Question

Suppose the required reserve ratio is 10%, excess reserves holdings are 65% of deposits, and currency holdings are 45% of deposits. If the Fed buys $500 million worth of securities, what will be the change in the money supply (measured in dollars)?

Answer 1

Excess reserve ratio (ER) = 65% = 0.65

Currency to deposit ratio (C/D) = 45% = 0.45

Required reserve ratio (RR) = 10% = 0.1

Money multiplier = [1 + (C/D)] / [(C/D) + ER + RR]

Money multiplier = [1 + 0.45] / [0.65 + 0.45 + 0.1]

Money multiplier = (1.45 / 1.20)

Money multiplier = 1.2083

Fed buys $500 million worth of securities. It will increase the monetary base by $500 million.

Change in money supply = Money multiplier * Change in monetary base.

=> Change in money supply = 1.2083 * ($500 million)

=> Change in money supply = $604.167 million.

Hence, the money supply will increase by $604.167 million