Scott Sumner recently issued a paper called "A Market-Driven Nominal GDP Targeting Regime." In it he comments that
it is not clear that the preceding five economists [Milton Friedman, Bennett McCallum, Robert Mundell, Robert Hall, and Michael Woodford] would even agree on what is meant by the term "monetary policy." Friedman and McCallum might argue that monetary policy is all about control of the quantity of money, however defined. Mundell and Hall might argue that monetary policy determines the price of money (in terms of foreign exchange, or gold, or a basket of commodities.) Woodford might see monetary policy in terms of changes in the rental cost of money (i.e., short-term interest rates). The quantity, price, and rental-cost approaches to policy have all been around for hundreds of years. And both the short-run sticky-price and long-run classical frameworks go back at least to David Hume. These differences of opinion will not be resolved anytime soon.
Here is my proposed solution: Monetary theory is about how the nominal supply of money adjusts to the real demand for money. Monetary policy is about the best way for the adjustment to happen.
Briefly, there is a demand to hold a certain amount of purchasing power as money, both in the narrow sense of the monetary base and in the broader sense of various credit aggregates. The demand is clearly not purely nominal. When currency redenominations happen and 1 new peso is made equal to 1,000 old pesos, people who kept 100,000 old pesos in their wallets will rarely try to keep 100,000 new pesos in their wallets. The demand for money is in a certain sense "fuzzier" than demand for many other goods, though, because of money's function as a store of value. If somebody were to give me a ton of apples, I would try to get rid of them immediately. I have all the apples I need right now and I don't need a ton rotting on my hands. If, however, somebody were to give me the equivalent value in money, which let us assume is $800, I might hold onto part or all of it for quite a while before spending it.
The nominal supply of money can adjust to the real demand for money through price, quantity, or quality. A frozen monetary base is an example of price adjustment: the monetary base does not change and the purchasing power of each unit adjusts. A gold standard is an example of quantity adjustment: the purchasing power of each unit is fairly stable and the quantity of units in existence adjusts. A change in exchange controls is an example of quality adjustment: tightening exchange controls when the real demand for money falls makes each unit of money less useful, reducing the quality-adjusted supply.
I think that the five economists Sumner mentions, and many others as well, would agree with my suggestion that they are trying to figure out the best way for the nominal supply of money to adjust to the real demand. Where they differ is in their proposed solutions: freezing the monetary base? Adopting a gold standard? Targeting short-term interest rates? Manipulating exchange controls? Targeting nominal GDP? One of the many other policies imaginable? Proponents of free banking would argue that discussions about "the best" policy imply a degree of knowledge that we do not in fact have, and that the pressing need is to let competing approaches work themselves out in the market so that we can discover what is best.