← Back to the lecture: Property Rights and Externalities
T5 Lecture Recap
Why a price cap on a taxed good makes things worse, why no owner means too much smog, how a tax or a market for permits can price the harm, and why the owner of a right matters less than you think.
Class meeting 14 · October 13, 2026 · 10-minute review · One session
Prices coordinate well when someone owns a resource and can charge for its use. No one owns the air, so no one can charge a driver for the smog a gallon of gasoline makes. Drivers then buy gallons that cost more, in all, than they are worth. A tax equal to the harm, or a market for the right to pollute, can make the buyer face the full cost. When rights are clear and bargaining is cheap, the resource goes to its highest-valued use no matter who holds the right; the right decides who ends up richer. Whether government picks the right tax or cap is a separate question.
How to use this page
This recap covers the October 13 class. Class began with a price cap on a taxed good, then moved to smog, a tax that prices in the harm, the ocean-view bargain, and a market for emission permits. Four TopHat items ran. Public goods and the commons were not reached. Read the four-step diagnostic first. Then use the lecture sections to connect each idea to an example from class. Finish with the application checks. The separate transcript has the full explanation, word for word.
Use these steps whenever a question asks whether a market produces too much or too little of something, and what could fix it.
What you should be able to do
Class went through the deck in order, from the price-cap question to the permit market.
A tax plus a price cap
A student asked last Thursday: why not tax gasoline $2 a gallon and also make it illegal to charge more than the old price of $5? Gasoline cleared at $5 and 10 million gallons a week. With the tax and no cap, the price rose to $6. With the cap, a station keeps only $5 − $2 = $3 a gallon, and at $3 stations offer just 6 million gallons. Drivers still want 10 million, so 4 million gallons are short.
TopHat check. How many gallons sell under the cap and the tax? The answer is 6 million: find what stations keep, $3, on the supply curve.
Stations send the state $2 × 6 million = $12 million. But a shortage has to be rationed somehow. Suppose drivers wait in line, and the wait costs $2 a gallon. The full price is $5 in cash plus $2 in time, or $7, which is more than the $6 drivers would pay with the tax and no cap. The cap does not stop drivers from paying; it changes the form of payment.
Now add up the loss. The trades that no longer happen are worth $8 million, and the time spent in line, $12 million, goes to no one. That is $20 million lost to raise $12 million. Society is $20 million worse off: the $12 million is not part of the loss, because it moves from drivers and stations to the state. With the tax alone, the loss was $2 million.
No one owns the air
A property right is control over a resource plus terms clear enough to sell it. Some rights in the air already exist: a homeowner owns the air up to a certain height, and the government auctions radio and cell-phone frequencies to the highest bidder. But smog drifts, so no one can own the air it fills. If I value clean air at $5 a day and one driver values driving at $4, I could pay that driver not to drive. With millions of drivers, the cost of all those bargains is far too high.
So each driver puts part of the cost of driving on other people, who cannot charge for it. Economists call that a negative externality. A shared resource that no one owns, like the air or open grazing land, tends to be overused: the tragedy of the commons.
Not every effect on others is this kind of problem. When a new AI model wins customers from an older one, the older firm loses, but the loss comes through prices. That is a pecuniary externality, and buyers gain from the competition. This course studies technical externalities, like smog, where one person’s choice directly harms another.
Pricing in the harm · political economy
Suppose each gallon puts $2 of smog on neighbors. The market still trades 10 million gallons at $5. The full cost of a gallon is the stations’ cost plus $2, so the full-cost line sits $2 above supply. If drivers paid the full cost, they would buy only 8 million gallons. Each gallon from 8 million to 10 million costs more than it is worth, and together they waste $2 million. Before, a tax caused too few trades; here the market makes too many.
TopHat check. Is the last gallon worth producing? No: it costs $7 in all but is worth only $5.
The reverse case is a positive externality, where others gain and the market makes too little. Education and having children are the usual examples; the instructor said he doubts the education argument. His rule for rounding up a grade (answer a question from class correctly and the grade goes up, answer wrongly and it goes down) makes students bear part of the cost of asking.
A $2 tax per gallon makes drivers face the full cost. Purchases fall to 8 million gallons, the deadweight loss disappears, and the state collects revenue. Here, a tax improves efficiency.
That works on paper. In practice, ask whether politicians have the incentive to do it. Few want to run on higher gas prices. Another approach is cap and trade: set a total amount of pollution and let firms trade the rights to emit it. But someone must still choose the cap. The instructor compared this with George Washington’s doctors, who drained his blood to cure a throat infection: a fix that sounds possible can make the problem worse.
Who gets the view? · the Coase theorem
A builder would earn $200,000 from a new floor that blocks the ocean view of the tenants next door, who value the view at $120,000. Suppose the right is clear and bargaining is cheap. If the tenants hold the right, the builder buys it for some price between $120,000 and $200,000, and the floor is built. If the builder holds the right, the tenants would have to pay more than $200,000 to stop it, and the view is worth only $120,000 to them, so the floor is built. This is the Coase theorem, after Ronald Coase: with clear rights and cheap bargaining, the resource goes to its highest-valued use either way.
TopHat check. Which statement is correct? The floor is built whichever side holds the right; only who ends up richer changes.
A student asked what price they would agree on. Economists call this a bilateral monopoly: one buyer and one seller, and no single price. We know only the range. At $160,000, each side gains $40,000; at $120,000 the builder gets all the gains, and at $200,000 the tenants do.
