Introduction to Finance

money multiplier
is the number of times the monetary base can be expanded or magni-
fi ed to produce a given money supply level. Conceptually, the M1 defi nition of the money 
supply is the monetary base (MB) multiplied by the money multiplier (
m
). In equation 
form we have, as follows:
M1 = MB × 
m
(5.2)
The size and stability of the money multiplier are important because the Fed can control 
the monetary base but it cannot directly control the size of the money supply. Changes in the 
money supply are caused by changes in the monetary base, in the money multiplier, or in 
both. The Fed can change the size of the monetary base through open-market operations or 
changes in the reserve ratio. The money multiplier is not constant. It can and does fl uctuate 
over time, depending on actions taken by the Fed, as well as by the nonbank public and the 
U.S. Treasury.
At the end of December 2015, the money multiplier was approximately .81, as determ-
ined by dividing the $3,093.8 billion M1 money stock by the $3,835.8 billion monetary base.
7
Taking into account the actions of the nonbank public and the Treasury, the formula for the 
money multiplier in today’s fi nancial system can be expressed as,
8
m
=
(1 +
k
)
[
r
(1 +
t
+
g
) +
k
]
(5.3)
where 
 r
= the ratio of reserves to total deposits (checkable, noncheckable time and savings, and 
government)
 k
= the ratio of currency held by the nonbank public to checkable deposits
 t 
= the ratio of noncheckable deposits to checkable deposits
g
= the ratio of government deposits to checkable deposits
Let’s illustrate how the size of the money multiplier is determined by returning to our previous 
example of a 20 percent reserve ratio. Recall that in a more simple fi nancial system, the money 
multiplier would be determined as 1 ÷ 
r
or 1 ÷ .20, which equals 5. However, in our complex 
system we also need to consider leakages into currency held by the nonbank public, noncheck-
able time and savings deposits, and government deposits. Let’s further assume that the reserve 
ratio applies to total deposits, a 
k
of 40 percent, a 
t
of 15 percent, and a 
g
of 10 percent. The 
money multiplier then would be estimated, as follows:
m
=
(1 + .40)
[
.20(1 + .15 + .10) + .40
]
=
1.40
.65
= 2.15
Of course, if a change occurred in any of the components, the money multiplier would adjust 
accordingly, as would the size of the money supply.
In Chapter 2 we briefl y discussed the link between the money supply and economic activ-
ity. You should be able to recall that the money supply (M1) is linked to the gross domestic 
product (GDP) via the velocity, or turnover, of money. More specifi cally, the