DSE Economics | Money Supply and Credit Creation Lesson-Prep Guide (Tutor Edition) | Deposit Multiplier, Cash Leakage and MV = PY

2026-11-02

Tutor lesson-prep guides · Secondary Economics

Students recite the multiplier as one over the reserve ratio, then fall apart once cash leakage appears. This lesson counts one deposit of 10,000 through the banking system.

Objectives — Students can: (1) turn a 20% reserve ratio into a multiplier of 5, and a 10,000 deposit into 50,000 of deposits and 40,000 of new money; (2) redo it at 25% for a multiplier of 4 and 30,000 of new money, then compute 4.4 with 10% cash leakage and 15% reserves; (3) use MV = PY with M of 400 and V of 5 to get PY of 2,000, and show that M must rise 25% when V falls to 4.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Bank balance sheets	Deposits are liabilities, loans are assets	State that both sides rise together
Reserves	Banks keep part of deposits	Define the ratio as reserves over deposits
Nominal and real	Current prices against constant prices	Give one numeric example

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-8 min	What money is	From medium of exchange to money supply	Write the M1 and M3 difference
8-20 min	Layer by layer	List deposits, reserves and loans	Add four layers alone
20-28 min	The multiplier	From 1 over 20% to 5, then verify	Compute 50,000 and 40,000
28-36 min	Cash leakage	Put cash and reserves in the denominator	Compute 4.4
36-43 min	MV = PY	Substitute 400 times 5	Compute the 25% rise in M
43-45 min	Exit check	Three questions answered aloud	All three right

03 Teaching script (read it out)

Scene 1: How one deposit becomes five

A customer deposits 10,000 with a reserve ratio of 20%. The bank keeps 2,000 and lends 8,000. The borrower deposits it elsewhere, that bank keeps 1,600 and lends 6,400, and so on.
Total deposits are 10,000 plus 8,000 plus 6,400 and onward: a geometric series with ratio 0.8, summing to 10,000 divided by 0.2, which is 50,000.
The shortcut is the multiplier, 1 over the reserve ratio, so 1 over 0.2 is 5, and 10,000 times 5 is 50,000.
New money is 50,000 minus 10,000, which is 40,000. The difference between total and new is the most common lost mark.
State the limits: the 5 is a ceiling, and it needs no cash holding, no excess reserves and willing borrowers.
Make students name all three before they use the formula.

Have students restate: the multiplier is a ceiling and needs three conditions.

Scene 2: Cash leakage shrinks the multiplier

At a 25% reserve ratio the multiplier is 1 over 0.25, which is 4, so 10,000 becomes 40,000 and new money is 30,000. A higher ratio means a smaller multiplier, which is how reserve requirements cool credit.
Now add cash leakage: the public holds 10% as cash and banks hold 15% as reserves. The multiplier is (1 plus cash ratio) over (reserve ratio plus cash ratio), so 1.10 over 0.25, which is 4.4.
The numerator carries the 1 because money supply includes cash in the hands of the public, not only deposits.
Apply it: 10,000 becomes 44,000, far below the 66,667 without leakage.
Ask what excess reserves do. They lower the multiplier the same way, because the actual reserve ratio exceeds the required one.
Close with one sentence: a bigger denominator means a smaller multiplier.

Have students restate: leakage and excess reserves both enlarge the denominator.

Scene 3: The arithmetic of MV = PY

The equation of exchange is MV = PY: money supply, velocity, price level and real output.
With M of 400 and V of 5, PY is 2,000. If V falls to 4 and PY must stay at 2,000, M has to rise to 500, which is 25% more.
If money supply rises 10% while V and Y are unchanged, prices rise 10%: the simple version of monetary neutrality.
Then nominal against real: nominal GDP up 6% with a deflator up 2% gives real growth of 1.06 over 1.02 minus 1, which is 3.92%, not 4%. The missing eighth of a point is compounding.
Add the limits: velocity moves in the short run and output may sit below potential, so printing money does not always produce inflation at once.
Give one reusable judgement: sustained inflation needs money growth faster than real output.

Have students restate: sustained inflation needs money growth above real output growth.

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Total deposits and new money	Deposit times multiplier, then subtract	50,000 and 40,000
Calculation	Multiplier with cash leakage	(1 plus c) over (r plus c)	4.4
Explanation	Three conditions for the multiplier	No leakage, no excess reserves, willing borrowers	All three named
Evaluation	Money growth and inflation	MV = PY plus long-run limits	Not automatic in the short run

Sanity check (teach this): The multiplier is 1 over the reserve ratio, not the ratio itself.
New money excludes the original deposit: 50,000 minus 10,000 is 40,000.
With leakage the numerator is 1 plus c, never 1 alone.
Real growth divides: 1.06 over 1.02, not 6% minus 2%.
The multiplier is a ceiling, limited by lending willingness.

05 Independent practice (3 questions)

Question	Answer	What to watch
Total deposits at 20% reserves on 10,000	50,000	Check the multiplication by 5
Multiplier at 10% cash and 15% reserves	4.4	Check the 1 is added to the numerator
Real growth with 6% nominal and 2% deflator	3.92%	Check division rather than subtraction

06 Common mistakes and what to say

Mistake	Student writes	Say this
Calling the total the multiplier	Answers that the multiplier is 50,000	The multiplier is 5; 50,000 is total deposits.
Forgetting the original deposit	Writes new money as 50,000	New money is 50,000 minus 10,000, which is 40,000.
Using 1 in the numerator with leakage	Uses 1 over 0.25 and gets 4.0	The numerator is 1.10, giving 4.4.
Subtracting rates	Writes 6% minus 2% equals 4%	Divide 1.06 by 1.02 for 3.92%.

07 Homework (paper, section and question numbers)

Secondary Economics chapter index — Money and banking unit, questions 1 to 5
GDP and national income — Redo the nominal to real conversion
Lesson-prep hub — Compare other subjects

08 Exit check (last 5 minutes)

Question	Answer	Decision
Multiplier at 20% reserves	5	All three right means policy is safe
Multiplier with 10% cash leakage	4.4	One wrong means re-teach act two
Real growth rate	3.92%	Two wrong means repeat act three

09 Tutor FAQ

Does the multiplier ever equal 5 in practice?

Rarely. Cash leakage, excess reserves and weak borrowing keep it lower, so 5 is a benchmark for comparison.

Does the central bank control money supply directly?

Only partly. It sets base money and interest rates; banks and the public determine the rest.

Is inflation always monetary?

In the long run money growth dominates, while supply shocks and demand shifts matter in the short run.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.