You may think that the Fed, the central bank of the U.S., has complete control, or at least some control of how many banknotes circulate in the economy. The fact is that the Fed has no power in this.

Banknotes enter in circulation anytime you request a teller machine to supply cash.  The machine debits your bank account and gives you cash.  Banknotes will disappear from circulation anytime someone decides to get rid of cash and deposits it in a bank.

Banks make sure they have an inventory of banknotes to accommodate any net withdrawals of banknotes. When they feel their inventory is excessive they send some banknotes back to the central bank (that will shred them). When they feel their inventory is short of their clients’ needs, banks have extra banknotes sent by the central bank (that will debit the bank’s account at the Fed—If the bank’s account balance is zero, the bank will borrow reserves and then have its account debited). Banknotes could completely disappear from the economy if only everyone felt that all payments could be handled through bank (or credit card) payments. This way, the amount of banknotes in the economy would endogenously go to zero with no decision of the Fed. On the other end of the spectrum, how large the amount of banknotes could go if only everyone decided to increase the use of cash? Very high indeed. But with a limit: when the willingness to hold banknotes is driven by a generalized loss of confidence in bank accounts, the process of conversion from accounts to banknotes could either a) continue until all bank accounts are converted into cash if the central bank decides to lend reserves to all banks (and if the central bank printing press is fast enough to keep pace with the requests) until people calm down and deposit their banknotes back into the banking system; or b) stop when banks fail and lose access to reserves; or c) stop when banks decide to refuse conversion to protect their liquidity; or d) stop when the central bank declares a bank holiday awaiting to restore confidence in the banking system. In no way, it is the Fed that decides the amount of banknotes in circulation.