Week 14 · Chapter

Chapter 14 — Externalities, Public Goods & Market Failure

Principles of Microeconomics Free sample edition

The module's primary reading · ~45–55 minutes · Objective 8 (analyze market failures — externalities, public goods, common resources, and asymmetric information — evaluate responses such as corrective taxes, cap-and-trade, and private bargaining, and survey behavioral economics and the measurement of inequality evenhandedly), with Objective 4 (measure consumer surplus, producer surplus, and market efficiency, and analyze price ceilings, price floors, taxes, and subsidies, including who bears a tax and the deadweight loss) · Read it first this week; the lecture, the slide deck, the tutorial, the quiz, and the Model Workshop all build on it.

In plain language

Some costs and benefits of a trade land on people who were never part of it. When a workshop's smoke drifts over the houses next door, the neighbors pay part of the cost of a good they never bought; that spillover is an externality (a cost or benefit that falls on bystanders). This week you will measure how far a market drifts from the best quantity when it ignores a spillover, and you will see three ways to fix it: a tax, a cap on the total, or a bargain between the people involved. You will also meet goods that markets struggle to supply at all, such as a public good (something anyone can enjoy and no one can be kept from), and shared resources that tend to be used up. Last, you will weigh carbon pricing as a debate with two strong sides.

Why you already care about this

Picture a street with a busy workshop at one end. Every unit it makes sends a little smoke over the homes nearby. Mei Ling hangs her laundry to dry and brings it back in gray. Tomás, two doors down, keeps his windows shut on summer nights. Neither of them buys what the workshop makes, and neither of them sells anything to it. Yet each of them pays part of the cost of every unit it makes.

Since Week 6 you have read the course's running market as a success story: at 6 dollars and 30 units a day, buyers and sellers make every trade that is worth making, and total surplus is as large as it can be. That story counted only the people inside the trade. This chapter asks what happens when some of the cost falls outside it, and the answer turns Week 7 upside down. The very 2-dollar tax that wasted surplus in Week 7 becomes the fix.

By the end of this chapter you will be able to:

tell a negative externality from a positive one, and private cost from social cost;
build marginal social cost from supply and find the efficient quantity where it meets marginal social benefit;
compute the deadweight loss of an externality and show how a corrective tax or subsidy removes it;
explain how cap-and-trade works and what the Coase theorem says about bargaining;
sort any good as private, public, common, or club by asking whether it is rival and excludable;
explain the free-rider problem and the tragedy of the commons, and lay out the carbon-pricing debate without picking a winner.

Carry this sentence with you: same tax, different market — a cost, then a cure.

Where we are

Already covered: Week 1 separated positive statements from normative ones. Weeks 3 and 4 built the running market, Qd = 90 − 10P and Qs = 10P − 30, with its equilibrium at 6 dollars and 30 units a day. Week 6 measured consumer and producer surplus as triangles, 45 dollars each. Week 7 put a 2-dollar tax and a 2-dollar subsidy on that market and measured a deadweight loss of 10 dollars a day for each.
This week: externalities, marginal social cost and benefit, the efficient quantity, corrective taxes and subsidies, cap-and-trade, the Coase theorem, the four kinds of goods, the free-rider problem, the tragedy of the commons, and the carbon-pricing debate.
How they connect: the same demand and supply lines and the same surplus triangles now include the people outside the trade, so Week 7's tax and subsidy get a second, opposite verdict.
Where we're going next: Week 15 closes the unit on market failure with markets where one side knows more than the other, then surveys behavioral economics and the measurement of inequality.

Two tools carry straight over. From Week 6: the demand curve, read as P = 9 − Q ⁄ 10, gives what buyers will pay for each unit, and the supply curve, P = 3 + Q ⁄ 10, gives what each unit costs its seller. From Week 7: a per-unit tax shifts supply up by the tax, opens a wedge between what buyers pay and what sellers keep, and shrinks the quantity traded. This week you add one more line to the same graph.

1. Name the spillover: externalities

You have met spillovers all your life. A neighbor's leaf blower at 7 in the morning costs you sleep. A neighbor's flower garden makes your walk to the bus nicer, and you pay nothing for it. When a classmate gets a flu shot, you are a little less likely to catch the flu, though you never paid for that shot. In each case a choice made by someone else changes your day, and no price passes between you.

An externality is a cost or benefit that falls on people outside a transaction, who neither buy nor sell the good.
A negative externality is a cost that a transaction imposes on bystanders, such as the workshop's smoke.
A positive externality is a benefit that a transaction gives to bystanders, such as the protection neighbors gain when one person is vaccinated.

To measure a spillover, split a good's cost into two parts.

