Money Supply and the Money Multiplier

Deposit $1,000 in a bank and the bank doesn't lock it in a vault. It keeps a slice as reserves and lends the rest out. That loan gets spent, and the money ends up as a deposit in another bank, which again keeps a slice and lends the rest — and so on. Each round adds new deposits without a single new dollar of central bank money entering the system. The textbook name for the total expansion this process implies is the money multiplier.

The mechanism, one round at a time

Suppose a reserve ratio $r$ is the fraction of each deposit a bank must hold back rather than lend out. Starting with an initial deposit $D_0$, the first bank lends out $D_0(1-r)$, which becomes a new deposit elsewhere. That bank lends out $(1-r)$ of that, and so on. Summing every round gives the multiplier:

$$m = \frac{1}{r}$$

In words: the total deposits eventually created from an initial reserve injection equal that injection divided by the reserve ratio — a smaller ratio means more rounds of lending survive before the leftover shrinks to nothing.

Worked example

A reserve ratio of 10% ($r = 0.10$) implies a multiplier of $1/0.10 = 10$. A $1,000 deposit into the banking system: the first bank keeps $100, lends $900. That $900 becomes a deposit elsewhere; that bank keeps $90, lends $810. Continuing this geometric series to its limit, total deposits created across the system approach 1{,}000 \times 10 = \10{,}000$ — ten times the original cash injection, purely from repeated lending and redepositing.

If the reserve ratio instead rose to 20%, the multiplier drops to $1/0.20 = 5$, and the same $1,000 would only support $5,000 of total deposits — a smaller required reserve buffer directly translates into a larger eventual money supply from the same base.

What this means in practice

The textbook multiplier is a clean starting model, but modern central banks — including the Federal Reserve since 2020 — don't actually set a binding reserve requirement for most banks, and empirically banks lend based on capital rules, demand for credit, and risk appetite far more than a fixed reserve ratio. The multiplier is still useful as an intuition for why the banking system as a whole creates more money than the central bank injects, even though the precise mechanical link the formula implies has weakened in practice.