Why is the actual multiplier below one over the reserve ratio?

The public holds some cash and banks keep excess reserves, so less is re-lent each round.

How does M1 differ from M2?

M1 counts only cash held by the public and demand deposits, while M2 adds savings and time deposits.

S4 Economics Money and Banking, Paper 4: credit creation, money supply and monetary policy

2026-11-02

Ten graded items on the deposit multiplier, required reserves, M1, real interest, money supply growth, actual versus theoretical multipliers and open market operations, each with an answer.

Focus　The multiplier is one over the reserve ratio, reserves come before lending, M1 counts cash and demand deposits, real interest nets out inflation and actual multipliers fall short of theory.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S4 Economics: Money and Banking
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationThe required reserve ratio is 20%. The banking system receives a new deposit of $8,000 and every bank lends out its excess reserves. What is the final total deposit?
FoundationWith a reserve ratio of 12.5%, what is the deposit multiplier, and what total deposit can a new $5,000 deposit create?
FoundationA bank takes a $20,000 deposit and the reserve ratio is 15%. How much is the required reserve and how much can be lent?
FoundationThe public holds $1,200 in cash and $3,800 in demand deposits. What is M1?
IntermediateThe nominal interest rate is 6% and inflation is 2.5%. What is the real interest rate?
IntermediateThe reserve ratio rises from 10% to 12.5%. By how much does the total deposit created from a new $10,000 deposit fall?
IntermediateMoney supply is $60 billion and velocity is 4. If money supply rises 10% with velocity unchanged, what happens to nominal output PY?
ChallengeThe actual deposit multiplier is only 4 while the reserve ratio of 20% implies 5. How far apart are the actual and theoretical totals for a new $2,000 deposit?
ChallengeThe central bank buys $50 billion of bonds and the reserve ratio is 20%, with no cash drain. By how much can money supply expand at most?
Error redoError repair: a student writes that a higher required reserve ratio makes banks stronger at creating deposits. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	$40,000	The deposit multiplier is 1 divided by 0.20, which gives 5, so 8,000 times 5 is 40,000.
2	A multiplier of 8 and total deposits of $40,000	One divided by 0.125 is 8, and 5,000 times 8 is 40,000.
3	$3,000 reserve and $17,000 lent out	Fifteen per cent of 20,000 is 3,000, so the remaining 17,000 can be lent out.
4	$5,000	M1 is currency held by the public plus demand deposits, so 1,200 plus 3,800 is 5,000.
5	About 3.5%	The real interest rate is roughly the nominal rate minus inflation, so 6 minus 2.5 is 3.5 per cent.
6	From $100,000 to $80,000	The multiplier falls from 10 to 8, so 10,000 times 10 becomes 10,000 times 8.
7	It rises from $240 billion to $264 billion	MV gives 600 times 4, or 2,400, and 660 times 4 gives 2,640.
8	$8,000 actual against $10,000 theoretical, a gap of $2,000	Currency held by the public and excess reserves held by banks push the actual multiplier below the theoretical one.
9	$250 billion	Buying bonds injects 50 billion of reserves, and with a multiplier of 5 the maximum expansion is 250 billion.
10	Wrong: a higher reserve ratio means a smaller multiplier and weaker deposit creation	The multiplier is 1 divided by the reserve ratio, so a higher ratio leaves a smaller fraction to lend and total deposits fall.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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