English
Banks operate on a fractional reserve 部分准备金 system: they keep a fraction of deposits as reserves 准备金 and lend the rest. The fraction they must keep is the required reserve ratio 法定准备金率 (rr). Lending creates new deposits, which are re-deposited and re-lent, expanding the money supply by the money multiplier:
$$\text{money multiplier}=\frac{1}{rr}.$$
A new $\$1000$ deposit with $rr=0.1$ leaves $\$900$ in excess reserves, so the banking system can expand the money supply by up to $900\times\frac{1}{0.1}=9\,000$. Use a bank's T-account (assets = reserves + loans; liabilities = deposits) to track required reserves and excess reserves 超额准备金 (the amount available to lend).
Worked example. A bank receives a $\$1000$ deposit with $rr=0.20$. It must hold $0.20\times1000=\$200$ as required reserves, leaving $\$800$ of excess reserves to lend. With a money multiplier of $\dfrac{1}{0.20}=5$, that $\$800$ of new lending can expand the money supply by up to $800\times5=\$4000$ across the banking system.
The T-account after a $1000 cash deposit ($rr=0.10$):
| Assets |
|
Liabilities |
|
| Required reserves |
$100 |
Demand deposits |
$1000 |
| Excess reserves |
$900 |
|
|
The two sides must balance. A single bank can lend only its excess reserves ($900); the banking system as a whole can create up to $900 $\times$ 10 = $9000 of new deposits.
Where the money comes from changes the answer. AP questions test this trap often:
- Cash already in circulation is deposited. The $1000 was already counted in M1 as currency, so the deposit itself does not change the money supply. Only the lending adds money: maximum change $=\$900\times10=\$9000$.
- The Fed buys $1000 of bonds from a bank. The bank swaps bonds for $1000 of reserves, all of them excess. Maximum change in the money supply $=\$1000\times10=\$10\,000$.
- The Fed buys $1000 of bonds from a household, which deposits the payment. The new deposit is new money (+$1000 at once), and banks can lend the $900 of excess reserves (+$9000). Total maximum change $=\$10\,000$.
The multiplier gives a maximum: the real change is smaller if banks keep extra reserves or people hold some of their loans as cash.
In practice. The Federal Reserve cut the required reserve ratio to zero in March 2020, and it has stayed there. The simple money multiplier is still on the AP exam, but in the real U.S. economy the Fed now controls short-term interest rates mainly through the interest it pays on reserves (see Monetary Policy below).
Exam skill: given a required reserve ratio and a deposit, compute excess reserves, the money multiplier, and the maximum change in the money supply.