money multiplier

Imagine the same banknote being put to work over and over. You deposit $1,000. Your bank keeps a little and lends most of it to someone, who spends it, and the receiver deposits it in their bank, which again keeps a little and lends most of it on, and so on. One original deposit ripples through the banking system, supporting far more than $1,000 of deposits in total. The money multiplier is the number that captures how big that final total grows relative to the original injection.

The textbook formula is simple: the money multiplier equals 1 divided by the reserve ratio. If banks keep 10% of deposits as reserves (a reserve ratio of 0.10), the multiplier is 1 / 0.10 = 10, meaning $1,000 of new reserves can ultimately support up to $10,000 of deposits. Trace it: deposit $1,000, the bank lends $900; that $900 is deposited elsewhere and $810 is lent; then $729 is lent; and the shrinking chain ($900 + $810 + $729 + ...) sums to $9,000 of new loans on top of the original $1,000 — $10,000 in all. The lower the reserve ratio, the bigger the multiplier; the more cash people hold outside banks, the smaller it gets, since cash under a mattress can't be re-lent.

The money multiplier is a clean way to see how fractional-reserve banking turns a small base of reserves into a much larger money supply. But economists today treat the simple formula with real caution. In modern systems the central bank usually sets interest rates, not a fixed quantity of reserves, and banks lend when they find creditworthy borrowers and then obtain reserves as needed — so causation often runs the other way (loans create deposits, deposits drive reserve needs). The textbook multiplier is a useful first picture of money creation, not a precise lever that policymakers actually pull.