1. Determinants of the Money Supply
Chapter 14
Determinants of the Money Supply

2. 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).

3. 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).

4. 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%.

5. 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

6. 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.

7. 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

8. 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.

9. 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 $____.

10. 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.

11. 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.

12. Example
If RRR increases from 10% to 15%.
m =
Result:
The money supply and the money multiplier are _________ related to the required reserve ratio.

13. 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.

14. 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 to
m =
Result:
The money multiplier and the money supply are __________related to the excess reserve ratio.

15. SUMMARY
VARIABLE CHANGE REPSONSE IN MS MB Increase ________ RRR Increase ________ C/D Increase ________ ER/D Increase ________