Calculating the money multiplier
Commercial banks lend out deposits and so create new money. How much money one euro of central bank money can turn into is limited by reserve requirements and the cash people keep.
Formulas and rules
- Simple multiplier without cash: m = 1 / r (r = reserve ratio)
- With currency ratio c = cash / deposits: m = (1 + c) / (c + r)
- Money supply M1 = m × monetary base
- A higher reserve ratio or more cash holding → smaller multiplier
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
The reserve ratio is 20% and the public’s currency ratio (cash relative to deposits) is 10%. The central bank supplies a monetary base of € 540 bn. Find the simple money multiplier without cash holding, the multiplier with cash holding and the money supply M1.
Simple multiplier 1/r
Multiplier with currency ratio
Money supply M1 in € bn
Numbers like 12.5 or 1,250; elasticities with their sign (−0.75); percentages as a number (12.5). Round to 2 decimal places.
Worked example
The reserve ratio is 10% and the public’s currency ratio (cash relative to deposits) is 10%. The central bank supplies a monetary base of € 690 bn. Find the simple money multiplier without cash holding, the multiplier with cash holding and the money supply M1.
Worked solution
- 1.Without cash: m = 1 / r = 1 / 0.1 = 10
- 2.With currency ratio c: m = (1 + c) / (c + r) = (1 + 0.1) / (0.1 + 0.1) = 5.5
- 3.M1 = m × base = 5.5 × 690 = 3,795
Typical mistake: Forgetting cash holding and using 1/r. Cash kept by the public does not come back as deposits, so the multiplier is smaller.
Common questions
Why does holding cash lower the multiplier?
Cash kept in someone’s wallet does not come back to a bank as a deposit and cannot be lent out again. The chain of loans stops sooner.
What is the monetary base?
The money created by the central bank: cash in circulation plus banks’ reserves at the central bank.