Intermediatemacroeconomics

The Money Multiplier

Overview

The money multiplier is the most famous formula in monetary economics: a single number linking the monetary base to the broad money supply. This lesson derives it from the fractional-reserve lending chain, works through a clean numerical example, and then explains — honestly — why actual multipliers are smaller, move around, and broke down after 2008. Treat it as an instructive upper bound, not a law of nature, and you will use it correctly.

Learning objectives

State the simple money multiplier formula and define each term.
Work a numerical example of deposit expansion through the banking system.
Explain why the textbook multiplier is a maximum, not a prediction.
Describe how currency drains and excess reserves shrink the multiplier.
Interpret the post-2008 collapse of the measured multiplier.

Deriving the Simple Multiplier

Start with the fractional-reserve chain: a $1,000 new deposit with a 10% reserve ratio lets the first bank lend$ 900, the next bank lend $810, the next$ 729, and so on. Each round's loan is 90% of the previous round's deposit, forming a geometric series: $1,000 +$ 900 + $810 + ... . The series sums to$ 1,000 / 0.10 = $10,000 in total deposits. In general, the maximum deposit expansion equals the initial reserves divided by the reserve ratio — so the simple money multiplier is 1 / rr, where rr is the reserve ratio. With rr = 10%, the multiplier is 10.

The formula

Simple money multiplier = 1 / reserve ratio. It gives the MAXIMUM broad-money expansion per unit of new reserves, assuming no leakages.

A Worked Example, Round by Round

Suppose the central bank buys $1,000 of bonds from Bank A, crediting its reserves. Bank A keeps$ 100 (10%) and lends $900 to a borrower, who pays a supplier; the supplier deposits$ 900 in Bank B. Bank B keeps $90, lends$ 810; Bank C keeps $81, lends$ 729. After three rounds, new deposits total $1,000 +$ 900 + $810 =$ 2,710, converging toward $10,000. Notice that at every step, total reserves never exceed the original$ 1,000 — the multiplication is in deposits, claims on reserves, not in reserves themselves.

Leakage 1: Currency Drains

The simple formula assumes every loan proceed is redeposited in a bank. In reality, borrowers and recipients hold some of the money as physical cash — a currency drain — and cash in wallets cannot be relent by banks. If the public holds a fraction c of deposits as currency, each lending round leaks, and the multiplier falls below 1/rr. This is why economists use a fuller formula with both the currency ratio and the reserve ratio. In cash-heavy economies, the currency drain is the biggest reason the textbook multiplier overstates reality.

Leakage 2: Excess Reserves

Banks are not forced to lend every dollar above required reserves; reserves they voluntarily hold back are excess reserves, and each idle dollar stops a lending chain cold. When banks are scared — fearing defaults or runs — they hoard excess reserves and the effective multiplier collapses. After 2008, banks sat on trillions in excess reserves while the monetary base exploded, and broad money grew only modestly. The episode proved the multiplier is driven by bank behavior, not mechanically by the base.

Not a policy lever

Central banks cannot simply 'set' the multiplier. They influence reserves and interest rates; banks and the public decide currency holdings and lending — so the multiplier is an outcome, not an instrument.

Using the Multiplier Correctly

The multiplier's real value is conceptual: it shows how fractional reserves amplify base money into broad money, and it organizes thinking about leakages. As a forecasting tool it is weak, because the currency ratio, the excess-reserve ratio, and credit demand all shift with the economy. Modern central banks therefore target interest rates, not money aggregates, and treat the multiplier as background theory. Remember it as an illuminating upper bound — 1/rr with no leakages — and you will never misuse it on an exam or in analysis.

Key points

The simple money multiplier equals 1 divided by the reserve ratio (maximum expansion).
Deposit expansion is a geometric series: each round lends (1 − rr) of the previous deposit.
Total reserves never multiply — only deposit claims on those reserves do.
Currency drains and excess reserves are leakages that shrink the actual multiplier.
After 2008, excess-reserve hoarding collapsed the measured multiplier, proving it is behavioral, not mechanical.

Common misconceptions

✗ Myth: If the central bank doubles the monetary base, the money supply doubles.

✓ Truth: That holds only if the multiplier is constant, which it is not. Banks may hoard the new reserves as excess reserves and the public may hold more cash, breaking the proportional link — exactly what happened after 2008.

✗ Myth: The money multiplier means banks multiply actual cash.

✓ Truth: Banks multiply deposit liabilities, which are claims on reserves. The stock of base money (cash + reserves) is unchanged by the lending chain; what grows is the pyramid of deposits built on top of it.

Practice questions

Q1. With a 20% reserve ratio and no leakages, $500 of new reserves can support a maximum of how much in new deposits?

$500
$2,500
$2,000
$10,000

Answer: B.

The simple multiplier is 1 / 0.20 = 5, so maximum new deposits = $500 × 5 =$ 2,500. This is the ceiling; any currency drain or excess reserves would lower it.

Q2. Which change would INCREASE the effective money multiplier?

Households hold more physical cash
Banks hold larger excess reserves
The reserve requirement is lowered
Borrowers default on more loans

Answer: C.

A lower reserve ratio means each bank keeps less and lends more per round, raising 1/rr and the effective multiplier. More cash holding and more excess reserves are leakages that shrink it.

Q3. After 2008 the US monetary base roughly tripled while M2 grew modestly. The best explanation is:

The reserve requirement was raised sharply
Banks held massive excess reserves instead of lending
Households stopped using bank deposits
The Fed destroyed the extra base money

Answer: B.

Banks hoarded the new reserves as excess reserves rather than extending loans, so the deposit multiplier collapsed. The base grew, but the transmission chain into broad money was broken by bank behavior.

Q4. In the deposit-expansion chain, what happens to total reserves as deposits multiply?

They grow in the same proportion as deposits
They remain equal to the initial injection
They are gradually converted into currency
They are destroyed when loans are repaid

Answer: B.

Reserves are just reshuffled between banks as deposits cascade; the system's total reserves stay at the initial injection. The multiplier expands deposit claims on a fixed reserve base.

Click a question to reveal the answer and explanation.

Frequently asked questions

What is the money multiplier with a 5% reserve ratio?

The simple multiplier is 1 / 0.05 = 20, so $1,000 of new reserves could support up to $20,000 in deposits. Remember this is a leakage-free maximum; currency drains and excess reserves would reduce it.

Why is it called a 'multiplier' if nothing is multiplied at the first bank?

One bank alone creates only one round of new deposits. The multiplication emerges across the banking system as reserves cascade from bank to bank, each keeping a fraction and lending the rest.

Does a 0% reserve requirement mean an infinite multiplier?

Mathematically 1/0 is undefined, but economically the multiplier stays finite: banks still hold reserves for payments, face capital requirements, and need willing borrowers. Behavior, not the formula, sets the limit.

How is the multiplier related to the money supply graphs in textbooks?

Textbook money-supply curves often assume the multiplier is stable so the central bank can shift money supply by changing the base. In practice the curve's position also depends on banks' willingness to lend.