中文（繁體）
中文（简体）
English
DSE Economics | Consumer and Producer Surplus Lesson-Prep Guide (Tutor Edition) | Demand Equations, Deadweight Loss and Policy Comparison
Students can draw the diagram but answer questions on total surplus with one word: cheaper. This lesson turns surplus into triangle areas from two equations, then prices a quota and a tax.
Objectives — Students can: (1) solve P = 100 minus 2Q against P = 20 plus 2Q for an equilibrium of 20 units at $60, and compute a consumer surplus of 400, a producer surplus of 400 and a total of 800; (2) price a quota of 15 units at a demand price of $70 and a supply price of $50, giving a deadweight loss of 50 and a total surplus of 750; (3) work a $20 per-unit tax to a quantity of 15, revenue of 300, an even split of the burden and a loss of 50.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Curve slopes | Demand falls, supply rises | Say what a slope of 2 means |
| Triangle area | Base times height over two | Compute 20 times 40 over 2 aloud |
| Equilibrium | Quantity demanded equals quantity supplied | Write the single equation |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-8 min | Equilibrium | Write both equations and solve together | Solve it again alone |
| 8-18 min | Three areas | Draw the two surplus triangles | Mark 400 and 400 |
| 18-28 min | Quota of 15 | Show how to read the demand price | Compute a loss of 50 |
| 28-36 min | Tax of $20 | Shift supply up and re-solve | Compute revenue of 300 |
| 36-42 min | Compare policies | Ask who receives the money | State the difference |
| 42-45 min | Exit check | Three questions, answers on the spot | All three right |
03 Teaching script (read it out)
Scene 1: Surplus is an area, not a feeling
Solve first: 100 minus 2Q equals 20 plus 2Q, so 80 equals 4Q and Q is 20, giving P of 60.
Consumer surplus is the triangle above the price and below demand: height 100 minus 60 is 40, base 20, so the area is 40 times 20 over 2, which is 400.
Producer surplus is the triangle below the price and above supply: height 60 minus 20 is 40, so again 400. Total surplus is 800, the value created by voluntary trade.
Say clearly that surplus is not profit. Producer surplus has variable cost deducted but not fixed cost, and fixed cost does not change the marginal decision, which is why the supply line measures it.
Check elasticity at the same point: slope 2 and P over Q of 3 give a magnitude of 1.5, so one equilibrium can carry both topics.
Consumer surplus is the triangle above the price and below demand: height 100 minus 60 is 40, base 20, so the area is 40 times 20 over 2, which is 400.
Producer surplus is the triangle below the price and above supply: height 60 minus 20 is 40, so again 400. Total surplus is 800, the value created by voluntary trade.
Say clearly that surplus is not profit. Producer surplus has variable cost deducted but not fixed cost, and fixed cost does not change the marginal decision, which is why the supply line measures it.
Check elasticity at the same point: slope 2 and P over Q of 3 give a magnitude of 1.5, so one equilibrium can carry both topics.
Have students restate: surplus is the triangle between the curve and the price.
Scene 2: A quota cuts quantity to 15
With a quota of 15, the price is read off demand: 100 minus 2 times 15 is 70. Sellers would accept 20 plus 2 times 15, which is 50. The $20 gap is quota rent, and who receives it depends on how licences are allocated.
Deadweight loss is half of (70 minus 50) times (20 minus 15): half of 20 times 5, which is 50. Total surplus falls from 800 to 750.
The usual misconception is that a higher price means society gains. The price rise only moves surplus between buyers, sellers and licence holders; society loses the 50 outright.
Ask what the loss would be with a quota of 20, the equilibrium quantity. The answer is zero, because no trade is excluded.
Deadweight loss is half of (70 minus 50) times (20 minus 15): half of 20 times 5, which is 50. Total surplus falls from 800 to 750.
The usual misconception is that a higher price means society gains. The price rise only moves surplus between buyers, sellers and licence holders; society loses the 50 outright.
Ask what the loss would be with a quota of 20, the equilibrium quantity. The answer is zero, because no trade is excluded.
