It Isn’t the Face Value that Determines How Much Each Type of Paper Currency is Worth. To see this role of a central bank clearly, consider a case where not only direct access to the central bank, but access to the banking system in general is problematic: the criminal underworld. Think of the standard scene in American mob movies in which the mobster demands a suitcase full of cash in tens and twenties. Why tens and twenties? Using the banking system often increases the chance that a criminal will get caught. Money can be laundered, but it is easier to launder tens and twenties. So, at least near the point of money laundering, ten ten-dollar bills are worth more than one hard-to-launder hundred-dollar bill. That means that if you bring me a suitcase full of one-hundred dollar bills with the same face value as a suitcase full of tens and twenties, you are bringing me less value—you have cheated me.
I was intrigued to read in the Economist article “High-denomination banknotes: Cash talk” about the exchange rate between different denominations when transportation is the immediate issue rather than laundering:
A report from Europol recounts how criminals will sometimes pay more than face value for high-value notes because of how convenient they are to transport.
This is one more example showing that it is not the face value that determines the relative price of different forms of money, but the rate at which they can be exchanged, whether at the cash window of the central bank, at a private bank or in the relevant market. For central banks, the possibility of modifying the exchange rate between different denominations is not particularly important, but the possibility of modifying the exchange rate between paper currency and electronic money is very important because it makes it easy to generate a negative rate of return on paper currency to match negative interest rates in bank accounts, and thereby eliminate any effective lower bound for interest rates.