Money multiplier
The textbook ratio m = 1/R describing the maximum deposit money a banking system could support on a given reserve base — a ceiling, not a description of how banks actually operate.
Also called: deposit multiplier, fractional reserve multiplier.
The model runs a chain: a deposit arrives, the bank keeps a fraction R and lends the rest, the loan is redeposited, and so on. Summed to infinity, one unit of base money supports 1/R units of deposits.
It is a useful first mental model and a poor description of reality. Modern central banks target an interest rate rather than a quantity of reserves, several have set reserve requirements to zero — the Fed did so in March 2020 — and banks are constrained by capital, regulation and demand for credit long before reserves bind.
Keeping the model while knowing its limits is the honest position. It tells you what an unconstrained system could do, and the gap between that and observed lending is itself the interesting quantity.
The mechanics
- Formula
- m = 1 / R, so total deposits M = D × (1 / R).
- Assumes
- No cash leakage, every bank lent to its limit, and a binding reserve requirement.
- Reality check
- Post-2008, base money multiplied while broad money did not.
The common misreading
That the multiplier describes causation — that reserves are lent out and multiply. Lending creates deposits first; reserves are managed afterwards, and the central bank supplies whatever quantity its rate target requires.
Related terms
- Broad moneyMoney the public can actually spend — currency plus bank deposits and close substitutes — most of which is created by commercial banks when they lend.
- Monetary baseThe total of banknotes in circulation and commercial bank reserves — every form of money that is a direct liability of the central bank.
- Bank reservesDeposits that commercial banks hold at the central bank — the settlement asset banks use to pay each other, and a liability of the central bank rather than an asset it owns.
Primary sources
Post it yourself
Reading a definition is not the same as being able to work the mechanism. The playable teaser walks you through a real central bank operation, entry by entry.
Try the T-account demo