1. Assume there are three time periods, t=0,1,2. There are 100 people with $1 each and one bank, Bank A. At time 0, everyone (including the bank) can invest in an illiquid asset that pays $2 at the end of period 2 . If someone decides to cash out on the illiquid asset before time 2 , they get one dollar back. Assume that there are two types of people, patient and impatient. An impatient person wants access to their funds immediately, whereas a patient person can wait for 2 periods to access their funds. Each individual has a choice between investing in the illiquid asset or depositing their dollar with Bank A. Bank A offers the following contract to all depositors: Withdraw at time 1 , and get $1.28 or Withdraw at time 2 , and get $1.81. Hence if they deposit their funds with Bank A, each person can access their deposit at any time. For example, if you are a depositor, you can wait two periods to withdraw your money from the bank, or you can withdraw after one period also and still make a positive return. In other words, bank deposits are liquid and available at any time. Assume that the bank receives $100 in deposits and knows 25 persons will withdraw at time 1 and 75 persons at time 2. (i) What essential function does the bank provides to depositors in this economy [Hint: bold terms will give you the answer] [2 marks] (ii) Show that Bank A's promise to pay 25 people $1.28 at the end of time 1 and $1.81 to 75 people at time 2 is feasible. [Hint: Bank A invests the funds that depositors will not demand at time 1 in the illiquid asset and use the return from the investment to pay depositors at time 2) [4 marks] (iii) Now assume that there is a rumour that Bank A has used the deposits to make some bad investments. How many people need to show up at time 1 to cause a bank run on Bank A (i:e., Bank A becomes insolvent at the end of time 1 and will not be able to pay all depositors, even their initial deposit)? [Hint, calculate how many people need to show up at time 1 for Bank A to become insolvent] 2 marks] 1. Assume there are three time periods, t=0,1,2. There are 100 people with $1 each and one bank, Bank A. At time 0, everyone (including the bank) can invest in an illiquid asset that pays $2 at the end of period 2 . If someone decides to cash out on the illiquid asset before time 2 , they get one dollar back. Assume that there are two types of people, patient and impatient. An impatient person wants access to their funds immediately, whereas a patient person can wait for 2 periods to access their funds. Each individual has a choice between investing in the illiquid asset or depositing their dollar with Bank A. Bank A offers the following contract to all depositors: Withdraw at time 1 , and get $1.28 or Withdraw at time 2 , and get $1.81. Hence if they deposit their funds with Bank A, each person can access their deposit at any time. For example, if you are a depositor, you can wait two periods to withdraw your money from the bank, or you can withdraw after one period also and still make a positive return. In other words, bank deposits are liquid and available at any time. Assume that the bank receives $100 in deposits and knows 25 persons will withdraw at time 1 and 75 persons at time 2. (i) What essential function does the bank provides to depositors in this economy [Hint: bold terms will give you the answer] [2 marks] (ii) Show that Bank A's promise to pay 25 people $1.28 at the end of time 1 and $1.81 to 75 people at time 2 is feasible. [Hint: Bank A invests the funds that depositors will not demand at time 1 in the illiquid asset and use the return from the investment to pay depositors at time 2) [4 marks] (iii) Now assume that there is a rumour that Bank A has used the deposits to make some bad investments. How many people need to show up at time 1 to cause a bank run on Bank A (i:e., Bank A becomes insolvent at the end of time 1 and will not be able to pay all depositors, even their initial deposit)? [Hint, calculate how many people need to show up at time 1 for Bank A to become insolvent] 2 marks]
