Question

Consider 2 banks. Each have $100 million in checkable deposits. Both face a required reserve ration of 10%. Bank A keeps no excess reserves, while Bank B keeps $10 million in excess reserves. Both banks loan out all remaining funds into loans. Now assume both banks face a deposit outflow of $5 million, calculate the new level of reserves required for Bank A and Bank B. Do either bank have a reserve short fall? If so what would the cost of making up the short fall be assuming they take a discount loan with a rate of .25%?

Answer 1

Bank A

Checkable deposits = $100 million

Reserve ratio = 10% or 0.10

Required reserves = Checkable deposits * Reserve ratio = $100 million * 0.10 = $10 million

Bank A has to maintain $10 million as required reserves.

Excess reserves = Checkable deposits - Required reserves = $100 million - $10 million = $90 million

Bank A has excess reserves of $90 million. However, it does not keep any excess reserves and loans out all excess reserves.

So, it has made loans of $90 million.

Now, Bank A faces a deposit outflow of $5 million.

This will reduce the checkable deposits of Bank A by $5 million. Now, it will have only $95 million as checkable deposits.

Its reserves will also reduce by $5 million and it will now have $5 million as reserves.

Calculate new level of required reserves -

New level of required reserves = New level of checkable deposits * Reserve ratio = $95 million * 0.10 = $9.5 million

Thus,

The new level of reserves required for Bank A is $9.5 million.

The Bank A has only $5 million in reserves.

Thus,

Bank A have a reserve shortfall.

So, it have to arrange additional $4.5 million.

For this Bank takes a discount loan with a rate of 0.25%.

Bank A will take the discount loan of $4.5 million.

Interest paid = $4.5 million * 0.0025 = $11,250

Thus,

The cost of making up the shortfall for Bank A is $11,250.

Bank B

Checkable deposits = $100 million

Reserve ratio = 10% or 0.10

Required reserves = Checkable deposits * Reserve ratio = $100 million * 0.10 = $10 million

Bank B has to maintain $10 million as required reserves.

Excess reserves = Checkable deposits - Required reserves = $100 million - $10 million = $90 million

Bank B has excess reserves of $90 million. However, it keeps $10 million excess reserves and loans out all the reamaining excess reserves.

So, it has made loans of $80 million.

Total reserve (required reserves + excess reserves held) of bank B is $20 million.

Now, Bank B faces a deposit outflow of $5 million.

This will reduce the checkable deposits of Bank B by $5 million. Now, it will have only $95 million as checkable deposits.

Its reserves will also reduce by $5 million and it will now have $15 million as reserves.

Calculate new level of required reserves -

New level of required reserves = New level of checkable deposits * Reserve ratio = $95 million * 0.10 = $9.5 million

Thus,

The new level of reserves required for Bank B is $9.5 million.

The Bank B has $15 million in reserves.

Thus,

Bank B does not have a reserve shortfall.