Questions: Bank Runs, Deposit Insurance, and the Lender of Last Resort

Question 1

A bank holds $10 million in reserves and $90 million in sound loans, funded by $92 million in deposits and $8 million of owners' equity. The loans would sell for only 60% of their value if sold today. Depositors suddenly demand $40 million. What happens?

• A. The bank pays easily from reserves and loses nothing
• B. To raise the other $30 million it must sell $50 million of loans, losing $20 million, which exceeds its equity and leaves it insolvent
• C. The money multiplier automatically raises the bank's reserves
• D. Depositors must accept interest instead of cash

Answer: (B)

Reserves cover $10 million. Raising $30 million more at 60 cents on the dollar means selling $50 million of loans, a $20 million loss. That loss is larger than the $8 million equity cushion, so the run itself turns a sound bank into an insolvent one.

Question 2

In the Diamond-Dybvig model of banking, a bank run can occur even when no depositor has new information that the bank's loans are bad.

• T. True
• F. False

Answer: True

The model has two equilibria. If each depositor expects others to wait, waiting is best. If each expects others to withdraw, withdrawing early is best, because late withdrawers may get nothing. A run can therefore be self-fulfilling, triggered by expectations alone.

Question 3

Which drawback of deposit insurance do economists most often point to?

• A. It increases the number of bank runs
• B. It reduces depositors' incentive to monitor bank risk, which can encourage banks to take more risk
• C. It makes bank deposits illiquid
• D. It forces banks to hold 100% reserves

Answer: (B)

When deposits are guaranteed, depositors care less about how safely a bank invests. This is a form of moral hazard, and it is one reason insured banks are also subject to capital requirements and supervision.

Question 4

Explain the difference between a bank being illiquid and a bank being insolvent, and why the distinction matters for a lender of last resort.

Model answer: An illiquid bank has assets worth more than its liabilities but cannot turn them into cash fast enough to meet withdrawals. An insolvent bank has assets worth less than its liabilities. A lender of last resort can lend safely to an illiquid bank against good collateral and stop a run, but lending to an insolvent bank only delays losses and shifts them to the lender.

This distinction underlies Walter Bagehot's 1873 advice in Lombard Street: lend freely, at a high rate, against good collateral.