THE MONEY MULTIPLIERS
The simple money multiplier, m, assumes that only one asset serves as
a perfectly liquid medium of exchange: DD's. Our definition of the money
supply, Ms, is correspondingly simple:
Our formula for the simple multiplier is as follows:
The complex money multiplier, mm, assumes there are two assets that serve
as a perfectly liquid medium of exchange: DD's and C. Our money supply
is now defined as:
The required reserve ratio, r, can be defined as follows:
The cash-deposit ratio, c, can be defined as follows:
The monetary base, MB, can be defined as follows:
The money supply can now be rewritten as:
Our complex money multiplier is the ratio of the money supply to the monetary
MB = RR + C
MB = rDD + cDD = DD(r+c)
mm = MS/MB = DD(1+c)/DD(r+c)
This complex multiplier will allow us to see the effects of a change in
the cash-deposit ratio, c, on the multiplier, mm. For example, assume r
= 10% and c = 20%. Our mm for these values is 4 (verify by doing the calculation).
Assume that people prefer to hold more of their money as cash so that c'
= 40%. Our new mm is now 2.8 (verify by doing the calculation).
mm = (1+c)/(r+c)