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Central Banking & Monetary Policyintermediate

The Money Supply Process and Multiplier

Three players make the money supply. The central bank sets the monetary base, commercial banks lend, and the public chooses how much cash to hold. The banking system multiplies the base into broader money through the money multiplier, which is one over the reserve ratio in the simplest case but shrinks once currency holdings and excess reserves leak out.

Try it yourself

The Money Multiplier

The simple model says one dollar of reserves becomes 1/rr of deposits. Add currency that the public holds (c) and reserves banks keep beyond the requirement (e) and the leakage shrinks the true multiplier to m = (1 + c) / (rr + e + c).

Simple multiplier 1/rr10.00×
Full multiplier m2.80×
Gap (overstatement)7.20×
ΔMoney from $1,000 reserves$2,800
Deposit-expansion cascade · $1,000 of new reserves
1$1,0002$6433$4134$2665$171678Lending round (each = previous × 0.64)
Each round, 35.7% leaks out as required reserves, excess reserves and currency, so the loan shrinks. Money created after round 8: $82 still to come.
Sum of all rounds → m × $1,000$2,800
Try this. Set c = 0 and e = 0: the full multiplier collapses onto the simple 1/rr. Now push c toward 1 (a cash-heavy crisis) and watch m fall far below 1/rr even though rr never changed.

Why it matters

The central bank controls the raw material, the base, not the final amount of money. When a bank lends a deposit out, the borrower redeposits it and the bank lends again, so one dollar of base supports several dollars of deposits. Two leakages, the cash the public keeps and the reserves banks hold beyond the requirement, break the chain and shrink the multiplier well below the textbook figure.

Formulas

Monetary base and money supply
MB=C+R,M=m×MBMB = C + R, \qquad M = m \times MB
MBMB is the monetary base (currency CC plus reserves RR), mm the money multiplier, and MM the money supply.
Money multiplier
m=1+crr+e+cm = \frac{1 + c}{rr + e + c}
rrrr is the required reserve ratio, cc the currency-to-deposit ratio, and ee the excess-reserve-to-deposit ratio.

Worked examples

Scenario

The central bank buys $1 billion of securities and the multiplier is about 2.8. What happens to the money supply?

Solution

The monetary base rises by $1 billion, and the money supply rises by the multiplier times that amount, so it grows by roughly $2.8 billion.

Scenario

Reserve ratio 10%, currency ratio 0.4, no excess reserves. Find the multiplier and compare with the simple case.

Solution

m = (1 + 0.4) / (0.10 + 0 + 0.4) = 1.4 / 0.5 = 2.8. The textbook simple case with no currency and no excess reserves would give 1 / 0.10 = 10, so the two leakages cut it from 10 down to 2.8.

Common mistakes

  • ✗The central bank directly sets the broad money supply. It sets the monetary base. Banks and the public determine the multiplier, so the final money supply is not fully under its control.
  • ✗The multiplier is fixed at one over the reserve ratio. Currency holdings and excess reserves cut it down, and it is not constant over time.
  • ✗A bigger base always means proportionally more money. After 2008 banks piled up excess reserves, the multiplier collapsed, and a huge base produced far less money than the simple model predicts.

Revision bullets

  • •Money supply equals the multiplier times the monetary base
  • •Monetary base is currency plus reserves
  • •Currency and excess reserves shrink the multiplier below 1/rr

Quick check

The monetary base is best described as

Holding the reserve ratio fixed, a rise in banks’ excess reserves makes the money multiplier

Connected topics

Central BankBank ReservesOpen Market Ops

Sources

  1. Mishkin (2018), Ch. 15
    Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.
    The money supply process and the derivation of the money multiplier, including the currency and excess-reserve leakages.
How to cite this page
Dr. Phil's Quant Lab. (2026). The Money Supply Process and Multiplier. Derivatives Atlas. https://phucnguyenvan.com/concept/mb-money-supply
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