1. Lecture 27: Money multiplier
Mishkin Ch14 – part A
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2. Review A simple model of multiple deposit creation.
The bank creates deposits by lending.
Initial $100 increase in reserves will result in $1000 in deposit. The increase is tenfold, the reciprocal of reserve ratio 10%.

3. Introduction
Fed’s control over checkable deposits is affected by two factors: holdings of currency; holdings of excess reserves.
a more advanced model: the money supply model
monetary base  money multiplier  money supply

4. The money supply model
Define money as currency plus checkable deposits: M = C + D
M1 definition of money
The Fed can control the monetary base better than it can control reserves
Link the money supply (M) to the monetary base (MB) and let m be the money multiplier

5. Deriving the money multiplier

6. Deriving the money multiplier II

7. Deriving the money multiplier III
An increase in the monetary base that goes into currency is NOT multiplied, whereas an increase that goes into supporting deposits is multiplied.
Also, an additional dollar of monetary base that goes into excess reserve does not support any additional deposits or currency.

8. Deriving the money multiplier IV

9. Example
If the required reserve ratio is 10 percent, currency in circulation is $400 billion, checkable deposits are $800 billion, and excess reserves total $0.8 billion,
What’s the money supply, monetary base and money multiplier?
c = C/D = 400/800 = 0.5; e = E/D = 0.8/800 = 0.001; r = 0.1;
m =(1+c)/(r+e+c) = 1.5/0.601 =
M = C + D = = $1200 billion
Can check: M = m * MB = m * (C+R) = *( *800) = $1200 billion

10. Intuition

11. Factors that determine the money multiplier
Required reserve ratio r:
the money multiplier and the money supply are negatively related to r
Currency ratio c:
the money multiplier and the money supply are negatively related to c.
Excess reserves ratio e:
the money multiplier and the money supply are negatively related to the excess reserves ratio e.

12. Factors that determine the money multiplier – cont’d
The excess reserves ratio e is negatively related to the market interest rate
Opportunity cost of holding excess reserves
Relative expected return on excess reserves relative to loans and securities
The excess reserves ratio e is positively related to expected deposit outflows
Excess reserves provide insurance against losses due to deposit outflows.

14. Recap Money multiplier
Currency and excessive reserves are NOT multiplied.
changes in c, e, r are negatively related to changes in m.
e is negatively related to market interest rate but positively related to expected deposit outflow.