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Chapter 14
Determinants of
the Money Supply
• In Chapter 13, we learned about the simple money
multiplier that linked: ReservesÆDeposits
∆D = 1/r × ∆R
• In this chapter we will learn about the money multiplier
that links:
∆MBÆ∆Ms
• Define money supply as currency plus checkable
deposits: M1
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14-2
The Money Supply Model
• Link the money supply (M) to the
monetary base (MB) and let m be the
money multiplier
M = m × MB
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14-3
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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
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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
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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
h $1 iincrease iin reserves supports
t ad
depositit
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
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14-6
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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
× MB
r +e+c
The money multiplier is then
M=
m=
1+ c
r +e+c
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14-7
• The money multiplier (m) shows how
much the money supply changes in
response to a change in the monetary
b
base
• m is a function of c, r, e (in the simple
multiplier, c=0, e=0)
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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
05
$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
c=
Although there is multiple expansion of deposits,
there is no such expansion for currency
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14-9
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• 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.
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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
Æless loans & securities
Æless deposit expansion
Æ m declines
• Empirically, r has been declining over time. This
component is not used as a tool to affect money
supply
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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
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• 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
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14-13
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14-14
•Our model can help explain monetary contractions
following banking crisis
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•c and e increase following crisis
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14-16
•Money supply declines
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