Microeconomics guide, Unit 6, step 22 of 28Previous step Next step

Step 22: Externalities

By the EconTutorials team. 11-minute read with 6 practice questions.

SyllabusAP Micro 6.1–6.2 · Cambridge 7.3–7.4 · IB 2.8

In 30 seconds

An externality is a cost or benefit that falls on a third party: someone who is neither the buyer nor the seller.
The key formulas are $ MSC = MPC + \text{external cost} $ and $ MSB = MPB + \text{external benefit} $. The social optimum is where $ MSB = MSC $.
Negative externalities (pollution) lead to overproduction. Positive externalities (vaccination, education) lead to underproduction. Both create a deadweight loss triangle between the market quantity and the optimal quantity.
The fixes are Pigouvian taxes, subsidies, regulation and cap-and-trade. The Coase theorem shows that private bargaining can work when property rights are clear and transaction costs are low.

Video lesson coming soonA short animated lesson for this step will appear here.

What is an externality?

Your neighbour throws a loud party until 2 a.m. the night before your exam. You pay a cost you never agreed to. Now flip it: your neighbour plants a beautiful garden and you enjoy the view for free. Either way, someone outside the deal is affected. These spillovers are externalities, the most important reason free markets fail.

Key termExternality: a cost or benefit of a transaction that affects a third party who is not involved in it, and that is not reflected in the market price.

A negative externality imposes a cost on third parties: pollution, noise, traffic congestion, passive smoking.
A positive externality gives a benefit to third parties: vaccination, education, research, bees pollinating a neighbour’s orchard.

Split each cost and benefit into a private and a social part:

Term	Meaning
Marginal private cost (MPC)	The cost the producer pays for one more unit. This is the market supply curve.
Marginal social cost (MSC)	MPC plus the external cost to third parties
Marginal private benefit (MPB)	The benefit to the buyer of one more unit. This is the market demand curve.
Marginal social benefit (MSB)	MPB plus the external benefit to third parties

\[ MSC = MPC + \text{external cost} \qquad MSB = MPB + \text{external benefit} \]

The market ignores the external parts. The social optimum $ Q^* $ is where $ MSB = MSC $.

Negative externalities: the market produces too much

A factory dumps waste into a river. People downstream suffer health damage and lost fishing income, but neither the factory nor its customers pays. Its private cost (MPC) is below the social cost (MSC), so it produces too much.

On a diagram, MSC sits above MPC by the external cost per unit. The market produces $ Q_m $ (demand meets MPC); the optimum $ Q^* $ (demand meets MSC) is smaller. Each unit between them costs society more than it is worth, and that loss is the deadweight loss (DWL).

Worked example

A paint factory has a constant private cost of $6 per tin. Each tin causes $3 of pollution damage. Demand is $ P = 24 – 0.25Q $. Find the market quantity, the socially optimal quantity and the deadweight loss.

Step 1Market: set $ MPC = D $: $ 6 = 24 – 0.25Q \Rightarrow 0.25Q = 18 \Rightarrow Q_m = 72 $

Step 2Social: $ MSC = 6 + 3 = 9 $; set $ 9 = 24 – 0.25Q \Rightarrow 0.25Q = 15 \Rightarrow Q^* = 60 $

Step 3$ DWL = \tfrac{1}{2} \times (72 – 60) \times 3 = \tfrac{1}{2} \times 12 \times 3 = \$18 $

The market makes 12 tins too many, costing society $18.

Exam tipFor a negative externality diagram, draw MSC above MPC (supply), label both curves, mark $ Q^* $ and $ Q_m $ on the axis, and shade the DWL triangle between $ Q^* $ and $ Q_m $, with its point at $ Q^* $ and its wide side at $ Q_m $. Examiners often lose marks for unlabelled curves.

Positive externalities: the market produces too little

A flu jab protects you and everyone you might have infected, but you ignore that extra benefit when deciding to pay. Private benefit (MPB) is below social benefit (MSB), so too few people get vaccinated. Education is similar: society gains a more productive economy, better-informed voters and lower crime, so governments subsidise schooling.

On the diagram, MSB sits above MPB. The market produces $ Q_m $, where MPB meets supply. The social optimum $ Q^* $, where MSB meets supply, is larger. The DWL triangle lies between $ Q_m $ and $ Q^* $: the benefit society misses out on.