Private cost is the cost of producing a good that the seller itself pays, such as materials, labor, and power; the supply curve shows it for each unit.
Social cost is the whole cost of producing a good to everyone in society: the seller's private cost plus any cost that falls on bystanders.

When there is no spillover, private cost and social cost are the same, and the market's quantity is the best one. When there is a spillover, they differ, and the market's quantity drifts away from the best one. That drift is a market failure: the market, left alone, does not reach the outcome that makes society as well off as it can be.

Misconception check. Students often think an externality is any cost a buyer dislikes, such as a high price. A high price is paid by someone inside the trade, so the market already counts it. The cure: ask who pays. If the person bearing the cost neither buys nor sells the good, it is an externality.

2. Add the smoke to the running market

Go back to the street with the workshop. In this classroom model, each unit of the running market's good puts 2 dollars of harm on the neighbors: cleaning bills, closed windows, sore throats. The 2 dollars is the same for every unit. That steady, unit-by-unit harm is an assumption of the model, and it keeps the arithmetic clean; real harm can grow faster as pollution piles up.

Write the pieces with letters you will use all week.

MPC is the marginal private cost: what one more unit costs its seller, read from the supply curve.
MEC is the marginal external cost: the cost that one more unit imposes on people outside the trade, here 2 dollars.
MSC is the marginal social cost: the full cost of one more unit to society, MSC = MPC + MEC.

Worked example — building marginal social cost. Start from supply and add the harm to every unit.

Marginal private cost. Supply is P = 3 + Q ⁄ 10. The 20th unit costs its seller 3 + 2 = 5 dollars, and the 30th costs 3 + 3 = 6 dollars.
Add the external cost. MSC = MPC + MEC = (3 + Q ⁄ 10) + 2.
Simplify. MSC = 5 + Q ⁄ 10.

In words: the true cost of each unit to society is 2 dollars above what the seller pays. The 20th unit costs society 5 + 2 = 7 dollars, and the 30th costs 6 + 2 = 8 dollars.

Picture the graph with units per day along the horizontal axis and dollars per unit up the vertical axis. Supply starts at 3 dollars and rises 1 dollar for every 10 units. Marginal social cost is a second line parallel to supply, starting at 5 dollars and sitting 2 dollars above supply at every quantity.

In practice (your tools). In Desmos, type y = 9 - x/10 for demand, y = 3 + x/10 for supply, and y = 5 + x/10 for marginal social cost. Tap each crossing to read its coordinates. In Google Sheets, put 0, 10, 20, 30, and 40 in cells A2 to A6, type =3+A2/10 in B2 for marginal private cost, =B2+2 in C2 for marginal social cost, and drag both down.

Misconception check. Students often shift the demand curve to show the smoke. The smoke is a cost of making the good, and the neighbors are not buyers. The cure: a negative externality from production adds a cost line above supply. Demand stays where it is.

3. Find the efficient quantity

Ask what quantity would be best for everyone on the street, neighbors included. Each unit is worth making only if what buyers value it at covers its full cost to society. Keep making units while that holds, and stop where it no longer does.

On the benefit side, write MPB for the marginal private benefit, the value of one more unit to its buyer, read from demand. Here nobody outside the trade gains from the good, so the marginal social benefit, written MSB, is the same line: MSB = MPB = 9 − Q ⁄ 10.

The efficient quantity is the quantity at which marginal social benefit equals marginal social cost, MSB = MSC, so every unit worth more to society than it costs is made and no other unit is.

Worked example — the efficient quantity on the running market. Set marginal social benefit equal to marginal social cost.

Set the two lines equal. 5 + Q ⁄ 10 = 9 − Q ⁄ 10.
Collect the Q terms. 2Q ⁄ 10 = 9 − 5 = 4, so Q ⁄ 5 = 4.
Solve. Q = 20 units per day.
The price on each line. Demand gives 9 − 20 ⁄ 10 = 7 dollars, and marginal social cost gives 5 + 20 ⁄ 10 = 7 dollars.
Compare with the market. Without the smoke counted, 9 − Q ⁄ 10 = 3 + Q ⁄ 10 gives Q = 30 at 6 dollars.

In words: the best quantity for the whole street is 20 units a day at 7 dollars. The market makes 30 versus 20, ten units too many, because sellers pay none of the neighbors' cost. A negative externality makes a market produce too much.

On the graph, the marginal-social-cost line crosses demand at 20 units and 7 dollars, up and to the left of the market's crossing at 30 units and 6 dollars.

Misconception check. Students often think pollution makes a market produce too little, because the harm sounds like a drag on the economy. The cure: sellers ignore the cost they push onto others, so the good looks cheaper to them than it is. They make more of it, not less: 30 units instead of 20.

