we will have to repay it".

"No problem" said Arlecchino, "here's a golden coin, now let me have a sip". So Pulcinella allows Arlecchino to have a sip, takes the coin and they proceed on their way.

However, later on Pulcinella asks for a sip of the wine, and thus gives a gold coin to Arlecchino....who later asks for another sip and so on, until the wine is all gone, in about 20 sips from each one.

When they arrive before their master, he asks them what the hell had they done with his wine "Oh, we drank it all, master, but we paid for it as we drank it, we gave 20 gold coins each!".

"So, give me those 40 gold coins and we'll call it even. Where are they?", says their master. And you can imagine how "well" things went from there ;-)

Does anyone with a formal education in economics know what's the actual term for this form of apparent paradox?

However, unlike the first sketch, in this case the "circular debt" should be immediately apparent to its participants and is of a much more short term.

[Creaphis]

Technician said:

Yah, you're cutting into Utahraptors territory.

It's alright, fellas. I've been getting lax about it anyway.

[Erik]

Resolving debt indirectly like this is kind of standard procedure with the crowd I socialize with.

[myk]

Maes said:
IMHO, this rises an interesting question: if those persons were all made fully aware of their mutual debts, could they have called it even on those grounds, without even an external factor triggering the events?

There are certainly situations where the answer may be No, if A gains more from having B in debt than for paying up to C, even if the sum is the same. This would break the chain, making a bunch, if not all, of the canceling agreements to go down. Or maybe C could offer to pay B the value of the debt of A and they could try ganging up to kick A out of the partnership :p

In such situations, not all the players have the same means to demand payment from others, which makes equal indebted sums practically uneven.

[Maes]

myk said:

In such situations, not all the players have the same means to demand payment from others, which makes equal indebted sums practically uneven.

Hmm, never thought about that but you are actually right: the original sketch portrayed the various creditors claiming their money on sight and getting them without a second though, having a peer-to-peer relationship and access to each other. In the real world, it's hard to have all debtors/creditors accessible on demand, let alone cooperative on demand regardless of their social status and/or power.

Still, in an ideal world...