DSE Economics | Market Failure and Externalities Tutor Prep Guide | MPC versus MSC, the DWL triangle and a corrective tax

2026-11-05

Tutor lesson-prep guides · Secondary Economics

Students can recite that externalities cause overproduction, but in an exam they write one line about government intervention and lose the diagram marks. This lesson turns the diagram into one repeatable answer template with three numbers.

Objectives — Students can: (1) state the difference between MPC and MSC and write both equations with an external cost of 10; (2) solve 100 – 2Q against 20 + Q to find the free-market and socially optimal quantities and the DWL area; (3) explain how a per-unit tax equal to MEC moves output, price and DWL, finishing nine quick items in the lesson.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Demand and supply	Where do P = 100 – 2Q and P = 20 + Q meet?	Solve to Q = 26.67 and P = 46.67
Marginal thinking	Is marginal cost the extra unit or the average unit?	The cost of one more unit, never the average
Efficiency	What is the name of the output where total surplus is greatest?	Allocative efficiency, where marginal benefit equals marginal cost

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Prior-knowledge check	Ask the three prior questions, circle the wrong one on the board	Answer orally, copy the wrong one
5-17 min	Act 1: the two cost curves differ by one number	Draw MSC exactly 10 above MPC	Copy the diagram, label the gap
17-33 min	Act 2: the market uses the wrong curve	Solve both equilibria: 26.67 and 23.33	Solve once alone and write both quantities
33-42 min	Act 3: DWL and the tax	Draw the triangle, area 16.67, then add a tax of 10	Compute the area, state the new price
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: two cost curves, one number apart

Draw a standard diagram with a downward demand curve and an upward MPC curve. Then make the key point: a firm only counts its own money, so it uses MPC. Society also counts the harm to third parties, so it uses MSC.
MSC = MPC + external cost per unit. Here the external cost is 10, so MSC is the whole MPC line shifted up by 10 and the slope is unchanged.
Common misconception box: students think the slope must change. When the external cost is a fixed amount per unit the lines stay parallel; the slope changes only when the external cost rises with output.

Ask students to repeat: MPC is what the firm pays, MSC is what society pays, and the gap is the external cost.

Scene 2: Act 2: the market follows the wrong curve, so output is too high

Free market: solve P = 100 – 2Q against P = 20 + Q to get Q = 26.67 and P = 46.67.
Social optimum: solve P = 100 – 2Q against P = 30 + Q to get Q = 23.33 and P = 53.33.
The market produces 3.33 units too many, and over that range social cost exceeds social benefit, so the extra units are a net loss.
DWL = half times external cost times the output gap = half times 10 times 3.33 = 16.67.
Common misconception box: students shade the DWL to the left of the equilibrium. For a negative externality the loss always sits to the right of the social optimum.

Ask students to repeat: the market overproduces because it never counts the third party.

Scene 3: Act 3: a per-unit tax internalises the external cost

With a tax of 10 per unit the firm cost becomes 20 + Q + 10, identical to MSC.
Output returns to 23.33, consumers pay 53.33, firms keep 43.33 and DWL falls to zero.
Say three things clearly: the tax must equal the external cost per unit to be exactly right; revenue is not the objective, correcting output is; if the external cost rises with output, a single per-unit tax can only reduce the loss and cannot restore the full optimum.
Common misconception box: students assume consumers bear the whole tax. The split depends on the slopes of the two curves.

Ask students to repeat: tax equals MEC and output returns to the social optimum.

04 Question types and worked steps

Type	Example	Steps	Answer
Free-market equilibrium	P = 100 – 2Q and MPC = 20 + Q. Find Q and P.	Equate, solve for Q, substitute back	Q = 26.67, P = 46.67
Social optimum	External cost is 10. Find the socially optimal output.	Write MSC, equate with demand, solve	Q = 23.33
Deadweight loss	Find the deadweight loss.	Find both quantities, subtract, halve times MEC times gap	16.67
Policy explanation	A tax of 10 per unit is imposed. Explain the effect on output and DWL.	Shift the cost curve, find the new equilibrium, compare	Output returns to the optimum and DWL disappears

Sanity check (teach this): Sanity checks: MSC must lie above MPC (30 + Q against 20 + Q), otherwise a sign is wrong; the socially optimal output must be smaller than the free-market output; the price firms keep (43.33) must be below the price consumers pay (53.33) by exactly 10; the DWL area must be positive, and a negative area means the two quantities were swapped.

05 Independent practice (3 questions)

Question	Answer	What to watch
With P = 100 – 2Q, MPC = 20 + Q and MEC = 10, find both quantities.	26.67 and 23.33	Whether MSC was written as MPC minus MEC
Find the DWL and shade it on the diagram.	16.67, to the right of the social optimum	Whether the base of the triangle is the output gap
Explain in 60 words why a tax equal to MEC reaches the social optimum.	The curves coincide, output returns, DWL disappears	Whether internalising the cost is named

06 Common mistakes and what to say

Mistake	Student writes	Say this
Drawing MSC below MPC	The external cost is a benefit, so MSC is lower.	The external cost is a real cost to society, so MSC sits above MPC by exactly that amount.
Shading DWL on the left	Deadweight loss is the area left of equilibrium.	A negative externality means too much output, so the loss is to the right of the optimum.
Using average instead of marginal cost	Average cost is 10, so the external cost is 10 per unit.	Efficiency compares the cost and benefit of one more unit, so only marginal values are relevant.
Confusing tax revenue with DWL	Every dollar of tax removes a dollar of DWL.	Tax is a transfer, not a loss; what matters is whether output returns to the optimum.

07 Homework (paper, section and question numbers)

Redo this chapter — Redo practice items 1 to 3; item 2 needs a labelled diagram with all three vertices
Economics chapter index — Open the price controls chapter and do item 1, then compare the two interventions
Comparison card — Write positive and negative externalities in two columns: curve position, output direction and DWL side, one question each

08 Exit check (last 5 minutes)

Question	Answer	Decision
Difference between MPC and MSC	Social cost adds the external cost to the private cost	If not, reteach Act 1
Is market output too high or too low	Too high, by 3.33 units	If too low, reteach Act 2
What must the per-unit tax equal	The external cost per unit	If DWL, reteach Act 3

09 Tutor FAQ

Must DWL be a triangle?

It is a triangle when both curves are straight lines, which is the usual DSE case.

What about positive externalities?

MSB exceeds MPB, output is too low, and a subsidy is the corrective tool.

Do consumers always pay the tax?

The split depends on the slopes; the steeper side bears more.

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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.