The proportion of deposits held by the public as cash is 0.5 and the proportion of deposits held by the banks for reserves is 0.5. If the broad money supply is £300million, what is the value of the narrow money supply? A £150 million B £200 million C £450 million D None of the above. I think I missed the point of this question, can anyone help? How do I get to the answer, B?
The formula you want is the one for the money multiplier: m = (1 + c)/(r + c) In this case r and c are both 0.5, so to be clear r relates to the proportion of deposits held by banks for reserves, and c relates to the proportion of deposits held by the public as cash. Thus m = 1.5. Broad money (say M4) is related to narrow money (say M0) by the formula M4 = m x M0, therefore if M4 is 300m, M0 must be £200m. See section 18.3 in the textbook for a full discussion of the money multiplier.