4. Measure the deadweight loss of the spillover

Look at the 10 units the market makes beyond 20. For each of them, the cost to society is higher than the value buyers place on it. Those units make society worse off, and the total of those losses is a deadweight loss, the same idea you met in Week 7.

Worked example — the deadweight loss of the externality. Find the gap on the last unit, then compute the triangle.

At Q = 20. Marginal social cost and demand both equal 7 dollars, so the gap is 0.
At Q = 30. Marginal social cost is 5 + 3 = 8 dollars, and buyers value the 30th unit at 9 − 3 = 6 dollars, so the gap is 8 − 6 = 2 dollars.
The triangle. Its base runs from 20 to 30 units and its height is the 2-dollar gap, so DWL = 1⁄2 × 2 × (30 − 20) = 1⁄2 × 2 × 10 = 10 dollars per day.

In words: making those last 10 units costs society 10 dollars a day more than they are worth to anyone. The neighbors carry that loss, and nobody gains it.

You can check the result by counting everyone's gains and losses. Call the total social surplus: the value buyers get minus every cost of making the good, sellers' and neighbors' alike.

At the efficient quantity. The area between demand and marginal social cost out to 20 units is 1⁄2 × 20 × (9 − 5) = 40 dollars per day.
At the market quantity, by parts. Consumer surplus 45 + producer surplus 45 − external cost 2 × 30 = 90 − 60 = 30 dollars per day.
The difference. 40 − 30 = 10, the deadweight loss.

Picture the loss on the graph as a thin triangle lying between the marginal-social-cost line above and the demand line below, from 20 units on the left, where the two lines meet, out to 30 units on the right, where they are 2 dollars apart.

A limitation of the model, said plainly: the 2-dollar harm is a number built for this course. Measuring real harm per unit is hard, and estimates of it are one reason the policy debates later in this chapter stay open.

Misconception check. Students often count the whole external cost, 2 × 30 = 60, as the deadweight loss. Most of that harm comes from units that are worth making even after the harm is counted. The cure: the deadweight loss is only the triangle on the units beyond the efficient quantity, 10 dollars a day.

5. Bring back Week 7's tax as a corrective tax

How could a government move the market from 30 units to 20? Make sellers feel the neighbors' cost. If each unit carries a tax equal to the harm it does, the seller's own cost line moves up onto the marginal-social-cost line. The economist Arthur Cecil Pigou proposed this idea in The Economics of Welfare (1920).

A corrective tax is a per-unit tax set equal to the marginal external cost at the efficient quantity, which makes sellers face the full social cost and moves the market to the efficient quantity; it is also called a Pigouvian tax.

Here the marginal external cost is 2 dollars at every unit, so the corrective tax is 2 dollars a unit. That is exactly the tax you studied in Week 7.

Worked example — the 2-dollar corrective tax. Shift supply up by the tax and solve.

Supply with the tax. Qs = 10 × (P − 2) − 30 = 10P − 50.
The new equilibrium. 90 − 10P = 10P − 50, so 20P = 140 and P = 7.
Prices and quantity. Buyers pay 7 dollars, sellers keep 7 − 2 = 5 dollars, and Q = 90 − 70 = 20 units per day.
Revenue. 2 × 20 = 40 dollars per day.
The check by parts. Consumer surplus 20 + producer surplus 20 + revenue 40 − external cost 2 × 20 = 80 − 40 = 40 dollars per day.

In words: the tax brings the market to 20 units at 7 dollars, the efficient quantity, and social surplus rises to its largest possible value, 40 dollars a day. The neighbors still bear 40 dollars of harm from the 20 units, but those units are worth making.

Now set the two weeks side by side.

The same 2-dollar tax on the running market, without and with a 2-dollar external cost per unit, in dollars per day (illustrative)
Case	Quantity before the tax	Quantity with the tax	Surplus before the tax	Surplus with the tax	Effect of the tax
Week 7: no externality	30	20	90	80	causes a deadweight loss of 10
Week 14: 2-dollar external cost	30	20	30	40	removes a deadweight loss of 10

The tax, the prices, and the quantity are identical in both rows. What changed is the market. In Week 7, 30 units was already the best quantity, so cutting to 20 threw away good trades. This week, 20 is the best quantity, so cutting to 20 throws away only bad ones.

Who pays the corrective tax? The same Week 7 incidence rule applies. Here buyers pay 1 dollar more and sellers keep 1 dollar less, only because the two curves are equally steep; whoever writes the check, the less responsive side bears more.

Misconception check. Students often set the corrective tax equal to the total external cost, 2 × 20 = 40 dollars. That is a day's harm in all, not the harm per unit. The cure: the corrective tax is per unit and equals the marginal external cost at the efficient quantity, 2 dollars.