Worked example

A clinic supplies flu jabs at a constant $12 each. Weekly private demand is $ Q = 90 – 3P $. Each jab gives $4 of external benefit to others. Find the market quantity, the optimal quantity and the deadweight loss.

Step 1Market: $ Q_m = 90 – 3(12) = 54 $

Step 2A subsidy equal to the external benefit cuts the buyer’s price to $ 12 – 4 = 8 $: $ Q^* = 90 – 3(8) = 66 $

Step 3$ DWL = \tfrac{1}{2} \times (66 – 54) \times 4 = \$24 $ a week

The market gives 54 jabs a week when 66 would be best. A $4 subsidy per jab closes the gap.

Common mistakePutting the DWL triangle on the wrong side. With a negative externality, the market quantity is too high, so the triangle is to the left of $ Q_m $ (between $ Q^* $ and $ Q_m $). With a positive externality, the market quantity is too low, so the triangle is to the right of $ Q_m $ (between $ Q_m $ and $ Q^* $).

How governments fix externalities

The goal is to internalise the externality: make decision-makers face the full social cost or benefit.

Pigouvian tax (for negative externalities). A per-unit tax equal to the external cost, named after Arthur Pigou (1920). It shifts the supply curve up from MPC to MSC, so the market produces $ Q^* $. In the paint example, a $3 tax per tin moves output from 72 to 60. A carbon tax on CO₂ is a real-world example.
Subsidy (for positive externalities). A per-unit payment equal to the external benefit. It shifts demand up from MPB to MSB, or equivalently lowers the price buyers pay, as in the vaccine example.
Regulation (command-and-control). Direct rules such as emission limits. Simple and enforceable, but it treats every firm the same, even when some could cut pollution far more cheaply.
Cap-and-trade (tradable permits). The government caps total pollution, issues permits equal to the cap and lets firms trade them, so the cap is met at the lowest total cost.

Key termPigouvian tax: a tax equal to the marginal external cost at the socially optimal quantity, designed to make producers pay the full social cost.

A Pigouvian tax fixes the price of pollution; cap-and-trade fixes the quantity. The EU Emissions Trading System (2005) is the world’s largest scheme. Too many early permits made the carbon price collapse, but after the cap was tightened it reached €90 to €100 per tonne by 2023, and covered emissions fell about 37% between 2005 and 2023.

Worked example

Under a cap-and-trade scheme, permits trade at $50 per tonne. Factory A can cut emissions for $20 a tonne; Factory B for $80 a tonne. What does each do?

Step 1Factory A: cutting costs $20 but a spare permit sells for $50, a gain of $ 50 – 20 = \$30 $ per tonne. A cuts emissions and sells permits.

Step 2Factory B: cutting costs $80 but a permit costs $50, a saving of $ 80 – 50 = \$30 $ per tonne. B buys permits.

Step 3Each tonne cut by A instead of B saves society $ 80 – 20 = \$60 $.

The cheapest cutter does the cutting, so the target is met at the lowest cost.

The Coase theorem: can people sort it out themselves?

Ronald Coase (1960) argued that if property rights are clear and transaction costs are low, polluter and victim can bargain to the efficient outcome without government.

If a fisherman has the right to a clean river, the polluting factory must pay him; if the factory has the right to pollute, he can pay it to cut back. Either way they reach the efficient level. The rights change who pays whom, not the outcome.

Key termCoase theorem: with clearly defined property rights and very low transaction costs, private bargaining leads to the efficient outcome whoever holds the rights.

In practice it often fails: transaction costs are high (you cannot negotiate with millions of pollution victims), rights are unclear (who owns the atmosphere?) and many affected parties means free-riding. Large problems like climate change need government action.

Exam tipEvaluate each policy with a strength and a weakness: a Pigouvian tax raises revenue but needs the external cost, which is hard to measure; cap-and-trade guarantees the pollution level but permit prices can swing wildly.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. A beekeeper’s bees pollinate a nearby apple orchard. Is this a positive or negative externality? Who is the third party, and does the market produce too many or too few bees? Show worked answer

It is a positive externality. The third party is the orchard owner, who gets free pollination.
The beekeeper counts only the private benefit (honey sales) and ignores the pollination benefit, so the market produces too few bees.

