externalities activitiesap microeconomicspigouvian taxcoase theoremmarket failure graph

Externalities Classroom Activities for AP Microeconomics

·8 min read
Jude Wallis

Jude Wallis

Founder of EconLearn · 2nd place internationally, Economics Olympiad (econolympiad.org)

An externalities activity earns its period when it shows students something a graph alone cannot teach: the market quantity and the socially optimal quantity differ, and closing that gap takes a specific policy. Below are six activities built around the live graph at the externality sandbox, each with a timing, the mechanics, and the debrief question that makes it land.

See it move

This is the live Externalities sandbox. Drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

A lecture on externalities produces students who can label marginal social cost above marginal private cost and still think the goal of policy is to eliminate pollution entirely. It is not. The goal is the quantity where the last unit's benefit still covers its full cost to everyone affected, a quantity that is almost never zero.

1. Predict then reveal, 5 minutes

Put the sandbox on the projector, set to a negative externality with the external cost slider at zero, so the private and social cost curves sit on top of each other. Have the class predict, in writing, what happens to the gap between the curves and to quantity once the external cost rises.

Most correctly predict the curve shifts up. Fewer predict the market quantity stays put, because nobody in the transaction pays the external cost. Only a policy moves it.

The debrief question: if pollution is now more costly to society, why did the factory not produce less. It never sees that cost, because it lands on someone else, and that is the whole unit in one sentence.

2. The paper ball pollution game, 25 minutes

Pair students into factory and neighbor. Each factory can crumple up to eight paper balls and toss them at a target bin for points; every ball, hit or miss, also drops scrap paper on the neighbor's desk.

Set the numbers so the arithmetic is exact. Each ball sold into the bin pays the factory a flat 20 points, its marginal private benefit. Producing costs effort points that rise by 3 each ball, 3 for the first, 6 for the second, up to 24 for the eighth, its marginal private cost. A rational factory produces while the next ball's benefit still exceeds its cost: true through the sixth ball, cost 18, and false at the seventh, cost 21. The market quantity is 6.

Every ball also costs the neighbor 9 points in cleanup, a constant marginal external cost. Add that to the factory's cost and the marginal social cost of the nth ball is 3n plus 9. Balls should get thrown only while the benefit of 20 exceeds that social cost: true through the third ball, cost 18, and false at the fourth, cost 21. The socially optimal quantity is 3.

Run two short rounds. Round one, no rule: factories throw 6, and the three balls between quantity 3 and quantity 6 destroy value on net, 1 point on the fourth, 4 on the fifth, 7 on the sixth, 12 points of deadweight loss per pair. Round two, a per unit tax of exactly 9 points, matching the marginal external cost: effective cost becomes 3n plus 9, the same math the social planner used, and factories stop at 3.

The debrief question: why 9 points and not some other number. Point at the neighbor's cleanup cost: a tax that undershoots it leaves overproduction in place, and one that overshoots blocks balls that were worth throwing. A Pigouvian tax has to equal the marginal external cost to land on the optimal quantity, not just move toward it.

The misconception it exposes: ask what the socially optimal number of paper balls was. Several will say zero, because the neighbor bears a cost. The arithmetic says 3, because the first three balls still create more value than the cleanup they cause. Zero pollution is not the goal of externality policy; the efficient quantity is, and it sits above zero whenever units still clear the social cost test.

3. The flu shot free rider round, 15 minutes

Now flip the sign. Each student can pay 3 tokens for a flu shot worth 2 tokens to them privately in fewer sick days, a private loss of 1 token. Left alone, nobody buys one, so the private market quantity is zero.

But every shot also protects the four nearest desks from the flu, worth 1 token to each neighbor, 4 tokens of external benefit per shot. Added to the private benefit of 2, the marginal social benefit is 6, above the 3 token cost. A subsidy sized to that 4 token external benefit flips the private math to 2 plus 4 against a cost of 3, and buying becomes worth it.

Run two rounds, no subsidy then subsidy, and tally purchases each time.

The debrief question: why did rational, self-interested students skip something that made the room better off. The benefit to the room was not the benefit they personally weighed. That is free riding on a positive externality, and it explains real underprovision of vaccination, education, and research.

