As we saw last Thursday, at the point at which the government can no longer collect taxes nor emit bills of credit to pay its bills, the value of all currency backed by government promises falls effectively to zero. The question is, what happens then?
To answer that, let's take the Quantity Theory of Money equation developed by Irving Fisher, M x V = P x Q. M is the money supply, V is the average number of times each unit of currency is spent in a year (the "velocity" of money), P is the price level, and Q is the number of transactions in the economy.
Now ask yourself: How many transactions are going to take place when the value of M is zero? That's right — none. Absent coercion, no sane person is going to sell you anything in exchange for something he or she believes is worthless. Why would anybody sell you anything for worthless "money"?
Another question: what happens to the price level when M = 0?
First, let's be realistic. The value of a paper or token fiat currency is never absolutely zero. It still has value as waste paper, kindling, or even toilet tissue. The value may be virtually infinitesimal, but it's there . . . somewhere. There just won't be any "money transactions" — restricting the meaning of "money" to government currency or substitutes, such as demand deposits. Q goes to zero.
To derive P (the price level), then, we divide M x V by Q, which gives us P = (M x V)/Q.
What did we learn in freshman algebra, however? That's right: you can't divide by zero. It's an irrational number. It doesn't mean anything. When the currency loses its value (i.e., the government can't tax the private sector to make good on its debt paper), the price level becomes . . . irrational, that is, it ceases to make sense.
In ordinary demand-pull inflation, the price level reacts to the quantity of money created. As more money is printed, the price level increases. If the money supply is decreased (deflation), the price level decreases. When M (and thus Q) falls effectively to zero, however, the amount of money becomes irrelevant. At the same time, V goes through the roof as people rush to spend money as fast as they possibly can before it loses even the infinitesimal value it might still retain, or even trade it as waste paper (as a barter item, not as currency) for something of value. The price level, P, approaches infinity — how many times can you divide a number, no matter how small, by zero? As many times as you like — it doesn't mean anything.
This is "hyperinflation." Prices go up at a tremendous rate because the unit in which the prices are measured has no meaning.
The question becomes what to do about it.