Monopoly over their money supply by the nations of the world is currently conducted in a money market. A market by definition is where something, including money, is bought and sold. The price of money is the rate of interest.
When central banks buy and sell money in exchange for government debt, as is currently universally the case around the world, they set the base interest rate based on the economic demand for money. This rate cascades along the value chain setting all other interest rates for the various financial products in the financial markets.
The way central banks set the rate can be operationally accomplished in many ways. The two most common approaches were: one, to simply inject money by buying government debt or to take it back to the burn bin by selling government debt. Paul Volcker’s disinflation had adopted this approach and the markets freely determined the rate of interest; two, the minimum balances the banks must maintain in their central bank accounts are raised and lowered by fiat. China still follows this reserve management approach.
The third approach is to target a specific rate, also by fiat, in a market for money that banks must maintain in their central bank accounts. Because the central bank targets the ex ante determined rate, it must supply or withdraw money by buying or selling government debt accordingly to maintain that rate. The United States calls this approach that it adopted since Alan Greenspan became the Chairman of the Fed the federal funds market.
In principle, there is no reason why any government that issues money by decree must buy or sell anything to issue it or take it back. The same decree that gives central banks the authority under law to issue and take back money can also permit them to do so without a market for that money. Both the rate of interest and money supply can be determined by fiat. The central banks then would be out of the market for financial instruments completely, true to the spirit of free markets, whether that be for government bonds or other types of financial assets, contrary to them being the elephants on the trading floors in today’s financial markets.
This approach combines rate setting by fiat with quantity changes of money in the market also by fiat. The central banks can then determine the base market rate to target. It could be the prime rate of borrowing. Financial institutions can be asked to return the funds when the central bank believes that there is excess money or supply more when the central bank thinks that there is a deficit, holding no other financial assets on its balance sheet.
This could mean that central bank operational budgets can no longer be financed by their monetary operations besides of course collecting fees for some of their activities such as for facilitating centralized payment systems. And this could be a good thing because it eliminates the potential conflict of interest in monetary policy by preventing central banks from manipulating policy to raise their incomes from their operations to expand their bureaucracies.