Chapter 14
Determinants
of the Money Supply:
The Money Multiplier
Dr. Reyadh Faras
Introduction


In Ch 13, we developed a simple model of multiple
deposit creation which showed that the Central
Bank can influence the amount of checking deposits
(D), bank reserves (R), and the monetary base (MB)
by changing the reserve requirement (RRR),
discount loans (DL) and OMOs.
However, the model assumes unrealistically that:
1) the public holds no cash (C) and;
2) banks hold no excess reserves (ER).
Dr. Reyadh Faras
THE MS MODEL AND THE
MONEY MULTIPLIER

We now develop a more realistic money supply
model that allows for the fact that the public does
hold cash balances.

We link the monetary base, which the central
bank can better control, to the money supply (M
for M1), using the money multiplier (m).
Dr. Reyadh Faras
Money Multiplier

It is a ratio that shows how much the money supply
changes for a given change in the monetary base.
MS = m x MB
(1)

Because the multiplier is larger than one, the
monetary base is called “high powered money”,
meaning that a change in MB by 1% leads to a
change in MS by more than 1%.
Dr. Reyadh Faras
Deriving the Money Multiplier


Here we account for the possibility that depositors
hold some cash (outside the banking system) and
banks hold excess reserves. These two decisions
affect (m).
We assume that holdings of currency (C) and excess
reserves (ER) grow proportionally with checkable
deposits (D), which means that the following ratios
are constants:
{C/D} = currency ratio
{ER/D} = excess reserve ratio
Dr. Reyadh Faras
Currency and Excess Reserve Ratios in Kuwait
Year
Cash with
Local Banks
(Million KDs)
Currency in
Circulation
(Million KDs)
Sight
Deposits
(Million KDs)
Excess
Reserve
Ratio
(ER/D)
(%)
46.9
355.2
758.8
6.2
46.8
Currency
Ratio
(C/D)
(%)
1993
1994
K-Net
1995
64.1
351.3
774.7
8.3
45.3
104.1
311.5
873.5
35.7
2004
75.3
531.0
2643.3
11.9
2.8
2005
105.9
578.7
3148.7
3.4
18.4
2006
148.6
656.3
2893.9
5.1
22.7
2007
115.2
641.5
3505.2
3.3
18.3
2008
161.4
707.8
3662.5
4.4
19.3
2009
168.1
775.7
3938.3
4.3
19.7
2010
163.7
842.9
4782.1
3.4
17.6
20.1





Next, we derive a formula showing how these ratios
plus the required reserve ratio affect m.
Total reserves equal the sum of required reserves
(RR) and excess reserves (ER):
R = RR + ER
We know that RR equals checking deposits
multiplied by the reserve requirement ratio, thus R
equals:
R = ( RRR x D ) + ER
But MB equals to C plus R, thus it can be rewritten
using the above equation as follows:
MB = R + C = ( RRR x D ) + ER + C
This equation shows the amount of MB needed to
support the existing amounts of checkable deposits,
currency and excess reserves.
Dr. Reyadh Faras



To derive a formula for m in terms of the currency and
excess reserve ratios, we rewrite the above equation
specifying
C as {C / D} X D and ER as {ER / D} X D, as follows:
MB = ( RRR x D ) + ({ER / D} X D) + ({C / D} X D)
= ( RRR + {ER / D} + {C / D}) X D
Next, divide both sides of the equation by the term inside
the parentheses to get an expression linking checkable
deposits (D) to the monetary base (MB):
D = [1 / (RRR + {ER / D} + {C / D})] X MB (2)
Using the definition of money supply as currency plus
checkable deposits (M = D + C) and specifying C as {C /
D} X D,
M = D + ({C / D} X D)
= (1 + {C/D}) X D
Dr. Reyadh Faras
Substituting equation (2) for D in the above equation,
we have
M = [(1+{C/D}) / (RRR + {ER / D} + {C / D})] X MB (3)


Equation (3) is a detailed form of equation (1)
(M = m x MB), to get an expression for m, we have to
divide both sides of equation (3) by MB:
m = [(1+ {C/D}) / (RRR + {ER / D} + {C / D})] (4)
Clearly, m depends on: {C/D} set by depositors,
{ER/D} set by banks, and {RRR} set by central bank.

Dr. Reyadh Faras
Example
Assume:
 RRR = 10%
ER = $0.8 billion
 C = $400 billion
D = $800 billion
 Calculate the currency and excess reserve ratios:
C/D =
/
=
ER/D =
/
=
 The money multiplier is calculated as follows:
m=
The multiplier shows that an increase in MB by % ___
leads to an increase in money supply by %____.
Dr. Reyadh Faras

The value of (m) is much smaller than 10, which was
expected from the model in chapter 13. There are
two reasons for the low value found here:

First, we allow for the possibility that the public
hold currency proportional to their holdings of
deposits.

Second, banks are also allowed to hold excess
reserves proportional to the value of deposits.
Dr. Reyadh Faras
Factors that Determine the Money Multiplier
1. Changes in RRR
 If RRR increases, more required reserves are
needed proportional to the level of checkable
deposits.
 This reduces the bank’s ability to lend, so loans will
decline and as a result (new) deposits decline too.
 Finally, money supply has to decline.
 But since money supply has declined while MB
didn’t change, this means that (m) must have
declined (M=m X MB).
 In other words, if RRR is higher, less multiple
expansion of checkable deposits occur which means
that (m) must fall.
Dr. Reyadh Faras
Example

If RRR increases from 10% to 15%.

m=
Result:
The money supply and the money multiplier are
_________ related to the required reserve ratio.
Dr. Reyadh Faras
2. Changes in {C/D}
 An increase in {C/D} means that depositors are
converting some of their checkable deposits into
currency.
 As it was shown in chapter 13, checkable deposits
undergo multiple expansion while currency does not.
 Therefore, an increase in currency results in a
decline in the level of multiple expansion and (m) too.
Example
 If {C/D} rises from 0.5 to 0.75.
m=
Result:
The money multiplier and the money supply are
_________ related to the currency ratio.
Dr. Reyadh Faras
3. Changes in {ER/D}
 When banks increase their holdings of excess
reserves,
this means that for the same level of MB, banks will
reduce their loans, causing a decline the level of
checkable deposits and a decline in the money
supply. As a result, m must fall.
Example
 If {ER/D} rises from 0.001 to 0.005.
m =
Result:
The money multiplier and the money supply are
__________related to the excess reserve ratio.
Dr. Reyadh Faras
Factors that Determine the Money Supply
Dr. Reyadh Faras
SUMMARY
VARIABLE
RRR
C/D
ER/D
MB
CHANGE
Increase
Increase
Increase
Increase
Dr. Reyadh Faras
REPSONSE IN MS
________
________
________
________
Excess Reserves Ratio and Interest Rate
Dr. Reyadh Faras
{ER/D}, {C/D}: 1929–33
Dr. Reyadh Faras
Money Supply and Monetary Base: 1929–33
Dr. Reyadh Faras
Required and Excess Reserves in the US: 2007- 2009