Question

What is the difference between the two Money Multiplier Formulas? 1/rr and C+D/C+RR+ER ?

Answer 1

Answer

Actual money multiplier = M/B where M = Money supply = C + D and B = Monetary Base = C + R where C =currency, D = deposit and R = reserves

So, Actual money multiplier = M/B = (C + D)/(C + R) and R = Reserves = RR + ER where ER = excess reserves and RR = required reserve.

=> Actual money multiplier = M/B = (C + D)/(C + RR + ER) ---------------------------------One formula

Now, Dividing numerator and denominator by D we get :

Actual money multiplier = (C/D + D/D)/(C/D + RR/D + ER/D) = (C/D + 1)/(C/D + RR/D + ER/D) where C/D = (1 + Cr)/(Cr + er + rr)

where Cr = C/D = currency to deposit ratio, RR/D = rr = required reserve ratio and er = excess reserve ratio.

Hence, Actual money multiplier = (1 + Cr)/(Cr + er + rr).

When banks hold no excess reserve and public hold no currency then C = 0 and ER = 0. Hence, in that case Cr = 0 and er = 0.

Then, new money multiplier = (1 + 0)/(0 + 0 + rr) = 1/rr -------------------------Second formula

Hence Actual money multiplier becomes new multiplier when public hold no currency and Banks hold no excess reserves.