Banking & the Money Multiplier

You’ll be able to

Explain how fractional-reserve banking creates money through lending
Calculate the money multiplier from the reserve requirement
Determine the maximum change in the money supply from a new deposit or reserves

Fractional-reserve banking

Banks operate on a fractional-reserve system: they keep only a fraction of deposits on hand as reserves and lend out the rest. The required reserve ratio (RR) is the fraction regulators require banks to hold; reserves above that are excess reserves, which banks can lend. When a bank makes a loan, the borrowed money is spent and redeposited in another bank, which keeps a fraction and lends the rest again — so the banking system as a whole creates money with each round of lending. A single new deposit therefore expands the money supply by a multiple of itself.

The money (deposit) multiplier

The money multiplier measures the maximum expansion of the money supply from a change in reserves. It equals 1 / RR (the reserve requirement expressed as a decimal). To find the maximum change in the money supply from new excess reserves, multiply the excess reserves by the money multiplier. The result is a maximum because it assumes banks lend out all excess reserves and no one holds cash outside the banking system — real-world leakages make the actual expansion smaller.

Money multiplier & maximum money creation

Money multiplier = 1 / RR · Max Δ money supply = Excess reserves × (1 / RR)

RR is the required reserve ratio as a decimal. From a new deposit, excess reserves = deposit × (1 − RR); the required portion is deposit × RR.

Worked example

The required reserve ratio is 20% (0.2). A customer deposits $1,000 in cash into a bank. Calculate (a) the money multiplier, (b) the bank’s excess reserves from this deposit, and (c) the maximum total increase in the money supply.

1.Money multiplier = 1 / RR = 1 / 0.2 = 5.
2.Required reserves on the deposit = $1,000 × 0.2 = $200; excess reserves = $1,000 − $200 = $800.
3.Maximum change in money supply = excess reserves × money multiplier = $800 × 5 = $4,000.
4.The initial $1,000 was already money; the new money created by lending is up to $4,000, for a total of $5,000 in deposits system-wide.

Answer: The money multiplier is 5. The bank holds $200 in required reserves and $800 in excess reserves; lending out that $800 can create up to $4,000 in new money across the banking system.

Checkpoint

The required reserve ratio is 10%. A bank receives a new deposit of $2,000. What is the maximum amount by which the money supply can increase as a result of lending this deposit’s excess reserves?

Watch out

Apply the money multiplier to excess reserves, not the full deposit. The required-reserve portion (deposit × RR) is not lent out and does not multiply. Multiplying the whole deposit overstates money creation.

Checkpoint

If the central bank lowers the required reserve ratio from 25% to 20%, the money multiplier will:

On the exam

On money-creation problems, separate the initial deposit from newly created money, and always start from excess reserves. If a question gives the reserve requirement as a percentage, convert to a decimal before taking the reciprocal.

Answer the 2 checkpoints as you read.