Money Multiplier Formula

The phenomenon in which money is created in the form of the creation of credits in the economy is referred to as the money multiplier and is based on the fractional reserve banking system. 

This is sometimes also known as the monetary multiplier. It is defined as the maximum limit to which the money supply is affected as there are changes in the amount of money deposited. This money multiplier effect is most commonly seen in commercial banks since deposits are accepted by them and after a while, they have kept the money as a reserve, to inject liquidity in the economy, they start distributing the money as loans.

The Reserve ratio is referred to as the total amount of money, for the withdrawal purposes by the customers, which should be kept by the commercial banks in their reserves. It is also known as the cash reserve ratio or the required reserve ratio.

Money Multiplier- Formula

The money multiplier effect is expressed in mathematical terms as-

Money Multiplier=\[\frac{1}{r}\]

where the required reserve ratio or the cash reserve ratio is represented by r which is described as the minimum ratio that is required legally for the commercial banks of the economy to keep the deposit with themselves. This also applies to the central bank of India which is the RBI.

The deposit creation by a commercial bank 

Money Multiplier- Example

Till the time the total deposits become equal to Rs. 1000, total loans lent become 900, and the total cash reserve becomes Rs. 100, the rounds following round 5 will be continued in the same manner.

More About the Money Multiplier Formula

The creation of the money supply is done by the banks through the deposits they receive and keeping a certain amount as reserves and thus using the rest of the amount for lending purposes. Money Multiplier in simple words is considered as the largest amount of money that can be created through this kind of banking. In this article, we will learn about this concept. We will learn the credit multiplier formula or deposit multiplier formula, its example, etc. which will help us to understand this concept clearly which plays a great role in the monetary policy of the Central Bank or we can say in the banking system of the economy.

Money Multiplier

The money multiplier is a concept which measures the amount of money created by banks with the help of deposits after excluding the amount set for reserves from the deposits. It tells the maximum number of times the amount will be increased with respect to the given change in the deposits. The money multiplier has an inverse relationship with the Legal Reserve Ratio (LRR). LRR refers to the number of deposits that the banks are required to keep with them as reserves all the time, to meet the uncertainties, and also to maintain the trust of the public. There are two types of reserves that the banks are required to maintain: 

1. Cash reserves ratio (CRR), the reserves which the banks have to maintain with the central bank. 

2. Statutory Liquidity ratio (SLR), which shows the number of reserves that the banks are required to maintain in the form of liquid assets with themselves. The simple money multiplier formula works as a great tool in the monetary economy for the Central Bank to control the money creation because it works as a total money supply formula that is used for calculating money supply.

Money Multiplier Formula 

Money multiplier =\[\frac{\text{1}}{\text {Reserve Ratio}}\]

Money multiplier = 1 ÷ LRR

Where LRR = Legal Reserve Requirements

Money Multiplier Equation

Money Multiplier =\[\frac{\Delta \text{ In Total Money Supply}}{\Delta \text{ In the Monetary Base}}\]

It is also known as the credit multiplier formula. The higher the LRR leads to a lower money multiplier because the commercial banks will have to maintain the larger reserves due to which there will be less amount available to lend to the public.

Example

Suppose an initial deposit of ₹10,000 is made into the bank. The Legal Reserve Ratio (LRR), which has to be maintained by the commercial banks, is 20%. All the payments and deposits are done through the bank. The banks keep only the minimum balance of LRR and lend the rest of the money to the public.

Solution: Money multiplier Formula = 1÷ LRR

Money multiplier = 1÷ 20%

Money multiplier = (1÷0.20) * 100

Money multiplier = 5 times

It shows that the initial deposit of ₹10,000 will be increased up to 5 times excluding the reserves.

The following table will explain the process:

Explanation

The initial deposits of ₹10,000 have been made into the bank, and the banks are required to maintain 20% of the deposits with them as the LRR is 20%, therefore the bank has to maintain 20% of ₹10,000 i.e. ₹2,000 with itself and can lend the rest of the money i.e. ₹8,000 as loans to the public. As all the payments are done through the banks, therefore the amount of ₹8,000 comes again to the bank and the bank will keep 20% of this amount i.e. ₹1,600 with itself, and will lend again the rest of the amount i.e. ₹6,400 to the public. This process will go again and again till the time the value of deposits doesn't become ₹50,000. As the value of the money multiplier is 5, it means the value of initial deposits of ₹10,000 will become ₹50,000 till the end. This process will continue till the initial deposits increase to ₹50,000.

Additional Information

Deposit Multiplier Formula: Mostly "deposit multiplier" as well as "money multiplier" terms are often confused with and are also used interchangeably. These both are very closely related and thus the distinction between them can become very difficult to grasp. 

• This deposit multiplier is also called the "deposit expansion multiplier".

• It is the basic process of money supply creation that is determined by the fractional reserve banking system. 

• Banks create checkable deposits as they loan out their reserves. 

• The reserve requirement ratio of the bank helps to determine how much money is available to loan out and hence the amount of these created deposits. 

• It is then the ratio of the amount of the checkable deposits and the amount of reserve. It is also considered as the inverse of the reserve requirement ratio ( RRR).

• This multiplier actually provides the basis for the money multiplier but on the other hand, if we talk about money multiplier, here due to various factors such as excess reserves, savings, and conversions to cash by the consumers, the value of money multiplier is ultimately less.

• The simple deposit multiplier formula is given below:

Deposit Multiplier =\[\frac{1}{\text{Required Reserve Ratio}}\]

Conclusion

Thus, to sum up, in the end, the money multiplier is one of the closely related ratios of commercial bank money under a fractional-reserve banking system in monetary economics or macroeconomics. It is simply related to the maximum amount of money that can be created. The Fractional-reserve banking system has legal reserve requirements and the total amount of loans is equal to a multiple of the amount of reserves. The money multiplier formula is also known as the credit multiplier formula and sometimes it is often used as a deposit multiplier formula as well which provides the base to it. The formula is said to be the inverse of the Legal reserve ratio.