Question

The banking system has $15 million in reserve, with a required reserve ratio of 25%. people hold $5 million of currency. If the required reserve ratio decrease to 20%, by how much does money supply change.

Answer 1

Ans. Reserves, R = $15 million

Required reserve ratio, r = 0.25 or 25%

Currency with people, C = $5 million

Total Deposits, D = R/r = $60 million

Currency to deposit ratio, c = C/D = 5 million / 60 million = 0.08333 or 8.333%
Monetary base, MB = D + C = 60 million + 5 million = $65 million

Money multiplier, m = (1+c)/(c+r) = (1+0.0833)/(0.08333+0.25) = 3.25

=> Money supply = m*MB = 3.25*65 million = $211.25 million

When requiredreserve ratio is decreased to 20%, then,

New money multiplier, m' = (1+0.08333)/(0.08333+0.20) = 3.82

New money supply = m' * MB = 3.82 * 65 million = $248.53 million

Thus, money supply increases by $37.28 million

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