Consider three positions:
1. The stock of money is determined by the demand for money, and not by the supply of money.
2. The stock of money is determined both by the demand for money and by the supply of money.
3. The stock of money is determined by the supply of money, and not by the demand for money.
In my last post, I showed that the first (demand only) position was wrong. The central bank's supply function matters too.
Most reasonable economists, who understand the distinction between supply (function or curve) and quantity supplied, who understand that the interest rate target is endogenous with respect to the stock of money, if inflation is to be kept on target, will say that the second position (both demand and supply) is the sensible position to take (unless the central bank has a perfectly inelastic supply function).
But I now want to argue for a more extreme position. I now want to advance deep into enemy territory.
Suppose, just suppose, that the central bank does target an exogenously fixed rate of interest, and ignore the Wicksellian indeterminacy this creates, and ignore the fact that this is incompatible with targeting inflation or anything vaguely sensible. That interest rate target is the central bank's money supply function, and a change in that interest rate target money supply function will cause a change in the stock of money.
Will it be true that the actual stock of money will always be equal to and determined by the quantity of money demanded at that target rate of interest?
Any sensible economist, who accepts the sensible middle-ground of position 2 (both demand and supply) would answer "yes". I will answer "no".
It is hard for me to explain this clearly, so please let me simplify as much as possible.
Let us consolidate the commercial banks and central bank into one big central bank that prints money and lends that money directly to people at a rate of interest it sets. The money itself (think of it as currency) always pays 0% interest, but the bank charges r% on loans of currency.
Ignore risk on loans. Anyone who wants a loan from the central bank can get one, at the rate of interest r, and they never default.
Take the standard assumption that the demand for money (the average stock of money people wish to hold) is a positive function of P and Y, and a negative function of r (the opportunity cost of holding money that pays 0% interest). Md=L(P,Y,r).
In this economy, the (change in) the stock of money is determined by the supply (function) of money (i.e. the rate of interest set by the central bank), and by the demand for loans. It is not determined by the demand for money. P and Y will (eventually) adjust until the quantity of money demanded equals the quantity of money created by the supply (function) for money and the demand for loans. The supply (function) of money, and the demand for loans, together determine the quantity of money created, and that quantity created (eventually) determines the quantity of money demanded.
It should be obvious really. When people borrow money, they (usually) borrow it to spend it; they do not (usually) borrow it to leave it in their pockets. Because money is the medium of exchange.
Take a simple example, just to illustrate my point. Suppose, just suppose, that the demand for money were perfectly interest inelastic. Desired velocity is fixed. So the money demand function is Md=L(P,Y)=PY. (Yes, I know that this assumption is empirically false, but just suppose.) Given this money demand function, the rate of interest set by the central bank has no direct effect on the quantity of money demanded. If the stock of money was determined by the quantity of money demanded, the central bank would be powerless to do anything that would cause the stock of money to increase. Cutting the rate of interest would not work. But we know it will work, provided the quantity of loans demanded depends on the rate of interest. By cutting the rate of interest, the central bank increases the quantity of loans from the central bank, which creates more money. Eventually P and/or Y will increase and the quantity of money demanded will increase in proportion to the quantity created.
The supply of money determines the quantity demanded, and not vice versa. Even with a perfectly interest-elastic supply function, at an exogenously fixed rate of interest. Money is weird like that. The medium of exchange is not like other assets.