# Money Multiplier

Money multiplier (also known as monetary multiplier) represents the maximum extent to which the money supply is affected by any change in the amount of deposits. It equals ratio of increase or decrease in money supply to the corresponding increase and decrease in deposits.

## Money multiplier effect

The money multiplier effect arises due to the phenomenon of credit creation. When a commercial bank receives an amount A, its total reserves are increased. The bank is required by the central bank to hold only an amount equal to r × A in hand to meet the demand for withdrawals, where r is the required reserve ratio. The bank is allowed to extend the excess reserves i.e. (A − r × A) as loans. When the borrower keeps the whole amount of loan in bank (it is assumed), it increases its total reserves by an amount equal to (A − r × A). Again, the bank is required to hold only a fraction of this second round of deposits and it can lend out the rest. This cycle continues such the ultimate increase in money supply due to an initial increase in checking deposits of amount A is equal to m × A, where m is the money multiplier. The opposite happens in case of a decrease in deposits through the same mechanism.

## Formula

 Money Multiplier = 1 Required Reserve Ratio

Required reserve ratio is the fraction of deposits which a bank is required to hold in hand. It can lend out an amount equals to excess reserves which equals (1 − required reserves).

Higher the required reserve ratio, lesser the excess reserves, lesser the banks can lend as loans, and lower the money multiplier. Lower the required reserve ratio, higher the excess reserves, more the banks can lend, and higher is the money multiplier.

In the above relationship it is assumed that there is no currency drainage, i.e. the borrowers keep 100% of the amount received in banks.

## Currency drainage

In reality, borrowers do keep a fraction of loans received in cash. This reduces the money multiplier. When there is some currency drainage, money multiplier is calculated as per following formula:

$$Money\ Multiplier\ (Currency\ Drainage)\\=\frac{1 + Drainage\ Ratio}{Required\ Reserve\ Ratio + Drainage\ Ratio}$$

 Money multiplier when there is currency drainage= 1 + drainage ratio required reserve ratio + drainage ratio

## Examples

### Example 1

Ishkebar is an alien country that has seen little financial innovation. Its central bank requires commercial banks to keep 100% of their deposits as reserves. Calculate money multiplier for the economy.

Money multiplier = 1/required reserve ratio = 1/100% = 1

The country has a money multiplier of 1. No money creation is possible because in response to an increase in bank deposits of say 100 million Ishkebar dollars (I$), the money supply will increase by 1 × I$100 million = I\$100 million.

### Example 2

North Sarrawak is run by a dictator who knows no economics and is not willing to listen to any advice. He thinks he can always print money whenever a depositor wants to withdraw so he does not think having any required reserve ratio for the sole bank of the country is necessary. What could be the consequences?

Zero required reserve ratio means infinite money multiplier and infinite money creation. Infinite money creation means no scarcity of money which means money would no longer be money since it would no longer be a store of value.

### Example 3

Palmolive has required reserve ratio of 30% and a currency drainage of 15%. Calculate the money multiplier and compare it with Parazuela, a country where drainage is zero and required reserve ratio is 30%.

Money multiplier in Palmolive = (1 + 15%) ÷ (30% + 15%) = 2.56

Money multiplier in Parazuela = 1/30% = 3.33

Parazuel has higher money multiplier which makes sense because it has zero drainage. Zero drainage means all of the excess reserves loaned out in round 1 form part of total reserves in round 2.