[jmherbener]

Rothbard is notable among economists for rejecting the “money in circulation” view and adopting the demand to hold money view. In this he follows Ludwig von Mises. They both claim that the entire stock of money is in someone’s cash balance or money holding at all times. The purchasing power of money is therefore determined in the same way as the price of other goods, namely, by the size of its stock and the total demand people have to hold it. Rothbard and Mises, then, reject the quantity theory approach, with its reliance on the concept of the velocity of money in circulation, to determining money’s purchasing power.

In chapter five, Rothbard, again following Mises, divides total demand for money into exchange demand, the demand people have to add to their existing money holdings, and reservation demand, the demand people have to hold onto their existing money holdings. But he does not use the concept of money in circulation when referring to people’s demand to hold money.

He uses the term “circulation” when referring to the use of money as a medium of exchange, but in this use he is not defining a concept for analysis. For example on page 58 he writes, “Government paper money, on the other hand, can decline…if inflation or loss of confidence causes it to depreciate or disappear from circulation.” Here “circulation” is synonymous with “use as a medium of exchange.”

In chapter seven on Deposit Banking Rothbard writes (p. 86), “Suppose, for example, that the initial money supply, when money is only god, is $100 million. Suppose now that $80 million in gold is deposited in deposit banks, and the warehouse receipts are now used as proxies, as substitutes, for gold. In the meanwhile, $20 million in gold coin and bullion are left outside the banking system in circulation.” Rothbard is again using the term to refer to money proper used as a medium of exchange, but in this case as distinguished from money proper used as reserves by banks against their money substitutes.

I presume in the quote you cite that Rothbard is making the same distinction. If so, then the ratio is the ratio of money proper to money substitutes. As Rothbard argues, (see p. 96) people determine in what form they will hold the medium of exchange, either as money or as money substitutes. But regardless of its form, the entire stock of the media of exchange is held by people in the money holdings.