6. Flip the sign: a positive externality and a corrective subsidy

Now suppose the good helps the neighbors instead. Picture a good whose every unit gives the street 2 dollars of benefit, the way a fresh coat of paint on one house lifts the look of the whole block. Write MEB for the marginal external benefit, the value one more unit gives to people outside the trade, here 2 dollars.

Worked example — the efficient quantity with an external benefit. Add the benefit to demand, then set the new line equal to supply.

Marginal social benefit. MSB = MPB + MEB = (9 − Q ⁄ 10) + 2 = 11 − Q ⁄ 10.
Set it equal to supply. 11 − Q ⁄ 10 = 3 + Q ⁄ 10, so Q ⁄ 5 = 8.
Solve. Q = 40 units per day, above the market's 30.

In words: this time the market makes too little. Buyers count only their own benefit, so they stop at 30 units even though units 31 to 40 are worth more to society than they cost.

The fix runs the other way: pay sellers for each unit. A corrective subsidy is a per-unit payment set equal to the marginal external benefit at the efficient quantity, which raises the quantity traded to the efficient quantity.

Worked example — the 2-dollar corrective subsidy. This is Week 7's subsidy.

Supply with the subsidy. Qs = 10 × (P + 2) − 30 = 10P − 10.
The new equilibrium. 90 − 10P = 10P − 10, so 20P = 100 and P = 5.
Prices and quantity. Buyers pay 5 dollars, sellers receive 5 + 2 = 7 dollars, and Q = 90 − 50 = 40 units per day.
Cost to taxpayers. 2 × 40 = 80 dollars per day.

In words: the subsidy moves the market to 40 units, the efficient quantity. In Week 7, with no external benefit, the same subsidy pushed the market past its best quantity and cost 10 dollars a day of surplus. With the benefit, it lands the market on its best quantity instead.

On the graph, marginal social benefit is a line parallel to demand and 2 dollars above it, starting at 11 dollars. It crosses supply at 40 units and 7 dollars, to the right of the market's crossing at 30.

Misconception check. Students often think every subsidy wastes money, since Week 7's subsidy created a deadweight loss. That result held only in a market with no spillover. The cure: ask whether bystanders gain. With an external benefit, a subsidy equal to that benefit moves the market to the efficient quantity.

7. Cap the total: cap-and-trade

A tax sets a price on pollution and lets the market decide how much pollution happens. A government can also turn that around: set the total amount of pollution and let a market decide its price. That is the idea behind cap-and-trade, a policy that caps the total amount of a pollutant and issues tradable permits for that amount.

An allowance is a tradable permit in a cap-and-trade program that lets its holder emit a fixed amount of a pollutant.

The United States has a long-running real case. According to the U.S. Environmental Protection Agency, the Acid Rain Program was established under Title IV of the Clean Air Act. It set a permanent cap on sulfur dioxide emissions from power plants, and sources may buy, sell, or bank allowances. Under the program, one allowance permits a unit to emit 1 ton of sulfur dioxide. Begun in 1995, it was the first national cap-and-trade program in the United States. The Readings & Resources page links the agency's own description.

Why let firms trade? Picture two power plants, one that can cut a ton of pollution cheaply and one for which cutting is expensive. The cheap cutter can cut extra tons and sell its spare allowances to the expensive one. The total stays at the cap, but more of the cutting happens where it costs least. A tax works the same way at the margin: each plant cuts until cutting one more ton costs more than paying the tax.

The difference between the tools is what each one fixes. A tax fixes the price of a unit of pollution, and the amount of pollution then depends on how firms respond. A cap fixes the amount, and the price of an allowance then depends on how hard cutting turns out to be. Neither tells you the right size of the tax or the cap; that rests on how large the harm is.

Misconception check. Students often think cap-and-trade lets polluters off the hook, because a firm can buy the right to pollute. The cure: the cap fixes the total, so every ton one plant emits beyond its allowances is a ton another plant does not emit. Trading moves the cutting around; it does not raise the total.

8. Bargain it out: the Coase theorem

Sometimes the people on both sides of a spillover can sort it out themselves. The economist R. H. Coase made this argument in "The Problem of Social Cost" (1960), and the result carries his name.

Picture a factory beside a laundry. In this classroom model, the factory's smoke does 300 dollars a month of damage to the laundry's clean sheets. A filter on the factory's chimney would stop the damage and costs 200 dollars a month. Whatever the law says, stopping 300 dollars of damage for 200 dollars is a good deal for the two of them together.

