This text applies to all remaining questions b)-e). Suppose there are 100 consumers. Each consumer has savings of £1000 at t=0, which she deposits in a bank. The bank incurs a safeguarding cost of £0.02 per pound kept in its vault. A fraction 0.2 of the depositors will face a liquidity shock and need then to withdraw the funds they deposited at t=1. The rest of the depositors will withdraw their funds at t=2. Suppose the bank can use the funds deposited to lend money to merchants. Each merchant needs to borrow £15,000 at t=0 to invest in a project. The project generates a revenue of £20,000 at t=2, but if prematurely liquidated at t=1 the project only yields £8,000. The bank charges the merchant an interest rate on the loan of 20%. (
b) [5 marks] What is the revenue the bank expects to receive at t=2 from each loan?
(c) [15 marks] Suppose the bank offers depositors who choose to withdraw at t=1 the amount deposited less the safeguarding costs incurred by the bank. What is the size of the cash reserves the bank needs to keep to meet the expected withdrawal requests at t=1? What are then the funds the bank can use to make loans to merchants? How many merchants can the bank lend to at t=0?
(d) [10 marks] Consider the total amount lent to merchants at t=0 you found in your answer to c). Given this amount of loans made at t=0 and the amount paid to depositors who withdraw at t=1, what are the funds the bank has available in period 2? If all these funds are paid to depositors who withdraw in period 2, what is the interest rate they receive? Is it higher than the interest rate paid to depositors who withdraw at t=1?
(e) [10 marks] Compare the amount (found in your answer to d) paid to each depositor who withdraws at t=2 with the one paid to each depositor who withdraws in t=1: will a depositor not subject to a liquidity shock prefer to withdraw at t=1 or t=2? Will the situation be different if now all other depositors choose to withdraw at t=1? When does a bank run occur?
