Introduction to the
Money Supply Process
Fundamental Property -- Money
supply expands when banks make
loans (or more generally, expand
loans or buy bonds)
Deposit Expansion:
The Individual Bank
Consider the following example.
(rD = 0.10, rT = 0.05)
Chase
R
$20000 D $70000
L
$90000 T $80000
Bonds $50000 E $10000
Computing Required and
Excess Reserves
Chase
R
$20000 D $70000
L
$90000 T $80000
Bonds $50000 E $10000
rD = 0.10
rT = 0.05
RR = rDD + rTT = (0.10)($70000) +
(0.05)($80000) = $11000
ER = R - RR = $20000 - $11000 = $9000
Loan of $9000
Step #1 -- Loan is Approved
Chase
R
$20000 D $79000
L
$99000 T $80000
Bonds $50000 E $10000
Borrower signs loan contract,
receives check from bank.
Step #2 -- Loan is Spent
Chase
R
$11000 D $70000
L
$99000 T $80000
Bonds $50000 E $10000
Seller deposits check in her bank.
R
HSBC
+ $9000 D + $9000
Bank Loaning and
Money Supply Expansion
Consider: M2 = C + D + T + MMMF
 M2 = C + D + T + MMMF
Our example:
M2 = $0 + $9000 + $0 + $0 = $9000
(Chase’s loan leads to
new deposits for HSBC.)
Key Concepts:
Money Supply Expansion
Key is step #1, Chase expands its
deposit commitments without
changing its reserves.
Note -- Process is symmetric.
Repayment or liquidation of loan
leads to decrease in M2 (by the
amount of the loan).
Deposit Expansion:
The Banking System
Multiple Expansion -- An initial
change in bank reserves prompted
by the Federal Reserve leads to an
eventual increase in the money
supply which is a multiple of that
initial change.
Developing a Formula
for Multiple Expansion
 Define -- The Monetary Base, or
High Powered Money (H)
H=C+R
Key Properties:
The Monetary Base
The monetary base (H) is unaffected by
changes in public asset holdings.
The monetary base (H) is also
unaffected by bank loaning.
Important factors that change H: Open
Market Operations and Discount Loans
(DL).
Discount Loans
and the Monetary Base
Example 1 -- Chase borrows $100
from the Federal Reserve.
R
Chase
+ $100 DL + $100
H = C + R = $0 + $100 = $100
Open Market Operations
and the Monetary Base
Example 2 -- The Federal Reserve
buys a $100 bond from Chase.
Bonds
R
Chase
- $100
+ $100
H = C + R = $0 + $100 = $100
The Nonborrowed Base
The Nonborrowed Base (HNON)
HNON = H - DL
Key property -- The nonborrowed
base is only affected by open
market operations.
A Formula for Money Supply
Determination
Define the following variables.
k = C/D
t = T/D
e = ER/D
Money Supply
Determination: The Formula
M2 =
(1 + k + t)
(HNON + DL) + MMMF
(k + rD + rTt + e)
The money multiplier (m2)
Computing the Money
Multiplier: An Example
Suppose that:
C = 550
rD = 0.10
D = 600
rT = 0.03
T = 3000
ER = 10.
Compute the money multiplier (m2).
Computing the Ratios
k = C/D = 550/600 = 0.917
t = T/D = 3000/600 = 5.000
e = ER/D = 10/600 = 0.0167
Plugging Into
The Multiplier Formula
m2 =
1+k+t
k + rD + rTt + e
m2 =
1 + 0.917 + 5.0
0.917 + 0.10 + (0.03)(5.0) + 0.0167
m2 =
5.84
Effects of HNON and DL
on M2 Determination
Since M2 = (m2)(HNON + DL),
M2 = (m2)( HNON),
M2 = (m2)(DL).
In other words,
HNON  M2
DL  M2
Changes in HNON or DL give banks
reserves, greater ability to loan.
Effects of Reserve Ratios
on M2 Determination
Increases in reserve ratios hinder
bank loaning, thereby decreasing
the multiplier and M2.
m2 =
1+k+t
k + rD + rTt + e
rD  m2  M2
rT  m2  M2
Effects of k (C/D) and t (T/D)
on M2 Determination
Changes in k and t (public’s desire to
reallocate assets) have different effects on
bank loaning, the multiplier, and M2.
m2 =
1+k+t
k + rD + rTt + e
k  m2  M2
t  m2  M2
Effects of e (ER/D) on M2
Changes in e (banks desire to hold
more excess reserves) affect the
multiplier, which affects M2.
m2 =
1+k+t
k + rD + rTt + e
e  m2  M2
M2 Determination: Summary
First, the formula again.
M2 =
(1 + k + t) (HNON + DL) + MMMF
(k + rD + rTt + e)
A Summary Table
HNON
DL
rD
rT
k
t
e
 M2
 M2
 M2
 M2
 M2
 M2
 M2
The Multiplier -- Trying to
Control the Money Supply
M2 =
(1 + k + t)
(HNON + DL) + MMMF
(k + rD + rTt + e)
Federal Reserve controls HNON, rD, and
rT and uses them as policy tools.
But M2 is also determined by public
asset holding (k, t, MMMF) and bank
behavior (e, DL).
Can the Federal Reserve
Control the Money Supply?
Practical Solution -- The Federal
Reserve tries to control money
supply growth within a given
target range. If actual M2 growth
falls within the range, M2 is
considered controlled.
The Multiplier Effect and
Controlling M2
Consider formula for M2
determination (apart from MMMF),
written as follows (recall that H =
HNON + DL).
M2 = (m2)(H)
M2 Determination in
Growth Rates
Since the levels are multiplicative,
the growth rates are additive
Growth in M2 
(Growth in m2) + (Growth in H)
Implications for M2 Control
Growth in M2 
(Growth in m2) + (Growth in H)
If the multiplier is roughly
constant over time (growth in m2 
0), then the growth rate of M2 will
approximate closely the growth
rate of the monetary base.
Difficulties in M2 Control
Growth in M2 
(Growth in m2) + (Growth in H)
But if the multiplier changes over
time (growth rate either positive or
negative), then the growth rate of
M2 will deviate from the growth
rate of the monetary base.
Non-Federal Reserve
Changes in M2
Best solution: constant multiplier,
zero DL. Unfortunately, not true.
Second best solution: predictable
multiplier and DL.
How to predict non-Fed controlled
changes in M2? What determines
movements in the components
(k, t, e, DL, MMMF)?