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 As 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]

hey im really stuck on this one question could you please help me out :)