EasyQ2. A firm’s MPC is $25 per unit and each unit causes $7 of noise damage to neighbours. What is the MSC, and what Pigouvian tax would correct the externality? Show worked answer

$ MSC = 25 + 7 = \$32 $ per unit.
The Pigouvian tax should equal the external cost: $7 per unit. This makes the firm’s costs rise from $25 to $32, matching the MSC.

MediumQ3. A chemical plant has $ MPC = \$10 $ per unit and an external cost of $4 per unit. Demand is $ P = 30 – 0.5Q $. Find the market quantity, the socially optimal quantity and the deadweight loss. Show worked answer

Market: $ 10 = 30 – 0.5Q \Rightarrow 0.5Q = 20 \Rightarrow Q_m = 40 $, $ P_m = \$10 $.
$ MSC = 10 + 4 = 14 $. Social: $ 14 = 30 – 0.5Q \Rightarrow 0.5Q = 16 \Rightarrow Q^* = 32 $, $ P^* = \$14 $.
$ DWL = \tfrac{1}{2} \times (40 – 32) \times 4 = \tfrac{1}{2} \times 8 \times 4 = \$16 $.

MediumQ4. Vaccines are supplied at a constant $15. Private demand is $ Q = 100 – 2P $, and each vaccine has an external benefit of $8. (a) Find the market quantity. (b) Find the optimal quantity with an $8 subsidy. (c) Would giving vaccines away free be efficient? Show worked answer

(a) $ Q_m = 100 – 2(15) = 70 $.
(b) The subsidy cuts the buyer’s price to $ 15 – 8 = 7 $: $ Q^* = 100 – 2(7) = 86 $.
(c) At a price of zero, $ Q = 100 $, which is more than 86. The last 14 vaccines would go to people whose social benefit is below the $15 cost, so it is not efficient unless the external benefit is larger (for example, for a highly contagious disease).

MediumQ5. 100 factories each emit 10 tonnes of CO₂. The government sets a cap of 500 tonnes with tradable permits. (a) By how much must emissions fall? (b) Why is this cheaper than ordering every factory to cut emissions by 50%? Show worked answer

(a) Current emissions $ = 100 \times 10 = 1{,}000 $ tonnes. Required fall $ = 1{,}000 – 500 = 500 $ tonnes.
(b) With trading, factories that can cut cheaply do most of the cutting and sell permits to high-cost factories. A 50% rule forces high-cost factories to cut too, so the same 500-tonne reduction costs more in total.

ExamQ6. Explain the Coase theorem. Give one example where it might work and one where it would fail. [4 marks] Show worked answer

If property rights are clearly defined and transaction costs are low, private bargaining reaches the efficient outcome, whoever holds the rights; the allocation of rights affects who pays, not efficiency. [2]
Works: a noisy bar and one neighbour. There are few parties and the rights are clear, so the bar could pay for double glazing or install soundproofing. [1]
Fails: air pollution from thousands of factories affecting millions of people. Transaction costs are huge, rights to clean air are unclear and free-riding stops collective bargaining, so government action is needed. [1]

Check yourself

1. A negative externality causes the free market to:

Producers ignore the external cost, so MPC is below MSC and output is too high.

2. A Pigouvian tax should be set equal to:

That tax lifts MPC to MSC, so the market produces Q*.

3. Compared with a Pigouvian tax, cap-and-trade:

The cap sets total emissions; trading sets the permit price.

Your score: 0 out of 3

The short version

An externality is a spillover cost or benefit to a third party that the market price ignores.
$ MSC = MPC + \text{external cost} $ and $ MSB = MPB + \text{external benefit} $. The social optimum is where $ MSB = MSC $.
Negative externalities lead to overproduction and positive externalities to underproduction. Each creates a DWL triangle between $ Q_m $ and $ Q^* $.
Fixes: a Pigouvian tax equal to the external cost, a subsidy equal to the external benefit, regulation, or cap-and-trade (which fixes quantity, as in the EU ETS).
The Coase theorem works only with clear property rights and low transaction costs. The full chapter in Economics Made Simple has 15 exam-style questions with complete answers.

Step 22: Externalities

What is an externality?

Negative externalities: the market produces too much

Positive externalities: the market produces too little

How governments fix externalities

The Coase theorem: can people sort it out themselves?

Practise: 6 questions

Check yourself

The short version

Further reading on EconTutorials

Contact Info

Quick Links

Success!