Chapter 14
Determinants
of the Money Supply
Introduction

In Ch 13, we developed a simple model of multiple
deposit creation which showed that the Central Bank
can influence MONEY SUPPLY through monetary
base. This is by using OMOs and discount loans.

However, the model assumes unrealistically that:
1) the public holds no cash (C) and;
2) banks hold no excess reserves (ER).
THE MONEY SUPPLY 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 and banks can hold excess
reserves.

We link the monetary base, which the central bank
can better control, to the money supply (M for M1),
using the money multiplier (m).
Money Multiplier (m)

It is a ratio that shows how much the money supply
changes for a given change in the monetary base.
M= m x MB
(1)

Because the multiplier is larger than one, the monetary
base is called “high powered money”, meaning that a
change in monetary base (MB) by 1% leads to a
change in money supply (M) by more than 1%.
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 the money
multiplier (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





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.



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
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 the central bank.

Example
Given: RRR = 10%, ER = $0.8 billion, C = $400 billion
, D = $800 billion, ………………Calculate m?
 We can calculate the currency and excess reserve ratios:
C/D =
/
=
ER/D =
/
=
 The money multiplier is calculated as follows:
m=
Given -----------------M= m(MB)
The multiplier shows that an increase in MB by( $ 1)
leads to an increase in money supply by $____.

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.
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 (MB)}.
 In other words, if RRR is higher, less multiple expansion
of checkable deposits occur which means that (m) must
fall.
Example

If RRR increases from 10% to 15%.

m=
Result:
The money supply and the money multiplier are
_________ related to the required reserve ratio.
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.
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.
SUMMARY
VARIABLE
MB
RRR
C/D
ER/D
CHANGE
Increase
Increase
Increase
Increase
REPSONSE IN MS
________
________
________
________