Suppose there are 20 commercial banks in Country A, including WBS Bank. Consider the following case for WBS Bank:

WBS Bank has 100 depositors; each of them has a deposit of £200 in the bank.

The current cash reserve ratio is 10% at WBS bank and the remaining deposits are all used to grant loans (loans provide a gross return rate of 1.15).

 

WBS Bank could also sell part of their loans to meet the cash demand in emergencies. The gross rate of return from loan sales (denoted by R) depends on the total amount of loans to be sold in the market (denoted by L), and it is given by

 

                                      

 

The manager of WBS bank estimates that the proportion of withdrawals is much lower than the required reserve ratio of 5% in Country A. In fact, he knows that usually less than 2% of depositors withdraw their deposits. The manager believes higher profits can be achieved by lowering their reserve ratio.

 

a)  Given the information above, calculate the gross return to WBS bank if they change the reserve ratio to the required rate in Country A and use the remaining money for loans.  

b)  Suppose that after changing the reserve ratio WBS bank faced higher than expected withdrawals (10% of depositors withdraw at Time 1) and decided to sell £1000 loans to meet the unforeseen withdrawals.

 Calculate the overall gross return to the bank (assuming that there are no other loan sales in the market).

 

c)  Critically discuss the potential issues with the previous results when there are externalities in the market. Use calculations in your analysis.