San José State University
Department of Economics

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Thayer Watkins
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& Tornado Alley
USA

The Derivation of Money Supply Multipliers

Definitions:

Derivation of m1

  • MB = R + C = RR + ER + C
    = rDD + (ER/D)D + (C/D)D
  • Therefore
    MB = [rD + (ER/D)+ (C/D)]D
  • But
    M1 = D + C = [1 + (C/D)]D
  • Therefore
    m1 = M1/MB
    m1=[1+(C/D)]D/[rD+(ER/D)+ (C/D]D
    and hence

  • m1=[1+(C/D)]/[rD+(ER/D)+ (C/D]

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 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 given by:


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

 

(To be continued.)

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