5.8: Fractional-Reserve Banking II

Fractional-reserve banking is a system in which banks are required to hold only a portion of their deposits as reserves, while the rest can be loaned out. Even if a bank lends from a deposit, the bank still owes the full deposit amount to its lenders. So, the original deposit remains a liability on the bank’s balance sheet. The bank’s assets include its reserves and the loans it makes.

As loans are made and re-deposited into other banks, this creates a cycle in which each bank lends a portion of the received deposits while retaining the rest as reserves.

This repeating process causes the money supply in the economy to expand beyond the amount of the original deposit. For example, if a bank lends out a portion of its funds and the recipient deposits this loan into another bank, the second bank also retains a fraction of the deposit as reserves and lends out the remainder. If this cycle continues across multiple banks, the cumulative effect can significantly increase the total amount of money supply in the economy.

The extent of this expansion depends on the reserve-deposit ratio—the percentage of deposits that banks are required to keep as reserves. A smaller reserve ratio results in a larger potential increase in the money supply. The formula used to calculate the total money supply generated by an initial deposit is the amount of the initial deposit multiplied by the reciprocal of the reserve-deposit ratio. For instance, if the initial deposit is one hundred dollars and the reserve ratio is ten percent, the total money supply grows to one thousand dollars. This model helps explain how money is created, but it is simplified and does not explain the complexities involved in real life.

In fractional-reserve banking, banks hold a portion of their deposits as reserves and lend the rest.

Recall the hypothetical economy where Bank A lent $90 out of its $100 deposits. Bank B keeps nine dollars as reserves and lends out eighty-one dollars of new loans.

This process of lending and redepositing continues across multiple banks.

In our example, the reserve-deposit ratio is ten percent.

The formula to calculate the change in the total money supply is:

Initial change in reserves × (1 / reserve-deposit ratio). The initial change in reserves represents a new injection of reserves into the banking system.

In this case, the initial change in reserves is $100, and the reserve-deposit ratio is ten percent. So, the change in the total money supply is $1,000. The expression, 1 divided by the reserve-deposit ratio, is known as the simple money multiplier. It tells us the maximum amount the money supply can increase for each dollar of new reserves.