ECONOMICS 0115
HANDOUT #3
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:

MS = DD
Our formula for the simple multiplier is as follows:
m = 1/r
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:
MS = DD + C
The required reserve ratio, r, can be defined as follows:
r = RR/DD
The cash-deposit ratio, c, can be defined as follows:
c = C/DD
The monetary base, MB, can be defined as follows:
MB = RR + C

MB = rDD + cDD = DD(r+c)

The money supply can now be rewritten as:
MS = DD + cDD = DD(1+c)
Our complex money multiplier is the ratio of the money supply to the monetary base:
mm = MS/MB = DD(1+c)/DD(r+c)

mm = (1+c)/(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).