Money Multiplier

Money is primarily used to quantitatively measure the value of goods or services and supply of money plays an important role in the determination of inflation and interest rates.

As the name suggests, money multiplier means ‘some’ supply of money creates a multiplier effect. Let’s see it in detail.

Now let’s say there is a country called “Gokul Dham” and this country has infinite banks and infinite population but one central bank and the central bank has deposited Rs 100 in one bank named Bank#1. We know that all the deposits in the bank are the bank's liability since they are obliged to give it back to the depositors at some point in time and loans are the bank's asset. Let’s consider for the sake of understanding that the Cash Reserve Ratio is 10%. Cash Reserve ratio (CRR) is the proportion of money that banks are asked by the RBI to keep with themselves i.e they have to maintain some cash reserve with themselves and can’t loan all the money they have.

Bank#1 can now loan Rs 90 out of Rs 100 from its asset side given the CRR is 10%. This loan is given to Jethalal and Jethalal deposits this Rs 90 to another bank Bank#2 and that bank now has loaned Rs 81 (CRR =10%) to some other person, say Bhide and this process keeps on continuing. 

Representing the above situation in tabular format.

High Powered Money	Deposits	Loans (Asset)	CRR (10%)
Bank#1	100	90	10
Bank#2	90	81	9
Bank#3	81	72.9	8.1
Bank#4	72.9	65.61	7.29
………	…………	………	……….
………	………..	…………..	………..
Bank#infinity	…………….	……………	………….

The total deposits with all the banks cumulative is 100+90+81+72.9 + …….., the series goes on till infinity. So, applying the geometric progression summation formula we get the total sum = a/(1-r) = 1000, where a = 100, r = 90/100

The money initially infused in the economy was Rs 100. 

The total bank’s deposits are Rs 1000 i.e 10 times more than the initial infused money, Rs 100. 

Hence the high powered money, initially infused money Rs 100 creates an impact of Rs 1000, hence the money multiplier is 10.

Money multiplier = Stock of total money (M3)/ Stock of high powered money(M0).

M0 = Money issued by central bank

M3 = Currency in circulation + Demand deposits in commercial banks (savings/current account) + time deposits in commercial banks (Fixed deposits/Recurring deposits etc.)

 

What if we only have 4 banks in the economy, the money multiplier would have been = (100+90+81+72.9) / 100 = 3.439

Since, in the above example we consider infinite banks so the money multiplier 10 obtained is the maximum.

The exercise demonstrates that the more the banking habits of the population, financial inclusion and penetration of banks more is the money multiplier effect.