The Coase theorem is the result that, when property rights are clear and transaction costs are low, private bargaining reaches the efficient outcome whichever side holds the right; who holds the right changes who pays whom, not what is produced.
Property rights are the legal rules that say who may use a resource and how, such as whether a factory may send smoke next door.
Transaction costs are the costs of reaching and keeping a bargain, such as finding the other parties, negotiating, and enforcing the deal.

Worked example — the factory and the laundry. Try each assignment of the right.

The laundry holds the right to clean air. The factory must either stop the smoke or pay for the damage. A 200-dollar filter beats 300 dollars of damage, because 200 < 300, so the factory installs the filter.
The factory holds the right to pollute. Now the laundry has a problem it must pay to fix. It loses 300 dollars a month to the smoke, and the filter costs 200. Any payment between 200 and 300 dollars leaves both sides better off, so the laundry pays the factory to install the filter.
The gain from the filter. 300 − 200 = 100 dollars a month, whichever side holds the right.

In words: the filter goes in either way. The right decides only who pays for it: the factory in the first case, the laundry in the second.

The theorem's conditions do the heavy lifting. Here there are two parties next door to each other, so talking is cheap. Now imagine the smoke drifting over 5,000 homes instead of one laundry. Finding everyone, agreeing on who pays what, and stopping each home from waiting for the others to settle would cost a great deal. With high transaction costs, bargaining often fails, which is why taxes and caps exist.

An honesty note: the low-transaction-cost condition is an assumption, named as one. The Coase theorem is a benchmark for when bargaining can work, not a claim that it usually does.

Misconception check. Students often think the Coase theorem says the side that holds the right decides what gets produced. The cure: with cheap bargaining, the efficient outcome happens either way, here the filter. The right changes who pays whom, not whether the filter goes in.

9. Sort goods by two questions: rival and excludable

Some goods seem to resist markets altogether. To see which ones, ask two questions about any good.

A good is rival when one person's use leaves less for others, such as a sandwich or a fish taken from a lake.
A good is excludable when people who do not pay can be kept from using it, such as a concert with a ticket gate.

The two answers sort every good into one of four groups.

A private good is a good that is both rival and excludable, such as a meal bought at a restaurant.
A public good is a good that is neither rival nor excludable, such as a fireworks show anyone nearby can watch.
A common resource is a good that is rival but not excludable, such as fish in open waters.
A club good is a good that is excludable but not rival, such as an uncrowded streaming service or toll road.

The four kinds of goods, sorted by whether each is rival and excludable, with one example of each
	Excludable	Not excludable
Rival	private good: a restaurant meal	common resource: fish in open waters
Not rival	club good: an uncrowded streaming service	public good: a fireworks show

The economist Paul A. Samuelson set out the theory of public goods in "The Pure Theory of Public Expenditure" (1954). Markets supply private goods well, because a seller can charge each user and each unit goes to one buyer. The trouble starts in the right-hand column, where no one can be kept out.

Misconception check. Students often call anything a government provides a public good. A public school seat or a city bus ride can be rival and can be limited to those who enroll or pay. The cure: test the two properties. A good is public only if it is neither rival nor excludable, whoever provides it.

10. See the free-rider problem

Picture a neighborhood planning a fireworks show for a summer evening. Anyone on a porch or a rooftop for blocks around can see it, and no one can be stopped from looking up. That makes the show a public good.

Worked example — the fireworks show. Compare the show's value with its cost.

Total value. 100 residents each value the show at 10 dollars, so it is worth 100 × 10 = 1,000 dollars.
Net gain. The show costs 600 dollars, so it adds 1,000 − 600 = 400 dollars of value to the neighborhood.
An equal share. Split evenly, the cost is 600 ⁄ 100 = 6 dollars a resident, less than each resident's value of 10.

In words: the show is well worth putting on, and an equal split would leave every resident 4 dollars ahead. Yet a collection jar might not reach 600 dollars.

The reason is the free-rider problem: the temptation to enjoy a good without paying for it when no one can be kept from using it, which leaves voluntary contributions for a public good short of its cost. Each resident thinks: "My 6 dollars barely changes whether the show happens, and I get to watch either way." If enough residents think that, the show never happens, and the neighborhood loses a gain of 400 dollars. This is why public goods are often paid for through taxes, dues, or a sponsor, rather than through voluntary sales.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Think of something in your life that anyone can use without paying, such as a free app, a park, or a public radio stream. In two sentences, say how it gets paid for and whether free riders put it at risk.
(b) Think of a group project, a shared kitchen, or a team chore where one person did less and still shared the result. In two sentences, explain how the free-rider problem showed up and what, if anything, fixed it.

Misconception check. Students often think free riders are only selfish people, so better people would fix the problem. The cure: the problem comes from the good's features, not from bad character. When no one can be excluded, each person's own payment changes little, so even generous people can end up short of the total.

