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can anyone help with this question?
What would happen to the money supply if the federal reserve made an open market sale of 5 billion worth of government securities to a private citizen. Assume that the bank with which the private citizen does business is all loaned up, has reserves of $20 million, deposits of $100 million and must follow a required reserve policy of 20%

As stated, the answer to your question is the bank goes bankrupt, chaos ensues.

Now, I presume you meant to say the open market sale is 5 Million, not 5 Billion. So, following Deep Throat's advice, Follow the Money.

From the initial sale, the citizen gets a 5-million security and writes a check for 5-million. So far, money supply goes down by 5-million.
The bank now has 15 million in reserves and deposits of 95 million. However, its new reserve requirement is .2*95 = 19 million. To meet the shortfall, the bank must "recall" some of its outstanding loans. (For now, nevermind how it does so). The bank recalls 4-million, which comes from the reserves of some other bank(s). So, money supply drops by another 4 million. Well, this causes a reserve short fall in other banks, causing them to recall their loans, causing further decreases in reserves, causing further decreases in the money supply.

Where will in all end you may ask.

By now, in your Macro class, you have learned something about the money multiplier. (Plz refer to your text for more details). The money multiplier is 1/rr, where rr is the reserve requirement ratio. So, 1/.2 = 5. The multiplier is 5. So, at the end of the process, the 5 million in securities sales results in a 5*5=25 million decrease in the money supply.

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