Question

1. Suppose the Fed decides to increase the money supply. It purchases a government bond worth $2,000 from Antonia, a private citizen. Antonia deposits the check in her account at First National Bank. Supposed the required reserve ratio is 0.2 (20%).

(a) Trace the effect of this change through three banks- First National, Second Federal, and Third State.

(b) How much money will be generated in this banking system?

Answer 1

a). When Antonia will deposit $2,000 in her checking account at First National Bank, the bank will keep 20% of this deposit as required reserves and will lend out( loan out) the excess reserves. Required reserves are a certain percentage of the deposits of the bank which it is required to keep with itself in the form of reserves.

Required reserves= deposits x required reserve ratio

Required reserves= $2,000 x 20%

Required reserves= $2,000 x 20/100

Required reserves= $2,000 x 0.2

Required reserves= $400

Excess reserves= deposits - required reserves

Excess reserves= $2,000 - $400

Excess reserves= $1,600

Hence, the First National Bank will keep $400 as required reserves and will loan out the excess reserves of $1,600.

Now, this amount of $1,600 will get deposited in Second Federal Bank. As such, Second Federal Bank will keep 20% of this deposit as required reserves and will loan out the excess reserves.

Required reserves= deposits x required reserve ratio

Required reserves= $1,600 x 20%

Required reserves= $1,600 x 20/100

Required reserves= $1,600 x 0.2

Required reserves= $320

Excess reserves= deposit - required reserves

Excess reserves= $1,600 - $320

Excess reserves= $1,280

Hence, Second Federal will keep required reserves of $320 and will loan out it's excess reserves of $1,280.

Now, this amount of $1,280 will get deposited at Third State Bank. Third State Bank will keep 20% of this deposit as required reserves and will loan out the excess reserves.

Required reserves= deposit x required reserve ratio

Required reserves= $1,280 x 20%

Required reserves= $1,280 x 20/100

Required reserves= $1,280 x 0.2

Required reserves= $256

Excess reserves= deposit - required reserves

Excess reserves= $1,280 - $256

Excess reserves= $1,024

Hence, Third State Bank will keep $256 as required reserves and will loan out it's excess reserve of $1,024.

So, the total amount of deposit created by tracing the three banks are- $2,000+ $1,600 + $1,280= $4,880.

The total amount of loans given by the three banks are- $1,600+ $1,280 + 1,024= $ 3,904

b) This process of depositing the money and loaning out the excess reserves by the banks will continue until the last amount deposited is too small to generate a new loan. The total amount of money generated in the banking system can be calculated as-

​​​​​​New deposits= 1/RR x  D

( Where RR is the required reserve ratio and D is change in initial deposit).

New deposits= 1/20% x $2,000

New deposits= 1/0.2 x $2,000

New deposits= 5 x $2,000

New deposits= $10,000

Hence, $10,000 will be generated in this bankings system.

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