11. Manage a commons

Common resources are rival but open to all, and that mix creates its own trouble. Picture a lake that several fishing families share. Each family gains the whole value of every extra fish it catches, but the cost of a thinner stock next year is spread across every family.

The tragedy of the commons is the overuse of a common resource, which is rival but open to all, because each user gains the full benefit of taking more while the cost of depletion is shared by everyone.

Garrett Hardin named the problem in his essay "The Tragedy of the Commons" (1968). His argument points toward two familiar fixes: divide the resource into private shares, or let a government set and enforce limits.

Elinor Ostrom added a third answer from the field. In Governing the Commons (1990) she documented communities that manage shared resources well through their own rules, without either privatization or central control. Users who know each other, watch each other, and agree on limits and penalties can keep a commons healthy for a long time. A commons does not have to end in tragedy.

Both ideas are positive claims about how people behave, tested against evidence: Hardin predicted overuse when access is open and unmanaged, and Ostrom documented the conditions under which communities avoid it. Which fix suits a particular lake or forest is a separate, normative choice.

Misconception check. Students often think the tragedy of the commons proves that only privatization or a government can save a shared resource. The cure: Ostrom's field studies documented communities that manage a commons through their own rules. The tragedy describes an open, unmanaged resource, not every shared one.

12. Weigh carbon pricing as a named debate

Carbon dioxide from burning fuel is a spillover on a world scale: the people who burn fuel pay for it, while the effects of the emissions spread far beyond the trade. Policies called carbon pricing put a price on those emissions, either through a tax per ton or through a cap-and-trade market in permits. Whether, how, and how much to price carbon is a contested policy question, and this course presents it as a debate.

Start with the positive claims, the ones evidence can test. In the model, a price on emissions raises the cost of the goods that emit, so buyers buy fewer of them and sellers look for cleaner ways to make them. A single price also means that the firms able to cut most cheaply cut first, the same logic as the two power plants in Section 7.

Now the two cases, each at full strength.

The case for pricing carbon. Supporters apply this chapter's model directly: an emitter that does not pay for its harm produces too much, and a price makes it face the full social cost. They argue that a price lets millions of households and firms choose their own cheapest cuts, rather than having a government pick technologies for them, and that the revenue can be returned to households or used to cut other taxes. Their normative claim is that people who cause a harm should pay for it, and that the interests of future people deserve real weight.
The case for caution or for other tools. Critics point to the limitation flagged in Section 4: the harm from a ton of carbon is hard to measure, and economists' estimates of it differ widely, so the right price is uncertain. They argue that higher energy prices can weigh most on households that spend a large share of their budgets on fuel and power, and that if only some places price carbon, production may move to places that do not. Some prefer standards for vehicles and buildings or public spending on new technology, which they see as more predictable or fairer. Their normative claim is that the costs to people living now, and how those costs are shared, deserve heavy weight.

Both sides accept the model's positive result that an unpriced negative externality leads to too much of the good. They disagree about how large the harm is, how people and firms will respond, which tool works best, and how to weigh people now against people later. Those last questions are normative. This course gives no verdict; the choice rests on evidence and on values.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) In two or three sentences, state the strongest point for pricing carbon and label which part is positive and which is normative.
(b) In two or three sentences, state the strongest point for caution or for another tool, and label which part is positive and which is normative.

Misconception check. Students often think the externality model settles the carbon-pricing debate, because it shows a deadweight loss. The model shows that a spillover causes one; it does not measure the real harm per ton or say how to weigh present and future costs. The cure: keep the positive result and the normative choice apart.

13. Check the classic wrong turns

Most mistakes this week come from forgetting the people outside the trade, or from treating a property of the good as a property of whoever supplies it. A short routine catches them.

Step one: who bears the cost or gains the benefit? If it is someone outside the trade, you have an externality.
Step two: which way does the market miss? An external cost means too much; an external benefit means too little.
Step three: what is the fix per unit? A corrective tax or subsidy equals the external cost or benefit per unit at the efficient quantity.
Step four: what kind of good is it? Ask whether it is rival and whether it is excludable, whoever provides it.

Worked example — checking a classmate's work. A classmate writes: "The workshop's smoke means the market makes too little. The fix is a tax of 40 dollars, the total harm at 20 units. And under the Coase theorem, if the factory holds the right, the filter never goes in."

The 'too little' claim. Sellers ignore the 2-dollar harm, so the market makes 30 units, more than the efficient 20.
The 40-dollar tax. The total harm at 20 units is 2 × 20 = 40 dollars a day, but the corrective tax is per unit: 2 dollars, the marginal external cost.
The Coase claim. If the factory holds the right, the laundry pays it between 200 and 300 dollars to install the filter, so the filter still goes in.

