A deposit of $4000 is made in a “first-generation” bank in a many-bank system wi

Question

A deposit of $4000 is made in a “first-generation” bank in a many-bank system with a 5 percent resents require­ment.

a. How much can this bank lend and still meet the reserve requirement?

b. What is the total maximum expansion of the money supply that will occur after all banks in the system have finished with the credit-expansion process?

c. What would be your answers to the above questions if all banks wish to carry 20 percent additional excess reserves?

d. What would be your answers if, in addition to the 20 percent excess reserves, somewhere along the chain of deposit expansion $1000 is removed from the banking system and placed in a cookie jar?

Explanation / Answer

(a) Money multiplier (MM) = 1 / Reserve requirement = 1 / 0.05 = 20

So, Bank has to set aside $4000 x 5% = $200 as required reserves, and can lend upto $(4000 - 200) = $3800 (which is called the excess reserves).

(b) Total maximum expansion = Initial deposit x MM = $4000 x 20 = $80,000

(c) New excess reserves = $3800 x 1.2 = $4560

So, Bank has to set aside $4000 x 5% = $200 as required reserves, and can lend upto $(4560 - 200) = $4360.

Total maximum expansion = Initial deposit x MM = $4000 x 20 = $80,000

(d) In this case, Currency drain (CD) = $1000 / $4000** = 0.25 (25%).

MM = (1 + CD) / (CD + reserve requirement) = (1 + 0.25) / (0.25 + 0.05) = 1.25 / 0.3 = 4.17

So, Bank has to set aside $4000 x 5% = $200 as required reserves, and can lend upto $(4560 - 200) = $4360.

Total maximum expansion = Initial deposit x MM = $4000 x 4.17 = $16,667

**Assuming $1000 is removed for every $4000 of new deposits

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