Assume there is no leakage from the banking system and that all commercial banks are loaned up. The required reserve ratio is 12.5%. If the Fed buys $20 million worth of government securities from the public, the change in the money supply will be

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When the Fed buys $20 million worth of government securities, the sellers receive a check drawn against the Fed's account, which increases the reserves of the banking system by $20 million. Given the required reserve ratio of 12.5%, this increase in reserves can support up to $160 million in new loans and deposits ($20 million/0.125). Therefore, the money supply will increase by $160 million.

Assume There Is No Leakage from the Banking System and That