Question

(c) Suppose the Fed injects $50 billion in reserves into the banking system. Will the total change in the money supply be larger when individuals hold 10% of their money as currency or when they hold 20% of their money as currency? Explain. Note: I am NOT asking you to calculate the change in the money supply.

Answer 1

If Cr = Currency Drainage Ratio and rr = Required reserves ratio, then

Money multiplier = (1 + Cr) / (Cr + rr), where 0 < Cr < 1 and 0 < rr < 1.

When Cr increases (from 10% = 0.1 to 20% = 0.2), then (1 + Cr) will increase more than (Cr + rr), since rr < 1. As a result, money multiplier will decrease. Since total change in money supply is the product of increase in monetary base and the money multiplier, a decrease in money multiplier will decrease total change in money supply.

So, change in money supply will be larger when individuals hold 10% of money as currency.