A 10% reserve ratio lets each round lend out 90% of what it receives
A bank receiving 1,000 in deposits must hold 100 against a 10% requirement and can lend 900. That 900 is deposited somewhere, 90 is held and 810 lent, and so on. The series sums to 1/0.10 = 10, so 1,000 of new reserves can support 10,000 of deposits. The multiplier is simply the reciprocal of the reserve ratio.
The relationship is steep at low ratios. A 5% requirement gives a multiplier of 20; a 20% requirement gives 5. This is why reserve requirements were historically a policy lever — changing them changes how much money the banking system can create from the same base.
Cash held outside banks and excess reserves both break the chain
The model assumes every loan returns to the banking system as a deposit and every bank lends to its legal limit. Neither holds. Cash withdrawn and held outside banks leaves the circuit entirely, and banks routinely hold reserves well above the requirement — since 2008 they have held enormous excess reserves, which pays interest and carries no credit risk.
The observed money multiplier in most developed economies has therefore run far below the textbook figure, and in the period after 2008 the US ratio of broad money to base money fell below the theoretical minimum the requirement implied. A model producing 10 when the observed figure is nearer 3 is describing a mechanism, not a measurement.
Banks lend first and find reserves after, rather than waiting to be given them
The multiplier model implies causality running from reserves to lending: the central bank supplies reserves and banks expand credit on top. Most central banks now describe the relationship the other way — banks extend credit when they see profitable lending opportunities and creditworthy borrowers, creating deposits in the act, and then obtain whatever reserves settlement requires.
Under that description the binding constraints are capital requirements, loan demand and risk appetite rather than reserve ratios. Several major economies, including the US since 2020, have set reserve requirements to zero outright, which makes the textbook multiplier undefined and the mechanism it describes purely historical.
A teaching model, and an upper bound
This is the standard model in every introductory course and remains a clear illustration of how fractional reserve banking creates money from a base. Treat the output as the maximum the requirement permits under ideal assumptions, not as a forecast of what an injection will do.
For the amount of money actually in circulation, the monetary aggregates — M1, M2 and their equivalents — are measured directly rather than inferred from a multiplier. Comparing the implied figure here against the observed aggregate is itself a useful exercise in how far the model sits from the system it describes.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.