Question 1: (Diamond-Dybvig Model) Consider an economy with a bank and four depositors, {A, B, C, D). Each depositor saves $1,000 in the bank at t = 0 (i.e., $4,000 in total). If the depositors withdraw their money at t = 1, they get $1000. If they withdraw at t = 2, they get $2000. The bank invests half of the deposits in long-term investments and half in short-term investments. The long-term investments pay two times the amount invested at t = 2. Early liquidation of the investments at t = 1 pays 0.5 times the original amount invested. The short-term investments pay the original amount if it is withdrawn at t = 1 or t = 2. The table below shows the initial bank balance sheet. Liabilities Asset Asset Long-term investments Short-term investments $2,000 $2,000 Deposits $4,000 a) Prove that the bank is not able to repay the depositors, if they all withdraw their money at t=1. The bank follows a first-come-first-serve principle. Depositor A knows that the other three depositors will withdraw their money at t = 1. Suppose that Depositor A does not discount future cash flows. b) Should A wait until t = 2 to withdraw or withdraw at t = 1? Explain. c) Suppose the government provides an insurance on depositors' bank accounts (i.e., the government will pay the promised return on deposits i the bank is not able to pay it). Should A wait or withdraw at t = 1? Explain