Money, Banking, and International FinanceMoney multiplier becomes the term within the brackets. We divide both the numerator and
denominator in the fraction by D, shown in Equation 12.
B
D
+R
D
C
CD+
M1=
1
( 12 )
Currency-deposit ratio equals C / D while the reserves-deposit ratio is R / D. Both ratios are
fixed.
For example, the currency in circulation equals $240 billion; checkable deposits equal $600
billion, and total bank reserves equal $60 billion. We substitute these numbers into the currency-
deposit ratio and total reserves-deposit ratio in Equations 13 and 14.
0.40
$ 600
$ 240
=
B
B
CD= ( 13 )
0.10
$ 600
$ 60
=
bB
RD= ( 14 )
We substitute the currency-deposit and reserve-deposit ratios into the money supply
equation, yielding Equation 15.
2.8B
0.4 0.1
0.4 1.0
M1=
B
+
+
M1=
( 15 )
Money multiplier equals 2.8. Although the money multiplier relates the total monetary base
to the money supply, the money multiplier also works for changes in the monetary base. For
example, if the Fed buys $100,000 in T-bills, then the monetary base increases by $100,000,
expanding the M1 money supply by $280,000. The multiplier assumes the banks lend their
entire excess reserves.
Banks can weaken the ratio between the monetary base and money supply. For example, if
the Fed increased the monetary base by buying $100,000 in T-bills and the banks hold the entire
excess reserves, subsequently, the money supply expands only by $100,000. Banks do not lend
any reserves, causing the money supply multiplier to equal one. We can prove this because R =
D.
We derive the money supply multiplier for M2 similarly. The M2 definition includes time
deposits, denoted by T. We define the M2 definition as M2 = C + D + T.
Similarly to the M1, we start with Equation 16. Monetary base (B) would cancel, leaving
M2 = M2.