Money Multiplier

How fractional-reserve banking turns base money into broad money, and the leaks in the process.

Equilibrium: B* = 40.0, M* = 80.0

Current equations

Broad money created: M = 2·BMonetary base: B = 40No banking (M = B): M = 1·B

Banks create money. When the central bank adds a dollar of base money, banks lend it, the loan gets deposited, most of it is lent again, and the process repeats. The steep line shows the broad money that emerges; the dashed 45-degree line is a world with no banks at all.

Shift the curves

Monetary base (central bank money)0

QE and open-market purchases push the base out; the banking system multiplies it.

Reserve ratio banks hold0

The more of each deposit banks keep as reserves, the smaller the multiplier.

The Money Multiplier model, in writing

Definition

The link from base money to broad money under fractional-reserve banking: deposits get re-lent, redeposited, and re-lent again.

Multiplier = 1/rr (simple), or (1+c)/(rr+c+e) with cash and excess reserves

The intuition

Your $100 deposit becomes someone's $90 loan becomes someone else's $90 deposit, and the geometric series sums to $1000 of money on $100 of base at a 10% reserve ratio. Leaks, cash holdings, cautious banks, shrink it, which is why crisis-era money printing didn't explode broad money.

Exam tip

The multiplier is a CEILING, not a mechanism, banks need willing creditworthy borrowers, not just reserves.

Related models in Macro Foundations

AS-AD (Aggregate Supply – Aggregate Demand) →Keynesian Cross & the Multiplier →Phillips Curve →Business Cycle Phases →