FED Buys and Sells Government Securities at whatever price to accomplish goal because the FED can just write a check and print the money. Profit is not goal of FED. Expand: Buy G
Bank 1: RR = 20%
Initial Position 10 G purchase New Loan

Bank 2: RR = 20% First term geo series is D D = 10 in Bank 2
Initial Position 10 deposit from BK 1 New loan

Second term geo series is D L = 8 in Bank 2 that becomes D D in Bank 3

Bank 3: RR = 20% Seconed term geo series is D D in Bank 3
Initial Position 8 deposit from BK 2 New loan

Third term geo series is D L = 6.4 in Bank 3 that becomes D D in Bank 4

Geometric series

First term = D G = 10

Second term = (1-RR)D G = 0.8(10) = 8

Third term = (1-RR)²D G= 0.8[0.8(10)] = 6.4

Notes:

1. The term FED stands for the US central bank which is the Federal Reserve System. Decisions are made in Washington at the Board of Governors of the Federal Reserve System. Greenspan is current the head of the FED. Many decisions are executed in New York by the open market committee.

2. There are many ways this expansion could take place. To avoid Murphy's Law we only consider one way.

3. The geometric series is the MAXIMUM possible expansion. The magnitude of the expansion varies during the business cycle. In good times banks are more willing to make loans than in bad times. Not all of the loan sequence is deposited in the US. Some goes abroad. Also, some proceeds are taken out in cash. In bad times banks are reluctant to make loans because they fear default on existing loans and want to increase free reserves to cover possible losses.

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