Betteridge's Law of Headlines Strikes again!

(first attempt at an R1 and wanted to try something a little bit different than normal, but still incredibly low hanging fruit. Let me know how to improve on it)

There are numerous sources out there that claim that there is a mathematical impossibility of paying off the total debt. Depending on the numbers they want to create, they’ll do anything from total governmental debt, to total debt of US government + businesses + personal, or just to be fun, they’ll use numbers including total notional derivatives value and get lovely numbers in the quadrillions. As a nice illustrative example of how widely this belief is held, I’ll use an illustration from one of the most esteemed and widely respected economics blogs in the world today*.

The point often revolves a couple key arguments. Primarily, interest makes it impossible. As the story goes, if the bank loans out $100 and charges $25 dollars in interest, in aggregate there will be no way for there to be enough money to pay back these loans. This leads to a system where debt is either inflated away or a giant debt bubble is fueled before bursting in a spectacular extravaganza of chaos where gold and lead reign supreme as money.

So, there’s a couple of problems with this line of thought. Firstly, there’s no need for aggregate debt to be paid off, government or otherwise. Nothing indicates that would have to be done. But that’s been hashed many times before. Governments aren’t households, debt serviceability is the more important metric, yada yada yada.

But these claims are stronger, that it is impossible for this debt to be repaid. In the Zero Hedge article there’s a large discussion of which version of money you use, but of course it doesn’t matter there’s not enough of it. The answer is simple, repaying debt doesn’t necessarily extinguish money, and though it certainly can it is not true for all debts and all money. Using a simple contrived model, I will show that that is not the case, that you don’t need an equal amount of money to pay off debt.

Let’s say 3 people, Alice, Bob, and Carol get stranded on an island. They all agree on the value of the US dollar, as they expect to get rescued and return to civilization where it is accepted. Bob’s wallet stayed with him during this ordeal, so he is the only one with money on the island. This is the only asset that exists on the island to start (besides of course human capital and undeveloped natural resources).

Alice wants to start a coconut water business, so borrows $100 from Bob and has to repay $150 at the end of 2 weeks. Alice uses the money to pay Carol to make a sharp rock tool to open the coconuts while Alice goes and collects coconuts. Alice comes back, opens the coconuts, and Carol buys 1/3 of the total for $100. Alice repays Bob $100 of the $150, and Bob summarily buys $50 worth of coconuts from Alice, who immediately finishes repaying the loan. In this, we went from a starting balance of $100 to ending with an ending balance of $100 (no debt), lots of coconuts, and a sharp rock tool. We’ve made assets, and even with interest it was possible to pay back the loan.

To be clear, in the short model above you don’t have to use USD, you could use kruggerands or rope vines, or really any asset of your choice, the model would work just as well. It would be easy to construct a model where you didn't have to do partial repayments but it would require a second source of money, but the analogy to a fractional reserve banking conspiracy theory is closer this way so I stuck with it (given that fractional reserve banking is usually tied up in these theories, even despite the fact that it isn't usually the best way of modelling it)

Now, there’s nothing to say that this is an example of how the world works. The world, and particularly the world of finance is significantly more complicated than this. But this should (hopefully) provide a simple model to show that just because the debts exceed the currency in circulation (or some broader measure of monetary base) there’s nothing mathematically impossible about repaying all the debt. The ultimate reason for that is due to the fact that money isn’t necessarily extinguished by debt and upon repaying debt can be further circulated in the economy.

*To be clear, Zero Hedge’s only serves two purposes: source of amazing conspiracy theories and hastening the heat death of the universe