Assume that the reserve requirement is 20%. Also, assume that banks do not hold excess reserves and there is no cash held by the public. The Federal Reserve decides that it wants to expand the money supply by $40 million.
a. If the Fed is using open-market operations, will it buy or sell bonds?
b. What quantity of bonds does the Fed need to buy or sell to accomplish the goal? Explain your reasoning.

Open market operations refer to buying 7 selling of government securities, to regulate money supply. To increase money supply, central bank buys the government bonds. As, purchase transaction from commercial bank or public imply they have more liquid money supplied.

Money multiplier reflects the multiple change in total money deposits, due to increase in initial deposits.

Final Deposits = (1 / RR) x Initial Deposits; where RR = Reserve requirement

Needed increase in money supply = 40 million, Reserve requirement = 20%

∴ 40 = ( 1 / 0.20 ) x Initial deposits

40 = 5 x Initial Deposits

Initial Deposits = 40 / 5

Initial deposits = 8