Lecture: Externalities, Public Goods & Market Failure
Lecture script · about 15–20 minutes spoken · Week 14
Opening
Picture a family two doors from a busy workshop. They bring their laundry in gray and keep the windows shut on warm nights. Now picture a fishing town that shares one lake, and a neighborhood passing a jar to pay for a fireworks show. Each of them faces the same question: who pays for a cost or a benefit that lands outside a market?
Here's where we are. In Weeks 3 and 4 you built the running market and found its equilibrium at 6 dollars and 30 units a day. In Week 6 you measured its surplus as two triangles of 45 dollars each. In Week 7 you put a 2-dollar tax on it and found a deadweight loss of 10 dollars a day.
In this lecture I'll add the people outside the trade to that same market. We'll see why the market makes too much of a good that pollutes, and how that same 2-dollar tax becomes the cure. Then we'll look at caps, bargains, goods no one can be kept from, and shared resources, and we'll finish with a real debate. Next week, in Week 15, one side of a market knows more than the other.
1. Externalities: costs that land outside the trade
Start with something you've felt. A neighbor's leaf blower wakes you early. You didn't buy anything, and no one paid you. A neighbor's garden makes your walk nicer, and you didn't pay for that either.
Economists call that spillover an externality: a cost or benefit that falls on people outside a transaction, who neither buy nor sell the good. Smoke is a negative externality, a cost. A classmate's flu shot, which makes you less likely to get sick, is a positive one.
To measure it, split cost in two. Private cost is what the seller itself pays. Social cost is the whole cost to everyone: the seller's private cost plus the cost to bystanders.
Pause and try this. A concert ticket costs more than you'd like. Is that high price an externality?
Ask who pays the cost.
Here's the answer. No. You're inside the trade, so the market already counts the price; an externality lands on someone outside it.
2. Marginal social cost on the running market
Now the workshop. In this classroom model, every unit of the running market's good does 2 dollars of harm to the neighbors. That steady 2 dollars a unit is an assumption, named as one.
The supply curve gives each unit's cost to its seller, its marginal private cost. The 20th unit costs the seller 5 dollars, and the 30th costs 6. Add the 2 dollars of harm and you get the marginal social cost: the full cost to society of one more unit, the marginal private cost plus the marginal external cost. So the 20th unit really costs society 7 dollars, and the 30th costs 8.
Picture the graph. Supply rises from 3 dollars. Marginal social cost is a second line, parallel to supply, sitting 2 dollars higher everywhere.
Pause and try this. Does the smoke shift the demand curve or add a line above supply?
Think about who bears the smoke.
Here's the answer. It adds a line above supply. The smoke is a cost of making the good, and the neighbors aren't buyers.
3. The efficient quantity
What quantity would be best for the whole street? Make each unit only if buyers value it at least at its full cost to society.
Demand tells you what buyers value each unit at, and here no one else gains from the good, so demand is also the marginal social benefit. The efficient quantity is where marginal social benefit equals marginal social cost. On the running market those two lines cross at 20 units a day and a price of 7 dollars.
The market ignores the smoke. It still trades where demand meets ordinary supply: 30 units at 6 dollars. That's 10 units too many. A negative externality makes a market produce too much, because the good looks cheaper to sellers than it really is.
Pause and try this. Does the market make more or fewer units than the efficient quantity, and by how many?
Compare 30 with 20.
Here's the answer. More, by 10 units, because sellers don't pay the neighbors' cost.
4. The deadweight loss of the spillover
Look at those 10 extra units. Each one costs society more than buyers value it. At the 20th unit the gap is zero. At the 30th, marginal social cost is 8 dollars and buyers value it at 6, a gap of 2.
Those losses form a thin triangle with a base of 10 units and a height of 2 dollars. Half of 2 times 10 is 10 dollars a day of deadweight loss.