Have students restate: the loss equals the value of the trades that no longer happen.
Scene 3: A tax moves money to the government
A $20 per-unit tax shifts supply from 20 plus 2Q to 40 plus 2Q. New equilibrium: quantity 15, buyers pay 70, sellers keep 50.
Revenue is 20 times 15, which is 300. Consumer surplus falls to half of 30 times 15, which is 225; producer surplus falls to half of 30 times 15, also 225. The three parts sum to 750, matching the quota.
The burden splits evenly because both curves have slope 2, so elasticities are symmetric. With inelastic demand the buyer share would exceed half.
Tax and quota differ in where the money goes, not in efficiency: the loss is 50 either way.
Require two layers in every comparison: efficiency (loss of 50) and distribution (who collects the 300).
Revenue is 20 times 15, which is 300. Consumer surplus falls to half of 30 times 15, which is 225; producer surplus falls to half of 30 times 15, also 225. The three parts sum to 750, matching the quota.
The burden splits evenly because both curves have slope 2, so elasticities are symmetric. With inelastic demand the buyer share would exceed half.
Tax and quota differ in where the money goes, not in efficiency: the loss is 50 either way.
Require two layers in every comparison: efficiency (loss of 50) and distribution (who collects the 300).
Have students restate: tax revenue is a transfer, not a loss.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Calculation | Equilibrium and surplus | Solve, draw, compute areas | 20 units, $60, 800 |
| Diagram | Mark the deadweight loss | Gap between demand and supply prices | $70 and $50, area 50 |
| Comparison | Quota against tax | Efficiency plus distribution | Same loss, different recipient |
| Evaluation | Who bears the tax | Compare slopes and elasticities | Even split when slopes match |
Sanity check (teach this): Fix units first: dollars per unit, so areas are in dollars.
The triangle height is the intercept minus the price, never the price itself.
The quota price comes from the demand curve, not the supply curve.
Re-solve with buyers paying sellers plus tax; do not halve the quantity.
Both policies must give the same loss, 50; if they differ, the algebra is wrong.
The triangle height is the intercept minus the price, never the price itself.
The quota price comes from the demand curve, not the supply curve.
Re-solve with buyers paying sellers plus tax; do not halve the quantity.
Both policies must give the same loss, 50; if they differ, the algebra is wrong.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Equilibrium quantity and price | 20 units, $60 | Check the two equations were set equal |
| Deadweight loss with a quota of 15 | 50 | Check the height uses 70 minus 50 |
| Tax revenue at $20 per unit | 300 | Check the multiplier is 15, not 20 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Calling surplus profit | Writes that the producer surplus of 400 is the firm profit | Surplus deducts variable but not fixed cost, and fixed cost does not affect the marginal decision. |
| Reading the wrong curve | Uses supply to get a quota price of $50 | Under a quota the price comes from demand: $70 at 15 units. |
| Wrong triangle height | Writes half of 20 times 60 | The height is 100 minus 60, which is 40, not 60. |
| Equating revenue with loss | Calls the 300 revenue the social loss | Revenue is a transfer; the loss is only 50. |
07 Homework (paper, section and question numbers)
- Secondary Economics chapter index — Markets and prices unit, questions 1 to 5
- Demand and supply elasticity — Redo the elasticity at the same point
- Lesson-prep hub — Compare other subjects
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Total surplus at equilibrium | 800 | All three right means policy comparison is safe |
| Deadweight loss under a quota of 15 | 50 | One wrong means re-teach act two |
| Revenue and burden split | $300, split evenly | Two wrong means repeat act three |
09 Tutor FAQ
Must the formulas be memorised?
No. Keep two moves: set the equations equal, and use base times height over two.
Why do tax and quota give the same loss?
Both cut quantity to 15, so the same trades are excluded; only the recipient of the money changes.
Do elasticities change the split?
Yes. The more inelastic side bears more, and equal slopes here give an even split.
Find a tutor — freeTutor Registration →
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.
