The goal of monetary policy is monetary equilibrium. This is true for any monetary arrangement that claims to serve a general interest among the population rather than to simply divert wealth to the ruler and his cronies.
Monetary equilibrium is a situation where the supply of money equals the demand, given a particular constellation of prices. The supply of money includes both the monetary base and various forms of credit. In monetary equilibrium, the monetary system is doing the most it can to facilitate beneficial trades. An excess supply of money induces people to make some trades that market participants will later judge not to have been beneficial. A deficient supply of money hinders people from making some beneficial trades.
Under free banking (so the argument goes), the profit motive guides banks toward monetary equilibrium. The way it has done so in historical cases of free banking is through the clearing system. The clearing system is where the supply and demand for credit meet. If a bank, or other credit-issuing institution, has issued a greater supply of credit than people are willing to hold, it experiences losses of reserves. Losses of reserves lead to monetary losses, because liquidating assets may involve selling them at a loss. On the other hand, if a bank or other credit-issuing institution is issuing less credit than people are willing to hold, it is missing an opportunity to make a profit. Other banks, if sufficiently alert, will seek to fill the gap and capture the profits for themselves.
Profit cannot guide central banks toward monetary equilibrium in the same way. By design, central banks have no direct competition. The result is that when a central bank issues an excess supply of the monetary base, under a rigid exchange rate it does not lose reserves as quickly as free banks would, because it loses reserves only from transactions connected with foreign trade, not also with those connected with domestic transactions as free banks would. Under a floating exchange rate the central bank is not subject to the competition in terms of quality that free banks would presumably offer. (Here one must be a bit speculative because as far as I know there has never been a historical free banking system where each bank’s issue constituted a distinct floating currency.)
When a central bank issues a deficient supply of the monetary base, the field is not open to rivals who have the incentive to fill the gap because it will earn them profits.
Because central banks cannot rely on profit to guide them toward monetary equilibrium, they need to find other indicators. Economists have devoted much thought to what indicators central banks should use, but have rarely acknowledged that what they are doing is devising substitutes for profit and loss signals. Moreover, there is not much work in the area that capably bridges theory and practice. The best book I know is Manuel Johnson and Robert Keleher’s Monetary Policy, a Market Price Approach (2001; $125 new, so try looking for it used), which explicitly uses the idea of monetary equilibrium as a guide.
It is widely understood that central banks can make large monopoly profits by issuing a grossly excessive supply of the monetary base and inducing high inflation. That is the rationale for pegged exchange rates, inflation targeting, and other ideas for restraining central banks’ discretionary powers. What is not so widely understood is the other side of monopoly: central banks have less incentive than free banks to avoid a deficient supply of money that leads to deflation. Unlike free banks, they do not lose market share or suffer the threat of absorption by rivals if they issue too little. They receive political criticism, but often can successfully deflect it because monetary policy is a technical subject.
ADDENDUM: Scott Sumner (see this post on his blog for his worldview) and several other economists advocate that central banks, at least in large economies, should target nominal gross domestic product and use a market in nominal GDP futures to guide how they achieve the target. Among the other economists are some who have been influenced by the idea of free banking, including Bill Woolsey, David Glasner, and David Beckworth. George Selgin and Steve Hanke also think nominal GDP targeting would get central banks closer to monetary equilibrium than the policies they have actually followed. So, for thinking about how guide central bank activity without the profit and loss signals that competition would generate, this is a well developed idea, even though it has not yet been elaborated at book length. Compared to inflation targeting, currently the standard practice for many central banks, nominal GDP targeting implies lower inflation rates or even deflation during periods of fast growth, and higher rates during periods of slow growth or recession.