Chapter 14
NOTE: This is
chapter 15 in the
10th edition but
Chapter 14 in the
solution manual
The Money
Supply Process
(Lecture 3)
The Money Supply Model
• Link the money supply (M) to the
monetary base (MB) and let m be the
money multiplier
M  m  MB
14-2
• So far, we learned about the simple money multiplier
that linked: ReservesDeposits
ΔD = 1/r × ΔR
• Next, we will learn about the money multiplier that
links:
ΔMBΔMs
• Define money supply as currency plus checkable
deposits: M1
14-3
Deriving the Money Multiplier I
Assume the desired level of currency C and excess reserves ER
grows proportionally with checkable deposits D
Then
c = {C / D} = currency ratio
e = {ER / D} = excess reserves ratio
• c and e are constants in equilibrium
• Recall that in the simple deposit multiplier:


ER=0  e=0, and
Currency holdings are not proportional to deposits  c=0
14-4
Deriving the Money Multiplier II
The total amount of reserves (R) equals the sum of
required reserves (RR) and excess reserves (ER).
R = RR + ER
The total amount of required reserves equals the required
reserve ratio times the amount of checkable deposits
RR = r × D
Subsituting for RR in the first equation
R = (r × D) + ER
The Fed sets r to less than 1
14-5
Deriving the Money Multiplier III
• MB = r×D + ER + C
• Multiple deposit expansion occurs due to the
r×D component where r < 1

each $1 increase in reserves supports a deposit
expansion that is greater than $1)
• Any increase in MB that is due to C or ER will
not generate a multiplier effect
• For a given amount of reserves, an increase in
C or ER will decrease the multiplier effect
14-6
Deriving the Money Multiplier IV
c = {C / D}  C = c  D and
e = {ER / D}  ER = e  D
Substituting in the previous equation
MB  (r  D)  (e  D)  (c  D)  (r  e  c)  D
Divide both sides by the term in parentheses
1
D
 MB
r  e c
M  D  C and C  c  D
M  D  (c  D)  (1 c)  D
Substituting again
1 c
M
 MB
r  e c
The money multiplier is then
1 c
m
r  e c
14-7
• The money multiplier (m) shows how
much the money supply changes in
response to a change in the monetary
base
• m is a function of c, r, e (in the simple
multiplier, c=0, e=0)
14-8
Example
r  required reserve ratio = 0.10
C  currency in circulation = $400B
D  checkable deposits = $800B
ER  excess reserves = $0.8B
M  money supply (M1) = C  D = $1,200B
$400B
 0.5
$800B
$0.8B
e
 0.001
$800B
1 0.5
1.5
m

 2.5
0.1 0.001 0.5 0.601
This is less than the simple deposit multiplier
Although there is multiple expansion of deposits,
there is no such expansion for currency
c
14-9
• In this example, an increase in the monetary
base by $1 increases money supply (M1) by
$2.5
• Under the simple deposit multiplier, an
increase in reserves (and hence monetary
base) by $1 would increase deposits (and
hence M1) by $10
• The money multiplier is smaller than the
simple deposit multiplier (1/r = 10) because
some of the increase in R is assumed to be
absorbed as currency and excess reserves.
14-10
Factors that Determine
the Money Multiplier
• Changes in the required reserve ratio r


The money multiplier and the money supply are negatively
related to r
when r increases banks need to hold a larger fraction of
customer deposits at CB
less loans & securities
less deposit expansion
 m declines
• Empirically, r has been declining over time. This
component is not used as a tool to affect money
supply in the US
• r has been used as a policy tool by the CBT during the
recent crisis
14-11
• Changes in the currency ratio c

The money multiplier and the money supply
are negatively related to c

when c increases less money will be held
on deposit, m declines
14-12
• Changes in the excess reserves ratio e


The money multiplier and the money supply are negatively
related to the excess reserves ratio e
when e increases,less loans are given out, less deposit
expansion, m declines
• What determines e?

market interest rates (opportunity cost for holding ER):
• i (up), e (down): The excess reserves ratio e is negatively
related to the market interest rate



interest rate the Fed pays on ER (very recent development)
expected deposit outflows: The excess reserves ratio e is
positively related to expected deposit outflows
overall confidence in the economy
14-13
•Our model can help explain monetary contractions
following banking crisis
14-14
•c and e increase following crisis
14-15
•Money supply declines
14-16
APPLICATION The 2007-2009 Financial Crisis
and the Money Supply
Figure 4 M1 and the Monetary Base, 2007-2009
Source: Federal Reserve; www.federalreserve.gov/releases.
Figure 5 Excess Reserves Ratio and Currency
Ratio, 2007-2009
Source: Federal Reserve; www.federalreserve.gov/releases.
• During the recent financial crisis, as shown in Figure
4, the monetary base more than tripled as a result of
the Fed's purchase of assets and new lending facilities
to stem the financial crisis
• Figure 5 shows the currency ratio c and the excess
reserves ratio e for the 2007-2009 period. We see
that the currency ratio fell somewhat during this
period, which our money supply model suggests
would raise the money multiplier and the money
supply because it would increase the overall level of
deposit expansion. However, the effects of the
decline in c were entirely offset by the extraordinary
rise in the excess reserves ratio e
End of chapter questions
• The answers for the end of chapter
questions are provided under “Chapter
14” in the solution manual, NOT under
Chapter 15.
• You can solve most of the end of chapter
questions.
• Likely quiz in a few lectures time (after
we finish the next chapter).
Selected end of chapter questions
Question 17
• If the Fed sells $2 million of bonds to
Irving the investor who pays for bonds
with cash, what happens to reserves and
monetary base?
14-21
Irving
Assets
Federal Reserve System
Liabilities
Securities
+$2mil
Currency
-$2mil
Assets
Sec
-$2 mil
Liabilities
CIC
-$2mil
Reserves remain unchanged
MB declines by $2 million.
13-22
Question 18
• If the Fed lends five banks an additional
total of $100 million but depositors
withdraw $50 and hold as currency, what
happens to reserves and monetary base.
14-23
Banks
Assets
Reserves
Federal Reserve System
Liabilities
+$100 Dep.
-$50
DW
-$50
Assets
DW
+$100
+$100
Liabilities
CIC
Reserves
+$50
+$100
-$50
Reserves increase by $50 million
MB increases by $100 million
13-24
Question 19
• Using T-accounts, show what happens
to checkable deposits in the banking
system when the Fed lends an
additional $1 million to FNB
14-25
FNB
Assets
RB
Federal Reserve System
Liabilities
+$1mil DW
+$1mil
Assets
DW
+$1mil
Liabilities
RB
+$1mil
Stage 1: Reserves increase by $1 million.
Stage 2: Using the simple deposit multiplier, deposits
increase by $1 million*10= $10 million
We can add another balance sheet for the banking
system (stage 2), increasing deposits and loans by $10
million.
13-26
Question 23
• If the Fed reduces reserves by selling $5
million of bonds to banks, what will the
T-account of the banking system look
like in equilibrium. What will happen to
checkable deposits?
14-27
Banking System
Stage 1
Assets
Banking System
Stage 2
Liabilities
Assets
Securities
+$5mil
Securit.
+$5mil
RB
-$5mil
RB
-$5 mil
Loans
-$50 mil
Liabilities
Dep.
-$50 mil.
Stage 1: Reserves decrease by $5 million.
Stage 2: Using the simple deposit multiplier, deposits decrease by
$5 million*10= $50 million
In terms of the final balance sheet, the decline in deposits means
that loans or securities decline by the same amount.
13-28