Suppose the reserve requirement is 20 percent and banks hold no excess reserves. A $1 billion purchase of government securities by the Fed will:

increase the money supply by $5 billion

Explanation:

When the Fed carries on an expansionary monetary policy it lowers interest rates and purchases government securities in order to increase the money supply in an attempt to boost economic growth.

The increase in the money supply is determined by the total amount of the open market operations carried out by the Fed ($1 billion) and the money multiplier ( = 1/reserve ratio = 1/20% = 5).

Total increase in money supply = $1 billion x 5 = $5 billion