Here's a check that counts everyone. The market's two surplus triangles add to 90 dollars, and the neighbors bear 2 dollars on each of 30 units, which is 60. So social surplus, the value to buyers minus every cost to society, is 30 dollars a day. At the efficient quantity it would be 40. The difference is the 10.
Pause and try this. Is the deadweight loss the full 60 dollars of harm?
Remember which units are worth making.
Here's the answer. No. Most of the harm comes with units worth making; the loss is only the triangle on the extra 10, which is 10 dollars.
5. Week 7's tax becomes the cure
So how do you get the market from 30 units to 20? Make sellers feel the harm. In 1920 the economist Arthur Cecil Pigou proposed it in The Economics of Welfare. 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.
Here the harm is 2 dollars a unit, so the tax is 2 dollars. You know this tax. Supply shifts up by 2. Buyers pay 7 dollars, sellers keep 5, and 20 units trade, raising 40 dollars a day.
Now the twist. In Week 7, with no smoke, this tax cut total surplus from 90 to 80, a loss of 10. With the smoke, it lifts social surplus from 30 to 40. The same tax removes a loss of 10.
Pause and try this. The neighbors bear 40 dollars of harm a day at 20 units. Should the corrective tax be 40 dollars?
Think per unit, not in total.
Here's the answer. No. The corrective tax is 2 dollars, the harm on each unit, not the day's total.
6. A positive externality and a subsidy
Flip the sign. Suppose each unit gives the neighbors 2 dollars of benefit, the way fresh paint on one house lifts a whole block. Now marginal social benefit sits 2 dollars above demand, and it meets supply at 40 units.
The market stops at 30, because buyers count only their own benefit. A positive externality makes a market produce too little.
The fix is a corrective subsidy: a per-unit payment set equal to the marginal external benefit at the efficient quantity. It's Week 7's 2-dollar subsidy. Buyers pay 5 dollars, sellers receive 7, and 40 units trade, at a cost of 80 dollars a day.
Pause and try this. In Week 7 that subsidy wasted surplus. Why does it help here?
Ask whether bystanders gain.
Here's the answer. Here each unit helps the neighbors, so 40 is now the efficient quantity, and the subsidy lands the market on it.
7. Cap-and-trade
A tax sets a price and lets firms choose how much to pollute. You can turn that around. Cap-and-trade caps the total amount of a pollutant and issues tradable permits for that amount.
The real case is the Environmental Protection Agency's Acid Rain Program, set up under Title IV of the Clean Air Act and begun in 1995. It caps sulfur dioxide from power plants. Each allowance permits 1 ton of sulfur dioxide, and plants may buy, sell, or bank allowances. It was the first national cap-and-trade program in the United States.
Why trade? A plant that can cut cheaply cuts extra and sells its spare allowances to a plant for which cutting is costly. The total stays at the cap, and the cutting happens where it costs least.
Pause and try this. If one plant buys extra allowances, does total pollution rise above the cap?
Think about where those allowances came from.
Here's the answer. No. The seller gave them up, so the total stays at the cap.
8. The Coase theorem
Sometimes the two sides can sort it out themselves. In 1960 the economist R. H. Coase made that case in "The Problem of Social Cost."
Picture a factory beside a laundry. The smoke does 300 dollars a month of damage, and a chimney filter costs 200. If the laundry holds the right to clean air, the factory installs the filter, since 200 is less than 300. If the factory holds the right to pollute, the laundry pays it between 200 and 300 to install it. Either way, the filter goes in.
That's the Coase theorem: when property rights are clear and transaction costs are low, private bargaining reaches the efficient outcome whichever side holds the right. The right decides who pays, not what happens. With many people affected, bargaining gets costly, and it often fails.
Pause and try this. If the factory holds the right, does the filter go in?
Ask what the laundry would do.
Here's the answer. Yes. The laundry pays the factory to install it, because stopping 300 dollars of damage is worth more than 200.
9. Rival and excludable
Some goods resist markets. Two questions sort them. Is a good rival: does one person's use leave less for others? Is it excludable: can people who don't pay be kept out?
