## USING THE MONEY MULTIPLIER FORMULA

In a system with multiple banks, the initial excess reserve amount that Singleton Bank decided to lend to Hank’s Auto Supply was deposited into First National Bank, which is free to loan out $8.1 million. If all banks loan out their excess reserves, the money supply will expand. In a multi-bank system, the amount of money that the system can create is found by using the money multiplier. The money multiplier tells us by how many times a loan will be “multiplied” as it is spent in the economy and then re-deposited in other banks. Fortunately, a formula exists for calculating the total of these many rounds of lending in a banking system. The money multiplier formula is: $\displaystyle\frac{1}{\text{Reserve Requirement}}$ The money multiplier is then multiplied by the change in excess reserves to determine the total amount of M1 money supply created in the banking system. Using the money multiplier for the example in this text: Step 1. In the case of Singleton Bank, for whom the reserve requirement is 10% (or 0.10), the money multiplier is 1 divided by .10, which is equal to 10. Step 2. We have identified that the excess reserves are$9 million, so, using the formula we can determine the total change in the M1 money supply:

$\displaystyle\text{Total change in the M1 Money Supply}=\frac{1}{\text{Reserve Requirement}}\times\text{Excess Requirement}$

$\displaystyle\text{Total change in the M1 Money Supply}=\frac{1}{0.10}\times{9}\text{ million}$

$\displaystyle\text{Total change in the M1 Money Supply}=10\times{9}\text{ million}$

$\displaystyle\text{Total change in the M1 Money Supply}=90\text{ million}$

Step 3. Thus, we can say that, in this example, the total quantity of money generated in this economy after all rounds of lending are completed will be \$90 million.

## Cautions about the Money Multiplier

The money multiplier will depend on the proportion of reserves that banks are required to hold by the Federal Reserve Bank. Additionally, a bank can also choose to hold extra reserves. Banks may decide to vary how much they hold in reserves for two reasons: macroeconomic conditions and government rules. When an economy is in recession, banks are likely to hold a higher proportion of reserves because they fear that loans are less likely to be repaid when the economy is slow. The Federal Reserve may also raise or lower the required reserves held by banks as a policy move to affect the quantity of money in an economy, as Monetary Policy and Bank Regulation will discuss.

The process of how banks create money shows how the quantity of money in an economy is closely linked to the quantity of lending or credit in the economy. Indeed, all of the money in the economy, except for the original reserves, is a result of bank loans that are re-deposited and loaned out, again, and again.

Finally, the money multiplier depends on people re-depositing the money that they receive in the banking system. If people instead store their cash in safe-deposit boxes or in shoeboxes hidden in their closets, then banks cannot recirculate the money in the form of loans. Indeed, central banks have an incentive to assure that bank deposits are safe because if people worry that they may lose their bank deposits, they may start holding more money in cash, instead of depositing it in banks, and the quantity of loans in an economy will decline. Low-income countries have what economists sometimes refer to as “mattress savings,” or money that people are hiding in their homes because they do not trust banks. When mattress savings in an economy are substantial, banks cannot lend out those funds and the money multiplier cannot operate as effectively. The overall quantity of money and loans in such an economy will decline.