How to Calculate the Money Multiplier
The money multiplier equals 1 divided by the required reserve ratio; multiply it by new excess reserves to find the maximum change in the money supply.
Formula
Money multiplier = 1 ÷ required reserve ratio | Δmoney supply = money multiplier × excess reserves
Steps
- 1Find the required reserve ratio. The fraction of deposits banks must hold (e.g., 10% = 0.10).
- 2Compute the multiplier. Money multiplier = 1 ÷ reserve ratio.
- 3Find excess reserves. New deposit minus required reserves on that deposit.
- 4Multiply. Maximum change in money supply = money multiplier × excess reserves.
Worked example
With a 10% (0.10) reserve ratio, the money multiplier = 1 ÷ 0.10 = 10. A $1,000 deposit creates $900 in excess reserves, which can expand the money supply by up to 10 × $900 = $9,000.
Frequently asked questions
Why is the real-world money multiplier smaller?
Banks may hold excess reserves and the public holds some cash instead of depositing it — both are leakages that shrink the actual multiplier.
How is it different from the spending multiplier?
The money multiplier expands the money supply through bank lending; the spending multiplier expands GDP through re-spending of income (1 ÷ (1 − MPC)).