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S5 Economics | Indirect tax and subsidy prep guide (for tutors) | incidence, revenue, elasticity
Students can shift a supply curve but answer “the consumer pays” when asked who really bears the tax. This lesson splits a 10 dollar tax into 6 and 4 using one demand curve.
Objectives — Students can: (1) draw the post-tax equilibrium price and quantity from demand and supply equations; (2) split the per-unit tax into consumer and producer shares and explain the split with elasticity; (3) compute tax revenue and subsidy cost, and explain why revenue is not the same as the social loss.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Market equilibrium | Qd = Qs | P = 30, Q = 60 |
| Shifting supply | a per-unit tax shifts it up | up by $10 |
| Price elasticity | steeper means less elastic | bears the larger share |
02 Lesson flow (50 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-10 min | Baseline equilibrium | P = 30, Q = 60 | state it before changing anything |
| 10-22 min | A $10 per-unit tax | new P = 36, Q = 48 | consumers pay 6 more |
| 22-32 min | Splitting the burden | sellers keep 26 | producer share 4 |
| 32-40 min | Revenue and elasticity | 10 x 48 | revenue $480 |
| 40-48 min | A $5 subsidy | new P = 27, Q = 66 | cost $330 |
| 48-50 min | Exit check | three questions collected | independent work |
03 Teaching script (read it out)
Scene 1: Set the baseline, then tax
Demand is Qd = 120 – 2P and supply is Qs = 3P – 30. Equilibrium sets 120 – 2P = 3P – 30, so 5P = 150, P = 30 and Q = 60.
With a $10 per-unit tax on sellers, the price sellers actually keep is what drives supply, so replace P by (P – 10): Qs = 3(P – 10) – 30. Setting Qd = Qs gives 120 – 2P = 3P – 60, 5P = 180, P = 36, Q = 48.
Point out the gap: the price rises by 6, not 10. Sellers absorb the other 4 because they keep 36 – 10 = 26, four less than before. This step is the whole chapter, so label three horizontal lines on the original diagram: what consumers pay, what sellers keep, and the tax wedge.
With a $10 per-unit tax on sellers, the price sellers actually keep is what drives supply, so replace P by (P – 10): Qs = 3(P – 10) – 30. Setting Qd = Qs gives 120 – 2P = 3P – 60, 5P = 180, P = 36, Q = 48.
Point out the gap: the price rises by 6, not 10. Sellers absorb the other 4 because they keep 36 – 10 = 26, four less than before. This step is the whole chapter, so label three horizontal lines on the original diagram: what consumers pay, what sellers keep, and the tax wedge.
Student task: mark P = 36, P = 26 and P = 30 on the diagram and say who each line belongs to.
Scene 2: Elasticity decides the split
The statutory taxpayer is the seller, but the burden is not theirs alone: consumers carry 6 and producers 4, which is 60 per cent of the tax.
The rule: the side with the less elastic curve (the steeper one) carries more, because it has less ability to walk away from the transaction.
Revenue is the tax rate times the new quantity, 10 x 48 = $480. Consumers and producers together pay 480, the same amount, since the two shares add to the tax rate. The real loss is elsewhere: quantity falls from 60 to 48, so the 12 mutually beneficial trades that no longer happen are gone. That deadweight loss is not part of the revenue figure.
The rule: the side with the less elastic curve (the steeper one) carries more, because it has less ability to walk away from the transaction.
Revenue is the tax rate times the new quantity, 10 x 48 = $480. Consumers and producers together pay 480, the same amount, since the two shares add to the tax rate. The real loss is elsewhere: quantity falls from 60 to 48, so the 12 mutually beneficial trades that no longer happen are gone. That deadweight loss is not part of the revenue figure.
Student task: redo the algebra with a $4 tax and explain why the consumer share is still 60 per cent.
Scene 3: Subsidy is the same diagram reversed
A $5 per-unit subsidy to producers makes supply Qs = 3(P + 5) – 30 = 3P – 15. Setting Qd = Qs gives 120 – 2P = 3P – 15, 5P = 135, P = 27, Q = 66.
The consumer price falls from 30 to 27, a saving of 3, while producers keep 32, two more than before; total cost is 5 x 66 = $330.
Stress the symmetry: a subsidy is a negative tax, the supply curve moves down and right, and every conclusion mirrors. It also creates deadweight loss, because units whose marginal cost exceeds what consumers will pay still get produced.
Close with one sentence: tax and subsidy change who pays, who receives and how much changes hands, but they cannot change the split that elasticity dictates.
The consumer price falls from 30 to 27, a saving of 3, while producers keep 32, two more than before; total cost is 5 x 66 = $330.
Stress the symmetry: a subsidy is a negative tax, the supply curve moves down and right, and every conclusion mirrors. It also creates deadweight loss, because units whose marginal cost exceeds what consumers will pay still get produced.
Close with one sentence: tax and subsidy change who pays, who receives and how much changes hands, but they cannot change the split that elasticity dictates.
Student task: draw the before and after diagrams for the subsidy and label the consumer and producer gains.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Find the new equilibrium | Qd = 120 – 2P, Qs = 3(P – t) – 30 | shift supply, then solve | P = 36, Q = 48 |
| Split the burden | tax of $10 | new price minus old price | 6 and 4 |
| Find revenue | Q = 48 | rate times quantity sold | $480 |
| Find subsidy cost | subsidy of $5 | new Q times the subsidy | $330 |
Sanity check (teach this): The consumer share 6 plus the producer share 4 must equal the tax 10; anything else means one curve was shifted the wrong way. The new quantity 48 must be below the original 60 for a tax, and 66 must be above 60 for a subsidy; the opposite price moves cross-check each other.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Qd = 100 – P, Qs = 2P – 20: find equilibrium. | P = 40, Q = 60 | set Qd = Qs first |
| With a $6 tax on sellers, find the new P and Q. | P = 44, Q = 56 | supply uses P – 6 |
| What is the tax revenue? | $336 | use the new Q, not the old one |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Adding the tax to the price | reports 30 + 10 = 40 as the new price | “The price rises by 6; the other 4 comes out of the seller. Solve, do not add.” |
| Revenue on the old quantity | computes 10 x 60 = 600 | “Only the 48 units still traded can be taxed.” |
| Confusing taxpayer with bearer | says the seller bears the whole tax | “Statutory liability and economic incidence are different things.” |
| Treating a subsidy as a price cut | subtracts 5 from the price | “A subsidy shifts supply; the price only falls by 3.” |
07 Homework (paper, section and question numbers)
- Secondary economics chapter index (demand and supply, costs, market structure, inflation, trade) — tax and subsidy before market structure
- Secondary prep guide hub — all subjects
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Qd = 120 – 2P, Qs = 3P – 30 with a $10 tax: new price? | 36 | wrong: redo act one |
| Consumer share of that tax? | 6 | wrong: redo the split in act two |
| Why is revenue not the social loss? | 12 units of trade disappear | two wrong: back to act three |
09 Tutor FAQ
Which year is this for?
S5 to S6; it covers the HKDSE price and market topics and the efficiency topic.
How many formulae are needed?
One: revenue equals rate times new quantity. Everything else is solving the two equations.
Is there practice attached?
The homework list links to the economics chapter index, pairing with the elasticity chapter.
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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.