In words: the corrected statement is "the market makes 30 units where 20 is efficient, a 2-dollar tax per unit fixes it, and the filter goes in whoever holds the right."

Misconception check. Students often think that once a corrective tax is in place, the neighbors suffer no harm at all. The tax moves the market to the efficient quantity, where the neighbors still bear 2 dollars of harm on each of 20 units. The cure: the goal is the efficient quantity, not zero harm, because those 20 units are worth more than their full cost.

Key terms

Externality — A cost or benefit that falls on people outside a transaction, who neither buy nor sell the good. (first used: 1. Name the spillover: externalities)
Negative externality — A cost that a transaction imposes on bystanders, such as smoke from a workshop drifting over nearby homes. (first used: 1. Name the spillover: externalities)
Positive externality — A benefit that a transaction gives to bystanders, such as the protection neighbors gain when one person is vaccinated. (first used: 1. Name the spillover: externalities)
Private cost — The cost of producing a good that the seller itself pays, such as materials, labor, and power; the supply curve shows the marginal private cost of each unit. (first used: 1. Name the spillover: externalities)
Social cost — The whole cost of producing a good to everyone in society: the seller's private cost plus any external cost that falls on bystanders. (first used: 1. Name the spillover: externalities)
Market failure — A situation in which a market left alone does not reach the outcome that makes society as well off as it can be, as when an externality pushes the quantity away from the efficient quantity. (first used: 1. Name the spillover: externalities)
Marginal external cost — The cost that one more unit of a good imposes on people outside the trade, measured in dollars per unit. (first used: 2. Add the smoke to the running market)
Marginal social cost — The full cost to society of one more unit of a good, equal to the marginal private cost plus the marginal external cost. (first used: 2. Add the smoke to the running market)
Marginal social benefit — The full value to society of one more unit of a good, equal to the buyer's marginal private benefit plus any marginal external benefit to bystanders. (first used: 3. Find the efficient quantity)
Efficient quantity — The quantity at which marginal social benefit equals marginal social cost, so every unit worth more to society than it costs is produced and no other unit is. (first used: 3. Find the efficient quantity)
Social surplus — The total value a good's buyers receive minus every cost of producing it, the sellers' costs and the costs to bystanders alike; it is largest at the efficient quantity. (first used: 4. Measure the deadweight loss of the spillover)
Corrective tax — A per-unit tax set equal to the marginal external cost at the efficient quantity, which makes sellers face the full social cost and moves the market to the efficient quantity; it is also called a Pigouvian tax. (first used: 5. Bring back Week 7's tax as a corrective tax)
Corrective subsidy — A per-unit payment set equal to the marginal external benefit at the efficient quantity, which raises the quantity traded to the efficient quantity when a good benefits bystanders. (first used: 6. Flip the sign: a positive externality and a corrective subsidy)
Cap-and-trade — A pollution policy that caps the total amount of a pollutant and issues tradable permits for that amount, so firms that can cut emissions cheaply sell permits to firms that cannot. (first used: 7. Cap the total: cap-and-trade)
Allowance — A tradable permit in a cap-and-trade program that lets its holder emit a fixed amount of a pollutant; in the Acid Rain Program each allowance covers 1 ton of sulfur dioxide. (first used: 7. Cap the total: cap-and-trade)
Coase theorem — The result that, when property rights are clear and transaction costs are low, private bargaining reaches the efficient outcome whichever side holds the right; who holds the right changes who pays whom, not what is produced. (first used: 8. Bargain it out: the Coase theorem)
Property rights — The legal rules that say who may use a resource and how, such as whether a factory may send smoke next door or a neighbor may demand clean air. (first used: 8. Bargain it out: the Coase theorem)
Transaction costs — The costs of reaching and keeping a bargain, such as finding the other parties, negotiating, and enforcing the deal; they rise quickly when many people are affected. (first used: 8. Bargain it out: the Coase theorem)
Rival — Describes a good for which one person's use leaves less for others, such as a sandwich or a fish taken from a lake. (first used: 9. Sort goods by two questions: rival and excludable)
Excludable — Describes a good that people who do not pay can be kept from using, such as a concert with a ticket gate or a streaming service with a password. (first used: 9. Sort goods by two questions: rival and excludable)
Private good — A good that is both rival and excludable, such as a meal bought at a restaurant; markets supply private goods well. (first used: 9. Sort goods by two questions: rival and excludable)
Public good — A good that is neither rival nor excludable, such as a fireworks show anyone nearby can watch; markets tend to provide too little of it because people can enjoy it without paying. (first used: 9. Sort goods by two questions: rival and excludable)
Common resource — A good that is rival but not excludable, such as fish in open waters, so each user takes from a shared stock that no one can fence off. (first used: 9. Sort goods by two questions: rival and excludable)
Club good — A good that is excludable but not rival, such as an uncrowded streaming service or toll road, where members can be charged but one member's use does not leave less for others. (first used: 9. Sort goods by two questions: rival and excludable)
Free-rider problem — The temptation to enjoy a good without paying for it when no one can be kept from using it, which leaves voluntary contributions for a public good short of its cost. (first used: 10. See the free-rider problem)
Tragedy of the commons — The overuse of a common resource, which is rival but open to all, because each user gains the full benefit of taking more while the cost of depletion is shared by everyone. (first used: 11. Manage a commons)
Carbon pricing — A policy that puts a price on carbon dioxide emissions, either directly through a tax per ton or indirectly through a cap-and-trade market in permits. (first used: 12. Weigh carbon pricing as a named debate)

