DSE Economics | Circular Flow and the Multiplier Tutor Prep Guide | Injections, leakages and the tax-adjusted multiplier

2026-11-05

Tutor lesson-prep guides · Secondary Economics

Students memorise one over one minus MPC, then freeze when asked how much national income rises after four rounds. Building the rounds by hand removes the mystery, because the total is the limit of a series they have already added.

Objectives — Students can: (1) label three injections and three leakages on the circular flow; (2) derive a multiplier of 4 from MPC 0.75 and explain why an injection of 300 raises income by 1200; (3) add the first four rounds to 820.31, explain the gap of 379.69, and compute a multiplier of 2.5 at a 20 percent tax rate.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
National income	How is GDP computed from the expenditure side?	C plus I plus G plus net exports
Proportions	What does MPC 0.75 mean?	Each extra dollar of income raises consumption by 0.75
Series	What does 1 + 0.75 + 0.75 squared sum to?	An infinite geometric series, one over one minus 0.75, which is 4

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Prior-knowledge check	Ask the three prior questions, write wrong ones on the board	Answer orally, copy the wrong one
5-17 min	Act 1: injections and leakages	Draw the flow, label three of each, state the equilibrium condition	Circle the six arrows themselves
17-33 min	Act 2: add the rounds until the pattern shows	Write 300, 225.00, 168.75, 126.56 and sum to 820.31	Add once and explain why it never finishes
33-42 min	Act 3: the multiplier with tax	MPC becomes 0.60, multiplier 2.5, total 750	Recompute and compare
42-43 min	Redo the worst items	Reteach only the two most-missed items	Correct in red and write one sentence
43-45 min	Exit check	Ask three exit questions and record who misses	Answer orally, note for next lesson

03 Teaching script (read it out)

Scene 1: Act 1: three injections, three leakages

Draw a circle with households on the left and firms on the right. Wages and rent flow one way, spending flows back.
Add three injections from outside: investment, government spending and exports. Add three leakages out: saving, tax and imports.
The equilibrium statement is one sentence: income stops changing when total injections equal total leakages.
Common misconception box: students treat saving as always harmful. Saving is a leakage, but it does not lower equilibrium as long as investment matches it; the problem is insufficient injections.

Ask students to repeat: income is stable when injections equal leakages.

Scene 2: Act 2: the multiplier is a shortcut for infinite rounds

The government injects 300. Recipients spend MPC 0.75 of it, so round two is 225.00, round three 168.75 and round four 126.56.
The first four rounds total 820.31, which is 379.69 short of 1200, because the later rounds never stop, they only shrink.
The formula k = 1 / (1 – MPC) = 1 / 0.25 = 4, so the total change is 4 times 300 = 1200.
Put the other way: four rounds cover only 68.36 percent of the total, which is exactly why students feel they cannot finish the sum.
Common misconception box: students report the multiplier as the total change. The multiplier is a multiple; it must be multiplied by the injection.

Ask students to repeat: four rounds never reach the total, so use the formula.

Scene 3: Act 3: tax makes the multiplier smaller

With a 20 percent tax rate each dollar of income loses 0.2 before it can be spent, leaving 0.8 to be multiplied by MPC 0.75, so the effective spending proportion is 0.60.
The new multiplier is 1 / (1 – 0.60) = 2.5, so the same injection of 300 now raises income by 750 instead of 1200, a difference of 450.
State the logic: tax is a leakage, and larger leakages leave less money circulating each round.
Common misconception box: students subtract the tax rate from one minus MPC. Multiply MPC by one minus the tax rate first, then apply the formula.

Ask students to repeat: more leakage means a smaller multiplier.

04 Question types and worked steps

Type	Example	Steps	Answer
Multiplier	MPC is 0.75. Find the multiplier.	One minus MPC, take the reciprocal, state it is a multiple	4
Total change	MPC is 0.75 and government spending rises by 300. Find the final change in income.	Find k, multiply by the injection, give units	1200
Round-by-round	Find the cumulative change over the first four rounds.	List four terms, add, compare with the total	820.31, which is 68.36 percent
Tax comparison	With a 20 percent tax rate, find the new multiplier and total.	MPC times one minus t, apply the formula, multiply	2.5 and 750

Sanity check (teach this): Sanity checks: the multiplier must exceed 1 (4 here), so a value below 1 means an inverted formula; MPC plus MPS must equal 1 (0.75 plus 0.25); the four-round sum (820.31) must be below the total (1200), and above it means too many rounds were added; the tax-adjusted multiplier (2.5) must be below the original (4), or the leakage direction is wrong.

05 Independent practice (3 questions)

Question	Answer	What to watch
MPC is 0.75. Find the multiplier and the total change from an injection of 300.	4 and 1200	Whether the multiplier was reported as money
List the first four rounds and their sum.	300, 225.00, 168.75, 126.56, totalling 820.31	Whether each round uses the same MPC
With a 20 percent tax rate and MPC 0.75, find the multiplier and explain the fall.	2.5, because tax is a leakage	Whether the leakage mechanism is named

06 Common mistakes and what to say

Mistake	Student writes	Say this
Reporting the multiplier as the total	The multiplier is 4, so income rises by 4.	The multiplier is a multiple; 4 times 300 gives 1200.
Inverting the wrong ratio	k equals MPC divided by one minus MPC.	The formula is 1 divided by one minus MPC; the numerator is 1, not MPC.
Ignoring tax as a leakage	Tax does not change the multiplier because government gets it back.	Tax cuts disposable income, so each round spends less and the multiplier falls.
Stopping after four rounds	Adding four rounds gives the answer.	Four rounds are only part of an infinite series; the formula gives the total.

07 Homework (paper, section and question numbers)

Redo this chapter — Redo practice items 1 to 3; add one leakage sentence beside item 3
Economics chapter index — Open the national income chapter and do item 3, comparing GDP and GNP
Round table — Repeat the round table with MPC 0.8 up to round six, then check against the formula

08 Exit check (last 5 minutes)

Question	Answer	Decision
Multiplier when MPC is 0.75	4	If 0.75, reteach Act 2
Multiplier versus total change	A multiple versus an amount that must be multiplied	If not, reteach Act 2
Does tax raise or lower the multiplier	Lower it, because tax is a leakage	If higher, reteach Act 3

09 Tutor FAQ

Is the multiplier always positive?

With MPC between zero and one it always exceeds 1; only a hypothetical negative MPC changes that.

Are exports an injection?

Yes, foreign demand puts money into the domestic flow.

Why use saving rather than tax in the denominator?

A closed economy without government leaks only through saving, so the denominator is MPS; with tax and imports all leakages must be counted.

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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.