San José State University
Department of Economics

applet-magic.com
 Thayer Watkins
Silicon Valley
& Tornado Alley
USA

The Derivation of Money Supply Multipliers

Definitions:

Derivation of m1

The M2 Money Multiplier

  • The M2 money supply is defined as
  • the M1 money supply
    plus time deposits T
    plus money market mutual fund shares
    plus money market deposit accounts
    plus overnight repurchase agreements
    plus overnight Eurodollars.
To keep matters simple all of the above four items will be grouped together as MMF. Thus

M2 = M1 + T + MMF.

Let rT be the required reserve ratio on time deposits. The required reserves at the Fed are then

RR = rDD + rTT.

Thus the monetary base and the M2 money supply are:

MB = rDD + rTT + ER + C
= (rD + rT(T/D) + ER/D + C/D)D
 
M2 = D + C + T + MMF
= (1 + C/D + T/D + MMF/D)D

The M2 money multiplier m2 is then given by:

m2 = M2/MB
m2 =     (1 + C/D + T/D + MMF/D)     
        (rD + rT(T/D) + ER/D + C/D)

For a handy calculator for computing the money multipliers and the money supplies see

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