Summary

An externality is a cost or benefit that lands on people outside the trade.
Social cost is private cost plus the cost to bystanders.
The efficient quantity is where marginal social benefit meets marginal social cost.
A negative externality means too much; a positive one means too little.
The deadweight loss of a spillover is the triangle beyond the efficient quantity.
A corrective tax equals the external cost per unit at the efficient quantity.
Week 7's 2-dollar tax caused a loss of 10; here it removes one of 10.
Cap-and-trade fixes the total amount and lets permits find a price.
Coase: with cheap bargaining, the right decides who pays, not what happens.
Goods sort by two questions: rival, and excludable.
Public goods invite free riders; common resources invite overuse.
Communities can manage a commons with their own rules.
Carbon pricing is a debate over evidence and values; the course gives no verdict.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A riverside paint plant (an illustrative case) faces demand P = 20 − Q and supply P = 4 + Q, with Q in thousands of gallons a week. Each thousand gallons does 4 dollars of harm to people fishing downstream. Find the market quantity, the efficient quantity, and the deadweight loss, and name the corrective tax.
In a small town, homeowners who plant a street tree (an illustrative case) give their neighbors shade worth 6 dollars a tree. Demand for trees is P = 30 − Q and supply is P = 10 + Q. Find the market quantity and the efficient quantity, and say what per-tree policy reaches it.
A rooftop bar's music does 500 dollars a month of damage to a recording studio next door, and soundproofing the bar costs 350 dollars a month. Explain what happens if the studio holds the right to quiet, what happens if the bar holds the right to play, and how large the gain from soundproofing is.
Classify each good as private, public, common resource, or club, and give the reason in terms of rival and excludable: a slice of pizza, a town's tornado siren, free parking on a crowded downtown street, and a members-only online library of cooking videos.

Answers (worked reasoning — read after attempting)

The market sets 20 − Q = 4 + Q, so 2Q = 16 and Q = 8 thousand gallons at 12 dollars. Marginal social cost is 4 + Q + 4 = 8 + Q, and 20 − Q = 8 + Q gives 2Q = 12, so the efficient quantity is 6 thousand gallons at 14 dollars. At the market quantity the gap between marginal social cost and demand is (8 + 8) − (20 − 8) = 16 − 12 = 4 dollars, so the deadweight loss is 1⁄2 × 4 × (8 − 6) = 4 dollars a week. The corrective tax is 4 dollars per thousand gallons, the harm per unit, not the total harm.
The market sets 30 − Q = 10 + Q, so Q = 10 trees. Marginal social benefit is 30 − Q + 6 = 36 − Q, and 36 − Q = 10 + Q gives 2Q = 26, so the efficient quantity is 13 trees. The market plants too few because each owner ignores the neighbors' shade. A subsidy of 6 dollars a tree, the external benefit per tree, reaches 13.
If the studio holds the right to quiet, the bar compares 350 dollars of soundproofing with 500 dollars of damage and soundproofs, because 350 < 500. If the bar holds the right to play, the studio is better off paying the bar anything between 350 and 500 dollars to soundproof, so the soundproofing still happens. Either way the gain is 500 − 350 = 150 dollars a month; the right decides only who pays, as long as the two can bargain cheaply.
The pizza slice is a private good: one person eating it leaves none for others, and the shop can refuse to hand it over without payment. The tornado siren is a public good: one person hearing it does not stop others from hearing it, and no one in range can be kept from hearing it. Free parking on a crowded street is a common resource: a space one driver takes is gone for others, but no one is charged or kept out. The members-only video library is a club good: one member watching does not use up a video for others, but non-members can be kept out with a password.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the lemons model shows what happens to a market when one side knows more than the other.

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