How fractional-reserve banking turns base money into broad money, and the leaks in the process.
Warming up the engine…
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
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.
The multiplier is a CEILING, not a mechanism, banks need willing creditworthy borrowers, not just reserves.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at B 40, M 80.
Equilibrium: B* = 40.0, M* = 80.0
Current equations
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.