The deal creates $80,000 of gains. If the builder had to go door to door and that would cost $90,000, the deal would not happen. If every tenant must agree, the last one can hold out for nearly all the gains. With eight tenants splitting the $80,000, each could gain $10,000, yet each has a reason to hold out: a collective action problem, like the group project where everyone hopes the others do the work. Tenants can solve it in advance by giving one decision maker, such as a homeowners’ association, the right to bargain for all, much as Odysseus had his crew tie him to the mast before he heard the sirens.
A market for the right to emit
In 1993 Southern California’s air district adopted RECLAIM for factories that emit nitrogen and sulfur oxides. The regulator caps the total number of credits, each factory must hold a credit for every unit it emits, and factories trade credits.
In the class example, a paint maker and a refiner each hold 20 of the 40 credits and use them all. One more unit of emissions is worth $2.87 to the paint maker and $1.10 to the refiner, and credits trade at $2.20. The paint maker buys and the refiner sells. The refiner cannot charge the paint maker $2.80, because the paint maker can buy at $2.20 in the market. A paint maker that buys at $2.20 gains 67 cents on that credit.
TopHat check. What happens? Most of the class chose the right answer: the paint maker buys from the refiner, and total emissions stay at 40. Trade moves the credits; the cap fixes the total.
Not reached in class
The October 13 class ended after the permit market. The deck’s last pages were not reached: public goods (rivalry and excludability, adding everyone’s value, the free-rider problem) and the commons on a lake. The fifth TopHat item, on public goods, did not run. This recap covers only what class did.
Do not memorize an example as a story. Use it to recover the economic principle.
| Example from class | Economic lesson |
|---|---|
| A $2 gas tax with the price capped at $5 | A price cap does not stop a tax from being paid. Drivers pay in waiting time instead, and that time goes to no one, so the loss grows from $2 million to $20 million. |
| Air rights above a house; frequency auctions | Rights in the air exist where use can be measured, controlled, and sold. |
| Paying every driver not to drive | When a bargain would need millions of people, its cost blocks it. The harm stays unpriced. |
| A rival AI model takes customers | A pecuniary externality works through prices. It is competition, not a problem to fix. |
| $2 of smog on every gallon | A negative externality leads to too many trades. Units worth less than their full cost are a deadweight loss. |
| The grade round-up rule | Make the person who decides bear the cost of the decision, and the decision changes. |
| George Washington’s doctors | A fix that works in theory can do harm in practice. Ask whether the people applying it have the knowledge and the incentive to get it right. |
| The builder and the ocean view | With clear rights and cheap bargaining, the resource goes to its highest-valued use. The right decides who is paid. |
| The last tenant; the group project | A holdout or free rider can block a deal that makes the group better off. |
| The homeowners’ association; Odysseus at the mast | A rule chosen in advance can stop a choice that is bad for everyone later. |
| RECLAIM credits: paint maker and refiner | Trade moves the right to emit to whoever values it most. The cap fixes the total. |
Answer before you open each one. Every question uses only material from class, with new numbers.
Sellers keep $6 − $2 = $4, so they offer 4 thousand cups; buyers want 6 thousand. The 4,000th cup is worth $8 to buyers, so they wait $2 a cup and the full price is $8, more than the $7 they would pay with the tax and no cap. The city raises $8 thousand. The time in line, $8 thousand, and the lost trades, $4 thousand, total $12 thousand, so society is $12 thousand worse off. The $8 thousand the city raises is a transfer, not a loss. The tax alone would have cost only $1 thousand of lost trades.
The full cost is P = Q + 2, which meets demand at 5 thousand cups and $7. The market trades 6 thousand, so the cups from 5 thousand to 6 thousand cost more than they are worth. The deadweight loss is ½ × 1 thousand × $2 = $1 thousand. A $2 tax per cup cuts sales to 5 thousand, removes that loss, and raises $10 thousand.
Too few. This is a positive externality: part of the gain goes to people who do not pay for it, so buyers stop before the value to everyone equals the cost.
No music either way. If the bar holds the right, the neighbor pays it between $30,000 and $45,000 to stay quiet. If the neighbor holds the right, the bar would offer at most $30,000, which is less than $45,000, so no deal. The right decides only who is paid.
The view is worth 10 × $30,000 = $300,000, so the deal creates $200,000 of gains. If the developer paid all $500,000, each owner would get $50,000. But $250,000 of bargaining costs is more than $200,000, so the deal does not happen, and each owner could also hold out. If the owners had given one association the right to bargain for all of them, the deal could go through.
Firm A buys, gaining $1.25 on the permit, and firm B sells, gaining $0.90 over its use. Total emissions stay at 60, the cap. Firm B cannot charge A more than $4.00, because A can buy in the market.
No. The loss comes through prices and customers: a pecuniary externality. Buyers gain from the competition. A tax would be like banning a new AI model to protect the old one.
Demand meets supply plus $4 at 4 thousand cups, so buyers pay $8. Now the cups from 4 to 5 thousand are worth more than their full cost, and blocking them loses $1 thousand. A tax larger than the harm creates a new deadweight loss, which is why the size of the tax matters.
Each rancher gains from one more animal but bears only a small part of the damage to the grass, so all of them graze too much: the tragedy of the commons. An owner would charge for grazing or limit it, to keep the land valuable.
Bottom line
Prices coordinate when someone owns the resource. When no one does, a buyer can put part of the cost on others, and the market trades too much. Capping the price of a taxed good only adds waiting to the loss. A tax equal to the harm, or a capped market for permits, can make buyers face the full cost, but someone must choose the tax or the cap, and their incentives matter. With clear rights and cheap bargaining, the resource goes to its highest-valued use whoever holds the right; holdouts and many parties can block that bargain.