Money multiplier theory of money supply

Money multiplier theory of money supply

Money multiplier theory of money supply

Money multiplier theory of money supply is one of the most vital topics in macro economics theories. Before going to multiplier theory we are discussing about money supply.

The supply of money is a stock concept at a particular point of time, but over time money supply is a flow concept. Total money supply at a particular point of time in an economy means total quantity of money held in economy at that time.

Total money supply in an economy basically depends on following determinants; below we are discussing the determinants of money supply and money multiplier one by one.

1)      Currency in public hand- The main and foremost determinants of money supply is currency held in public hand. People held currency in the form of paper notes or coins, these types of currency consider as a most liquid assets. These types of currency people can spend at any time anywhere and it has acceptable. So, currency notes and coins consider as a most liquid assets. We consider currency in public hand as C.

2)      Commercial bank reserves- commercial banks reserves a certain amount of liquid money from the bank deposits, to meet up the immediate public demands. We indicate it as R.

3)      Total bank deposits- Here we indicate total bank deposits as D. people deposits money in the bank ,after reserves a certain amount, bank lending the rest amount of money to the public as per demand.Here bank does not lend money in cash instead of that bank deposited the lending amount in customers passbook. So here bank create some amount of money in books of accounts. This created money is also the part of money supply, known as demand deposits.

Must read-1)Stock and Flow concept.

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    High powered money-     High powered money indicated as H .High powered money is the sum of the currency held in public hand in the forms of notes and coins, and commercial bank reserves. So, high powered money is the most important and vital part of money multiplier because it is in liquid form. We indicate it as,   H=C+R

Total money supply- Total money supply in the economy is the sum total of currency held in public hand and total demand deposits. Here money indicates as M.

So,   M= C+D

Now the Algebraic derivation of money multiplier is discussed below

We got two equations   M=C+D…………..1

                                         H=C+R ……………….2

Dividing equation 2 by M We get…

H/M=C/M+R/M …………..3

We can write    R/M= R/D*D/M …………4

[If we divided equation no 1 by M then we get 

 M/M=C/M+D/M

Or, 1=C/M+D/M

Or, 1- C/M=D/M]

Putting the value of D/M in equation no 4 we get

R/M=R/D*(1-C/M)

Putting the value of R/M in equation no 3 we get

       H/M= C/M+ R/D (1-C/M)

Or, M/H =1/{C/M +R/D (1-C/M)}

Or, M= [1/{C/M +R/D (1-C/M)}]* H

Or, M= mH

Here, m is the money multiplier and m= 1/{C/M +R/D (1-C/M)}

C/M is the ratio of Public desire to hold currency out of total money supply.

R/D is the ratio of total reserves of commercial banks out of deposits liabilities.

Conclusion- The money multiplier identity M= mH, shows the mechanical dependency of the money supply on the stock of high powered money. So it can be said there is a direct relationship between high powered money and money supply. So if the high powered money increases in the economy money supply will be increased.