4. Coase negotiation with assigned property rights, 15 minutes

Return to the same factory and neighbor pair from activity 2: a flat benefit of 20 per ball, a private cost rising 3 per ball, a marginal external cost of 9. Remove the tax, assign a property right instead, and let the two bargain freely.

Round one: give the neighbor the right to a clean desk. The factory must pay for permission to toss each ball, at least 9, the cleanup cost, and it only pays when its own net benefit, 20 minus that ball's cost, still exceeds 9. That holds through the third ball, net benefit 11, so bargaining settles at 3, the same optimal quantity from activity 2.

Round two: give the factory the right to toss freely and let the neighbor pay it to stop. Left alone the factory would throw 6, but the neighbor buys back any ball whose 9 point cleanup saving beats the factory's own net benefit, true for balls four through six. Bargaining again settles at 3.

The debrief question: why did both rounds land on the same quantity when the starting rights were opposite. Whoever starts without the right pays the other side until the marginal ball is worth exactly its cost, which is the Coase theorem: when property rights are clear and bargaining is cheap, the efficient quantity is reached no matter who holds the right at the start. What changes is who ends up richer, not how much gets produced.

5. Which policy sort, 10 minutes

Hand out cards naming a real policy: a carbon tax, a solar tax credit, an emissions cap, fishing quotas on a shared lake, a flu shot subsidy, an airport noise ordinance, water rights on a river, a bottle deposit refund. Students sort each into one of four bins: tax, subsidy, regulation, or property rights.

Several cards fit two bins depending on wording, and that ambiguity is the point. A cap and trade system is a quantity regulation until permits become tradable, at which point it is also a property right being bought and sold.

The debrief question: for one card in each bin, ask what number a regulator needs to size the policy correctly. A tax needs the marginal external cost. A permit cap needs the socially optimal quantity. Naming the missing number separates a policy a class can defend from one it can only describe.

6. Build the externality yourself, 10 minutes

Open the externality sandbox, hand control to a student, and have the class direct the external cost slider. Raise it and watch the social cost curve pull away from the private cost curve, the deadweight loss triangle appear between the market and optimal quantities, then set a per unit tax until the triangle collapses to nothing. Switch to the positive case and repeat with a subsidy.

The debrief question: the tax that collapsed the triangle to nothing matched the external cost slider's number exactly, so why does the deadweight loss disappear only at that number and not some other one. As in the paper ball game, a tax below the external cost would leave some overproduction in place, and a tax above it would block balls that still clear the social cost test.

Student driven and unscripted, which makes it a strong closer: the questions asked while dragging the slider reveal which piece of the model the class still does not trust.

Sequencing

A workable arc across a lesson or two: predict then reveal to show the market will not correct itself, the paper ball game to build tax intuition with checked numbers, the flu shot round to flip the sign to a positive externality, Coase negotiation to show clear property rights reach the same answer without a government setting a price, the policy sort to connect the model to real law, and the sandbox to close. On why the last few units still clear the cost test and why the flu shot problem generalizes, see what deadweight loss actually measures and the free rider problem explained.

The graphs, vocabulary, and practice questions for this unit live in the public goods and externalities module, and full timings, objectives, and exit tickets for every AP Economics unit are in the lesson plans library.

Frequently asked questions

Why isn't the socially optimal quantity of pollution zero?

Because some units of a polluting activity still create more benefit than the external cost they cause. The efficient quantity sits where marginal social benefit equals marginal social cost, not where the externality disappears. Once the last unit's cost to everyone exceeds its benefit, production should stop, but every unit before that point still adds value on net.

How do you teach a Pigouvian tax without just defining it?

Run a game where each unit of production earns points but imposes a fixed external cost on a classmate. Set the tax exactly equal to that external cost, then watch students' own production choice shift to match the socially optimal quantity, so the tax's size, not its existence, becomes the lesson.

What is a simple way to demonstrate the Coase theorem in class?

Assign one student the property right to a clean desk and the other the right to pollute freely, then let them negotiate a price with no other rules. Run both versions with the same underlying costs and benefits, and the class discovers production settles at the same efficient quantity either way, only the money moves differently.

How do you show a positive externality without a demand curve lecture?

Use a free rider game: give a purchase a private cost above its private benefit so nobody buys it alone, then add an external benefit to others nearby. Once the class sees the socially optimal choice differs from what anyone would choose individually, a subsidy sized to the external benefit stops feeling arbitrary.

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