Assume there is $400 billion of currency in circulation in the economy outside the banking system, that depository institutions in the economy have $800 billion in checkable deposits, and that those same depository institutions have $80 billion in reserves on deposit at the central bank. All depository institutions are "loaned out" -- that is, there are no excess reserves in the financial system.
If the central bank plans to add $10 billion to the supply of currency in circulation outside the banking system, what amount of open market purchases or sales of Treasury securities must it undertake in order to increase the M1 money supply by $100 billion?
Formula: Money Supply = Bank deposits + currency in circulation
Formula: Reserve Deposit Ratio = Reserve/bank deposits
Reserve deposit ratio = 80/800 = ...
The solution find outs how much the central bank will purchases or sales of Treasury securities must it undertake in order to increase the M1 money supply by $100 billion.