Externality diagrams: market and social optimum and welfare loss

Negative production externality

Diagram in words: price, costs and benefits on the vertical axis; quantity on the horizontal axis.

• The MPB = MSB curve slopes down (marginal private benefit, the demand curve; with no consumption externality it equals marginal social benefit).
• The MPC curve slopes up (marginal private cost, the supply curve).
• The MSC curve lies above MPC; the vertical gap is the marginal external cost.
• Market equilibrium: MPB = MPC at Qm, Pm. Social optimum: MSB = MSC at Q*, P*, a lower quantity and higher price.
• The welfare loss is the triangle between MSC and MSB from Q* to Qm, pointing towards the social optimum. These units cost society more than they are worth to it.

Marginal analysis: for every unit beyond Q*, MSC is greater than MSB, so society would gain by producing less.

Positive consumption externality

Diagram in words: MPC = MSC slopes up. MPB slopes down; MSB lies above MPB, the gap being the marginal external benefit.

• Market equilibrium where MPB = MPC: Qm. Social optimum where MSB = MSC: Q*, a higher quantity.
• The welfare loss (or potential welfare gain from correcting it) is the triangle between MSB and MSC from Qm to Q*: units society values more than they cost but which the market does not produce.

The same logic gives a negative consumption externality (MSB below MPB; over-consumption) and a positive production externality (MSC below MPC; under-production).

Exam technique: labelling

Label every curve (MPC, MSC, MPB, MSB), both quantities (Qm and Q*) and prices, and shade and name the welfare loss triangle. Point the triangle towards the social optimum. In written analysis, say which units have MSC greater than MSB (or MSB greater than MSC) and why the market ignores the gap. Evaluation: the external cost is very hard to measure in money, so the size of the welfare loss, and the correct tax or subsidy, is uncertain.

Worked example

MPB = MSB = 100 - Q and MPC = 20 + Q. Production creates a constant external cost of $20 per unit. Find the market output, the socially optimal output and the welfare loss.

1. Market: 100 - Q = 20 + Q, so Qm = 40.
2. MSC = 20 + Q + 20. Social optimum: 100 - Q = 40 + Q, so Q* = 30.
3. Welfare loss triangle: height = external cost 20, base = 40 - 30 = 10. Area = 1/2 x 20 x 10 = 100.

Answer: Qm = 40, Q* = 30, welfare loss = 100.

Check yourself

1. MPB = MSB = 100 - Q and MPC = 20 + Q, with a marginal external benefit of consumption of $10 per unit (so MSB = 110 - Q, MPC = MSC). Find the socially optimal output.
   Show answer

   45 units. 110 - Q = 20 + Q, so Q* = 45.

2. For the same market (market output 40, social optimum 45, external benefit $10 per unit), calculate the welfare loss.
   Show answer

   $25. 1/2 x 10 x (45 - 40) = 25.

3. In the lesson's negative externality example, by how many units does the market over-produce?
   Show answer

   10 units. 40 - 30 = 10.

4. On a negative production externality diagram, the vertical distance between MSC and MPC represents
   • the price of the good
   • consumer surplus
   • the producer's profit
   • the marginal external cost
   Show answer

   the marginal external cost. MSC = MPC + marginal external cost.

5. With a positive consumption externality, the free market quantity is
   • greater than the socially optimal quantity
   • less than the socially optimal quantity
   • equal to the socially optimal quantity
   • zero
   Show answer

   less than the socially optimal quantity. Consumers ignore the benefit to others, so they buy too little.

6. Where is the welfare loss triangle on a negative production externality diagram?
   • Between MPC and the price axis
   • Under the MPB curve from zero to the market quantity
   • Between MPB and MSB, from zero to the social optimum
   • Between MSC and MSB, from the social optimum quantity to the market quantity
   Show answer

   Between MSC and MSB, from the social optimum quantity to the market quantity. These over-produced units have MSC greater than MSB.

7. Give one reason why it is difficult to calculate the welfare loss from pollution accurately.
   Show answer

   External costs such as health damage or loss of wildlife are hard to measure and value in money terms, so the position of the MSC curve, and the size of the welfare loss triangle, are uncertain.. Measurement and valuation problems.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics specification (2018)

Last updated 8 November 2026. Spotted a mistake? Tell us.