Module 04 · Chapters 4

Money Multiplier & Banks

How €1 of base money becomes €5 of broad money.

“Where deposits, reserves, and lending make their own money.”

~25 min· 3 sub-skills·4 exercises0% mastered

Banks don't lock up every euro you deposit — they keep a fraction (θ, reserve ratio) and lend the rest. The lent funds are deposited in another bank, fraction θ kept again, and so on. This lending cascade turns base money H into broad money M several times larger.
Money multiplier
$M \;=\; \frac{1}{c + \theta(1-c)}\,H$
$M$
broad money supply (cash + deposits)
$H$
high-powered / base money (cash + bank reserves)
$c$
currency-deposit ratio (cash / total money)
$\theta$
reserve-deposit ratio
When c = 0 (no cash held outside banks), the multiplier is just 1/θ.
Figure · Lending rounds — animated
Modern (rate-targeting): CB picks i, M^s adjusts to clear.
Each round keeps θ as reserves, lends out (1 − θ). The geometric series sums to the multiplier.
Watch out·Modern caveat: M is endogenous
In the modern central-banking framework (Module 3), the CB targets i, and supplies whatever H is needed. The multiplier is now a description of the plumbing, not a policy lever. It still matters: it tells you the link between the operational instrument (H, reserves) and household-facing M.
Worked example · Worked example — compute M
H = 200, c = 0, θ = 0.20.
1. 1
  Plug into the formula: M = 1/[0 + 0.2(1 − 0)] · 200.
  $M = (1/0.20) \cdot 200$
2. 2
  = 5 × 200 = 1,000.
  $M = 1000$
✓ M = €1,000 bn (multiplier = 5).
Exercise · multiple choice · +8 XP
What's in M, what's in H?
Which is part of broad money M but not base money H?
Exercise · numerical · +12 XP
Compute the multiplier
θ = 0.10, c = 0. Compute the money multiplier.
Your answer
Exercise · numerical · +14 XP
With currency leakage
θ = 0.20, c = 0.10. Compute the multiplier.
Your answer
Exercise · true false · +10 XP
Balance-sheet identity
On a commercial bank's balance sheet, deposits are a liability and reserves are an asset.
"On a commercial bank's balance sheet, deposits are a liability and reserves are an asset."

Mastery check

5 questions · pass with 80%

Answer all five to confirm you've internalised the module. A passing run unlocks the next module.

Q1
If households hold no cash (c = 0) and θ = 0.25, the multiplier is:
Q2
"M ≥ H is always true."
Q3
Households shift towards cash (c rises). What happens to the multiplier?
Δc > 0, θ unchanged.
Q4
θ = 0.05, c = 0. Multiplier = ?
Q5
When a bank lends €100, what happens on its balance sheet?

0 / 5 answered

Exam pitfalls

Stating the multiplier as 1/θ when c > 0. Always use 1/[c + θ(1−c)].
Confusing M (broad) with H (base). Each has its own dynamics.
Treating M^s as exogenous in the modern framework — it isn't; the CB picks i, M^s adjusts.