# Is money’s value inversely proportional to how much there is?

Last time in this series, we considered the effect of halving the number of New Zealand Dollars, and halving every NZD-denominated debt. In particular, would this double the value of the dollar? It didn’t seem tenable that it wouldn’t at least have the tendency to double the value of the dollar, although stickiness and other constraints may work against that tendency.

So if we accept that halving the stock of money, and all the money-denominated debts, has the tendency to double the value of money, then we might wonder whether both debt-halving and money-halving are necessary. So today, let’s consider the situation where we just halve the stock of money (in circulation and in hoards and stockpiles), without halving everyone’s debts. Would this on its own be enough to double the value of the dollar?

Actually, let’s be a little more precise. Is the value of the dollar inversely proportional to the number of dollars in existence? That is, if everyone keeps only one $n$th of the dollars they have, does the value of the dollar multiply by $n$? Or if everyone is given more money so that they all have $n$ times as many dollars as they started with, does the value of the dollar drop to $\frac{1}{n}$ times what it was?

Suppose that that was true.

According to the Reserve Bank, as of December 2012, there’s $5,052,000,000 in circulation. But banks have claims on the Reserve Bank amounting to$6,946,000,000; since the Reserve Bank is (I assume) able to print money to satisfy claims against itself, I’ll assume that these claims are as good as money in circulation. That’s $11,998,000,000 in existence, for our purposes. Let’s call it$12 billion.

The Reserve Bank surveys a number of “M3 institutions”, which I think are banks. Among other things, they count the amount of “M3 money”. They say:

M3 is the broadest monetary aggregate. It represents all New Zealand dollar funding of M3 institutions and any Reserve Bank repos with non-M3 institutions. M3 consists of notes & coin held by the public plus NZ dollar funding minus inter-M3 institutional claims and minus central government deposits.

(Roughly speaking, M1 money is money in circulation, plus chequable deposits; M2 money is all this, plus on-call deposits.) The amount of M3 money is (as of December 2012) $253,611,000,000. Now suppose that there’s a coalition of people who have net claims to$12.5 billion of this M3 money, which is less than 5% of all M3 money. They agree to withdraw (gradually, if necessary) $6 billion of these claims, and permanently take that money out of circulation. According to our hypothesis, that the value of money is inversely proportional to how much exists, this would double the value of the dollar. This means that the$6.5 billion of claims that the coalition still holds are now worth what $13 billion used to be worth. So the coalition has made a profit by throwing money away. If our hypothesis is correct, then we need to explain why we don’t see people trying to form such coalitions, to profit from throwing money away. One possible explanation is that, because everyone outside the coalition profits much more than those inside the coalition, everyone will want to be a free-rider, and will refuse to join the coalition, so no coalition will be possible. But even without arguing that the non-existence of such coalitions is evidence against our hypothesis, we can continue the thought experiment, and see that it leads to even greater absurdities. If, instead of taking only$6 billion out of circulation, the coalition takes $11 billion out of circulation, then according to our hypothesis, a dollar will end up being worth 12 times what it used to be worth. So the$1.5 billion of claims the coalition still has are now worth what $18 billion used to be worth. By throwing away more money, the coalition profits even more. There’s no reason to stop there. The coalition can keep profiting by throwing away more and more money, until none is left, and their remaining claim to$500 million of non-existent money is infinitely valuable.

This is clearly absurd, so our hypothesis must be incorrect. It must be the case that although halving all the debts and money would double the value of money, halving all the money on its own won’t always have the full effect.

So we must conclude that debts are part of what determines the value of a fiat currency.

Stay tuned for more on what this means.