Question

Assume 20% of the money is held as currency and the remainder as demand deposits. The banks keep the excess reserves at zero. The required reserves are 15% of the demand deposits. If the Fed increases the reserves by $10 million what will be the increase in the money supply?

31.25 million

33.45 million

35.23 million

36.53 million

Answer 1

Money multiplier(m) = (1 + c)/(c + r + e)

where c = Currency to deposit ratio = 20/80 = 0.25(It is given that it holds 20% as currency and 80% as deposit), e = excess reserve ratio = 0 and r = required reserve ratio = 15% = 0.15

Thus, Money multiplier(m) = (1 + 0.25)/(0.25 + 0.15 + 0) = 3.125

Here reserves increase by 10 million

Thus, Increase in Money supply = Money multiplier*Increase in reserves(more precisely increase in monetary base)

=> Increase in Money supply = 3.125*10 million = 31.25 million

Hence, the correct answer is (a) 31.25 million.