Check Your Understanding

1. Question

   Suppose you are a depositor at First Street Bank. You hear a rumor that the bank has suffered serious losses on its loans. Every depositor knows that the rumor isn’t true, but each thinks that most other depositors believe the rumor. Why, in the absence of deposit insurance, could this lead to a bank run? How does deposit insurance change the situation?

   Even though you know that the rumor about the bank is not true, you are concerned about other depositors pulling their money out of the bank. And you know that if enough other depositors pull out their money, the bank will fail. In that case, it is rational for you to withdraw your money before the bank fails. All depositors will think like this, so even if they all know that the rumor is false, they may still rationally pull out their money, leading to a bank run. Deposit insurance leads depositors to worry less about the possibility of a bank run. Even if a bank fails, the FDIC will currently pay each depositor up to $250,000 per account. This will make you much less likely to withdraw your money in response to a rumor. Since other depositors will think the same, there will be no bank run.

2. Question

   A con artist has a great idea: he’ll open a bank without investing any capital and lend all the deposits at high interest rates to real estate developers. If the real estate market booms, the loans will be repaid and he’ll make high profits. If the real estate market goes bust, the loans won’t be repaid and the bank will fail—but he will not lose any of his own wealth. How would modern bank regulation frustrate his scheme?

   The aspects of modern bank regulation that would frustrate this scheme are capital requirements and reserve requirements. Capital requirements mean that a bank has to have a certain amount of capital—the difference between its assets (loans plus reserves) and its liabilities (deposits). Thus, the con artist could not open a bank without putting in any of his own wealth because his bank would need the required amount of capital—that is, it would need to hold more assets (loans plus reserves) than deposits. So the con artist would be at risk of losing his own wealth if his loans turned out badly. Also, the reserve requirement would prevent the con artist from lending out all of the deposits.

3. Question

   Assume that total reserves are equal to $200 and total checkable bank deposits are equal to $1,000. Also assume that the public does not hold any currency and banks hold no excess reserves. Now suppose that the required reserve ratio falls from 20% to 10%. Trace out how this leads to an expansion in bank deposits.

   Since they have to hold only $100 in reserves, instead of $200, banks now lend out $100 of their reserves. Whoever borrows the $100 will deposit it in a bank (or spend it, and the recipient will deposit it in a bank), which will lend out $100 × (1 − rr ) = $100 × 0.9 = $90. The borrowed $90 will likewise find its way into a bank, which will lend out $90 × 0.9 = $81, and so on. Overall, deposits will increase by $100/0.1 = $1,000.

4. Question

   Take the example of Silas depositing his $1,000 in cash into First Street Bank and assume that the required reserve ratio is 10%. But now assume that each recipient of a bank loan keeps half the loan in cash and deposits the rest. Trace out the resulting expansion in the money supply through at least three rounds of deposits.

   Silas puts $1,000 in the bank, of which the bank lends out $1,000 × (1 − rr ) = $1,000 × 0.9 = $900. Whoever borrows the $900 will keep $450 in cash and deposit $450 in the bank. The bank will lend out $450 × 0.9 = $405. Whoever borrows the $405 will keep $202.50 in cash and deposit $202.50 in the bank. The bank will lend out $202.50 × 0.9 = $182.25, and so on. Overall, this leads to an increase in deposits of $1,000 + $450 + $202.50 + . . . . Unlike the case in which loan recipients deposit their entire loans, this story involves loans partially held as cash. That cash is part of the money supply, so the calculation of the change in the money supply must account for both the reduction in cash holdings by Silas and the additional amounts held in cash by borrowers. That is, the amount of currency in circulation changes by −$1,000 + $450 + $202.50 + . . . . The money supply therefore increases by the sum of the increase in deposits and the change in currency in circulation, which is $1,000 − $1,000 + $450 + $450 + $202.50 + $202.50 + . . . and so on.