Money multiplier shows the ratio of change in total money supply due to a given change in the quantity of high powered money or ratio of M to H. Money supply is given by the equation
M = C + D (i)
Where M is the supply of money, C is currency with the public and D shows demand deposits with the banks.
Supply of high powered money is given by the equation
H = C + R
Where H is the supply of high powered money, C is currency with the public and R refers to cash reserve of the banks.
From equation (i) and (ii), we get
M / H = C + D/C + R
Dividing the right hand side numerator and denominator by D,
M/H = C + D /D / C + R / D = C + D + 1 / C/D + R/D
Since, C/D is the ratio of cash of bank, deposits held by public symbolically written as b and R/D is the ratio of cash reserve kept by banks against deposits written as x, the equation becomes
M / H = b + 1/b + x
The money multiplier, viz., the ratio of change in the total money supply M to a given change in the quantity of high powered money H is thus given us
M / H = b + 1/b + x
Where b + 1/b + x is the money multiplier.
The total money supply thus is given as
M = b + 1/ b + x . H
and increase in money supply due to increase in high powered money will be
ΔM = b + 1/b + x ΔH.
Money supply thus depends upon the quantity of the high powered money H and the money supplier b + 1/b + x. The money multiplier tells us how much bigger the money supply is than the cash base of the economy.