A restaurant meal is both, a private good. A fireworks show is neither, a public good. Fish in open waters are rival but not excludable, a common resource. An uncrowded streaming service is excludable but not rival, a club good. The economist Paul A. Samuelson set out the theory of public goods in 1954.
Pause and try this. A city provides a bus ride that you pay for, and a full bus leaves riders at the curb. Is it a public good?
Test both questions.
Here's the answer. No. A full bus makes it rival and the fare makes it excludable, whoever runs it.
10. The free-rider problem
Back to the fireworks. In Dataset Q, 100 residents each value the show at 10 dollars, so it's worth 1,000 dollars, and it costs 600. Split evenly, that's 6 dollars each, less than each person's 10.
Yet the jar may come up short. The free-rider problem is the temptation to enjoy a good without paying when no one can be kept from it. Each resident thinks, "My share barely matters, and I'll see the show anyway." Enough people think that, and a show worth 400 dollars more than its cost never happens. That's why public goods are often paid for through taxes or dues.
Pause and try this. Is the free-rider problem caused by bad people?
Think about the good, not the people.
Here's the answer. No. It comes from the good itself: no one can be kept out, so each payment seems to matter little.
11. Managing a commons
Now a lake that several fishing families share. Each family keeps the whole value of every extra fish, but a thinner stock next year hurts every family. That's the tragedy of the commons: the overuse of a resource that is rival but open to all. Garrett Hardin named it in 1968.
Elinor Ostrom added an answer from the field. In Governing the Commons, in 1990, she documented communities that manage shared resources well through their own rules, without either privatization or central control. A commons doesn't have to end in tragedy.
Pause and try this. Does the tragedy of the commons mean only a government can save a shared lake?
Remember Ostrom's field studies.
Here's the answer. No. Communities can manage a commons with their own agreed limits and penalties.
12. Carbon pricing, a named debate
Carbon dioxide from burning fuel is a spillover on a world scale. Carbon pricing puts a price on those emissions, through a tax per ton or a cap-and-trade market.
The positive claims can be tested: a price raises the cost of goods that emit, and the firms that can cut cheaply cut first. Supporters say a price makes emitters face the full social cost and lets each household and firm pick its own cheapest cuts. Their normative claim is that whoever causes harm should pay, and future people count. Critics say the harm per ton is hard to measure, energy costs can weigh most on tight budgets, and production may move to places with no price. Some prefer standards or public spending on technology. Their normative claim is that costs for people now, and how they're shared, deserve heavy weight. This course gives no verdict.
Pause and try this. Is "people who cause harm should pay for it" a positive or a normative claim?
Ask whether evidence alone could settle it.
Here's the answer. Normative. It rests on a value judgment, not on a testable prediction.
13. The classic wrong turns
Four slips catch most people. A negative externality means too much, not too little. The corrective tax is the harm per unit, 2 dollars, not the total. Under Coase, the right changes who pays, not whether the filter goes in. And a good isn't public because a government provides it.
Pause and try this. A classmate says the smoke makes the market produce too little. What's the fix?
Compare the market's 30 with the efficient 20.
Here's the answer. The market makes too much: 30 units where 20 is efficient, because sellers ignore the harm.
Closing
Let me pull it together. An externality lands outside the trade, so social cost is private cost plus the harm to others. The efficient quantity is where marginal social benefit meets marginal social cost: 20 units, not the market's 30. The 10 extra units cost 10 dollars a day. Week 7's 2-dollar tax becomes a cure, and Week 7's subsidy fixes a positive spillover. A cap fixes the total, and Coase shows bargaining can work when it's cheap. Rival and excludable sort every good, public goods invite free riders, and communities can manage a commons. Carbon pricing stays a debate.
Next in this module come the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. Next week, in Week 15, we look at asymmetric information, behavioral economics, and inequality.
Built with The Course Maker · samples.thecoursemaker.com