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DSE Economics – Market Failure and Government Intervention: Lesson Prep Guide (Tutor Edition)
Students can say pollution is bad but cannot compute how far the market quantity sits from the optimum or how large the welfare loss is. This lesson uses one set of numbers to link external cost, tax, permits and public goods: the gap between marginal private and marginal social cost is what policy has to close.
Objectives — Students can: (1) use marginal private cost 40 + 2Q, marginal external cost 12 and marginal social benefit 100 – Q to find the free-market quantity 20 and the social optimum 16, then compute a deadweight loss of 24; (2) explain how a per-unit tax of 12 shifts private cost onto social cost, why the tax rate equals marginal external cost, and why tax revenue is not the same as deadweight loss; (3) compare permits with a flat cut: two firms with abatement costs 2e and 4e cutting 60 units in total spend 2400 under trading against 2700 under an even split, a saving of 300, and use three residents with combined willingness to pay of 18 against a cost of 10 to explain public provision.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Demand and supply | What does the equilibrium point mean? | Quantity demanded equals quantity supplied, willingness to pay equals marginal cost |
| Elasticity | With inelastic demand, who bears a tax? | Mostly the consumer |
| Marginal analysis | Where is the optimal quantity? | Where marginal benefit equals marginal cost |
| Efficiency | What does maximum total surplus mean? | No trade is left that benefits both sides |
02 Lesson flow (60 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-10 min | Cost warm-up | Write the difference between private and social cost | The gap is the external cost |
| 10-22 min | Draw three lines | MPC 40 + 2Q, MEC 12, MSB 100 – Q | MSC 52 + 2Q |
| 22-32 min | Find two quantities | Solve MPC = MSB and MSC = MSB | 20 and 16 |
| 32-44 min | Loss and tax | Triangle area, tax rate 12 | 24 |
| 44-52 min | Question drill | One calculation, one diagram, one policy comparison, one public good | Eight minutes unaided |
| 52-60 min | Exit check | Three written questions marked on the spot | Done independently |
03 Teaching script (read it out)
Scene 1: The gap between private and social cost
The firm sees only its own cost, 40 + 2Q, so the market stops where MPC equals MSB, at 20 units and a price of 80. Society also bears 12 of damage per unit, so social cost is 52 + 2Q and the optimum is 16 units at 84. The market produces four extra units whose social cost exceeds their benefit, and that triangle is the 24 deadweight loss. Make students say it plainly: the extra units are not wasteful in themselves, they are units whose cost someone else pays.
Ask the student to restate why the market quantity exceeds the optimum here.
Scene 2: Set the tax at marginal external cost
A tax of 12 lifts MPC to 52 + 2Q, exactly on MSC, so the firm stops at 16 by itself. A smaller tax misses the optimum and a larger one over-cuts output, creating a new loss. Keep three money flows apart: revenue goes to the treasury, consumer and producer surplus fall, and the original 24 of deadweight loss disappears. Revenue is a transfer, not a loss; if it compensates the victims, the efficiency case is complete.
Ask the student to name the two different areas for tax revenue and deadweight loss.
Scene 3: Permits and public goods are different tools
Trading lets the cheap abater do more: with costs 2e and 4e and 60 units total, e equals 40 and 20 at a common marginal cost of 80, costing 2400; an even split of 30 each costs 2700, or 300 more. Same target, different cost. Public goods are another matter: non-rival and non-excludable, so the marginal willingness to pay of 8, 6 and 4 must be added vertically to 18, which exceeds the 10 cost, so provision is efficient; yet each resident gains by hiding their valuation and free-riding, so voluntary supply usually falls short.
Ask the student to restate why public-good willingness to pay is summed vertically.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| External cost | MPC 40 + 2Q, MEC 12, MSB 100 – Q | 1) Solve MPC = MSB 2) Solve MSC = MSB 3) Half the gap times external cost | 20 and 16, loss 24 |
| Policy tool | Reach the social optimum with a per-unit tax | 1) Tax equals MEC 2) Shift MPC up 3) Read the new quantity and revenue | Tax 12, quantity 16 |
| Permit comparison | Two firms with MAC 2e and 4e cutting 60 | 1) Equalise marginal costs 2) Solve the two equations 3) Compare with a flat split | 40 and 20, saving 300 |
| Public good | Three residents value it at 8, 6 and 4; cost is 10 | 1) Add vertically 2) Compare with cost 3) Explain free-riding | 18 exceeds 10, so provide |
Sanity check (teach this): Sanity checks: with a negative externality the market quantity must exceed the optimum; deadweight loss is a triangle, not a rectangle; tax revenue is not a loss; the efficient tax equals marginal external cost; permit trading only stops when marginal costs are equal; public-good valuations add vertically while private goods add horizontally; keep all money units consistent.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| MPC 40 + 2Q and MSB 100 – Q: the free-market quantity? | 20 | Check the student sets the two expressions equal before solving |
| MSC 52 + 2Q and MSB 100 – Q: the optimum? | 16 | Check the student uses social rather than private cost |
| MAC 2e and 4e with 60 units to cut: the cheapest split? | 40 and 20 | Check the student equalises marginal costs |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Using private cost for the optimum | The optimum is where MPC equals MSB | Add the external cost first; the optimum is 16, not 20. |
| Counting revenue as a loss | Taxes are a social loss | Revenue is a transfer; the loss is the vanished triangle. |
| Adding public-good valuations horizontally | Add the three valuations and divide by the number of people | A public good is shared, so add marginal valuations vertically. |
| Assuming an even split is cheapest | Everyone cutting half is fair and cheapest | Equalise marginal costs: 40 and 20 saves 300 against 30 each. |
07 Homework (paper, section and question numbers)
- Secondary Economics chapter index — Copy three keywords from the market-failure chapter listed there and define each in one sentence
- Market equilibrium (S4 chapter) — Redo practice question 1 and write out how equilibrium price and quantity are found
- Price controls and taxes (S4 chapter) — Use the tax-incidence example there to explain why a tax equal to marginal external cost is efficient
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| MSC 52 + 2Q and MSB 100 – Q: the optimum quantity? | 16 | Wrong answer 20 means re-teach social cost |
| What is the deadweight loss when external cost is 12? | 24 | A rectangle answer means re-teach the triangle |
| How are public-good marginal valuations combined? | Vertically | A horizontal answer means re-teach non-rivalry |
09 Tutor FAQ
Which year is this for?
S6 market failure and government intervention; S5 classes can start with the external-cost diagram.
Is 60 minutes enough?
Yes; if algebra is weak spend five minutes on rearranging, and treat permits as a result only.
Is there practice attached?
The homework links to in-site chapters whose practice questions carry answers.
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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.