San José State University|
Department of Economics
& Tornado Alley
Derivation of m1
MB = [rD + (ER/D)+ (C/D)]D
M1 = D + C = [1 + (C/D)]D
m1 = M1/MB =[1+(C/D)]D/[rD+(ER/D)+ (C/D]D
The M2 money supply is defined as the M1 money supply
To keep matters simple all of the above items will be grouped together
as MMF. Thus
plus money market mutual fund shares
plus money market deposit accounts
plus overnight repurchase agreements
plus overnight Eurodollars.
M2 = M1 + T + MMF.
Let rT be the required reserve ratio on time deposits. The required reserves at the Fed are then
The M2 money multiplier m2 is then given by:
|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 money.
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