Unformatted text preview: the amount of
excess reserves. Eco 029 Chapter 10, Chapter 14 Determining Money Supply (c'td) Changes in the required reserves ratio
The money supply is negatively related to the required reserve
ratio. Changes in currency holdings
The money supply is negatively related to currency holdings. Changes in excess reserves
The money supply is negatively related to the amount of
excess reserves. Eco 029 Chapter 10, Chapter 14 The Money Multiplier Dene money as currency plus checkable deposits: M1
Link the money supply (M) to the monetary base (MB) and
let m be the money multiplier
M = m × MB Eco 029 Chapter 10, Chapter 14 Deriving the Money Multiplier Assume that the desired holdings of currency C and excess
reserves ER grow proportionally with checkable deposits D.
Then,
c = {C/D} = currency ratio
e = {ER/D} = excess reserves ratio Eco 029 Chapter 10, Chapter 14 Deriving the Money Multiplier c'td Total reserves (R)= required reserves (RR)+ excess reserves
(ER)
Required reserves= reserve ratio times the amount of
checkable deposits: RR=r×D
Substituting, we get R = r × D + ER
r < 1. Why? Eco 029 Chapter 10, Chapter 14 Deriving the Money Multiplier c'td c = C /D → C = c × D ; e = ER /D → ER = e × D Substituting, we get
MB = RR + C + ER = r × D + e × D + c × D = (r + e + c ) × D
1
Rewriting, we get D = r +e +c × MB
M = D + C and C = c × D , so M = D + c × D = (1 + c ) × D
1c
Substituting again, we get M = r +++c × MB
e
1+c
The money multiplier is m = r +e +c Eco 029 Chapter 10, Chapter 14 Intuition Behind the Multiplier Let r = 0.1,C=$400B, D=$800, ER=$0.8B
M=M1=C+D=$1,200B
c=C/D=0.5
e=ER/D=0.001
.5
m = 0.1+1+0.5+0.5 = 01601 = 2.5
0.001
.
This is smaller than the simple deposit multiplier (no
expansion for currency) Eco 029 Chapter 10, Chapter 14 Application: The 20072009 Financial Crisis During the recent nancial crisis, the monetary base more than
tripled as a result of the Fed's purchase of assets and new
lending facilities to stem the nancial crisis
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 eects of the decline
in c were entirely oset by the extraordinary rise in the excess
reserves ratio e Eco 029 Chapter 10, Chapter 14 M1 and the Monetary Base 20072009 Eco 029 Chapter 10, Chapter 14 Excess Reserves Ratio and Currency Ratio, 20072009...
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 Spring '10
 ARONSON
 Economics, Monetary Policy, Federal Reserve System, Fractionalreserve banking, monetary base

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