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This recap covers the October 8 class, the one session on taxes and subsidies. Class worked through a $2 gasoline tax on gas stations, then the same tax on drivers, the payroll tax, steeper demand and steeper supply, what a tax costs beyond its revenue, a $2 subsidy, a housing voucher, and real-world evidence. Four TopHat items ran. Read the four-step diagnostic first. Then use the lecture sections to reconnect each idea to an example from class. Finish with the application checks. The separate transcript has the full explanation, word for word.

What you should be able to do

1. Show a per-unit tax as a wedge on a supply-and-demand graph, and find the quantity, the price buyers pay, and the price sellers keep.
2. Explain why putting the tax on buyers or on sellers gives the same result (legal incidence versus economic incidence).
3. Predict which side bears more of a tax or gets more of a subsidy from which side can more easily cut back or go elsewhere, including the two extreme cases.
4. Compute tax revenue and deadweight loss from the graph, and explain why the revenue is a transfer but the deadweight loss is a cost that no one receives.
5. Explain why a tax on something people cannot easily avoid blocks fewer trades, and why a subsidy creates deadweight loss from too many trades.

Who writes the check · who pays

Florida’s gas-tax holiday

For the month of October 2022, Florida suspended 25.3 cents of its tax on each gallon of gasoline. The question for the lecture: how much of those 25.3 cents actually went to drivers? Drivers do not send the gas tax to the state; the businesses selling the fuel do. So the question is the same one politicians skip: not who delivers a tax to the government, but who bears it. Class also took up a student question on electric cars, which are heavier and pay no gas tax, and the counter-arguments on both sides (not on the slide); economics shows the incentives, not which policy is right.

A $2 tax on gas stations

Without a tax, gasoline clears at $5 a gallon and 10 million gallons a week. Now each station must send the state $2 for every gallon it sells. A tax on sellers like this is an excise tax; the tax you pay at a store is a sales tax. Each station now needs $2 more than before to sell the same amount, so supply shifts up by $2: to sell 10 million gallons, stations now need $7. But at $7, drivers want only 6 million gallons while stations offer 10 million, a surplus, so the price falls back. The new market clears at 8 million gallons: drivers pay $6, and after sending $2 to the state, a station keeps $4. Drivers bear $1 of the tax and stations bear $1, even though the law put all of it on stations. The state collects $2 × 8 million = $16 million a week: the rectangle between the two prices. The gains lost on the 2 million gallons no longer traded are the deadweight loss, the small triangle.

A student asked whether a law could forbid stations from passing on the tax. Stations would find another margin: shorter hours, higher prices for the drinks in the cooler, or, as in the 1970s gasoline controls, lower-octane fuel. Like water through a dam, block one hole and the pressure finds another.

Put the $2 on drivers instead

Now the law makes each driver pay the state $2 a gallon at the pump. Demand, as stations see it, falls by $2. The new market: 8 million gallons, stations receive $4, drivers pay $4 + $2 = $6. Every number is the same as before. The legal incidence (who the law says pays) differs from the economic incidence (who actually bears the tax), and supply and demand, not the law, decide the economic incidence.

Your pay stub shows the same idea. The law splits the Social Security and Medicare (payroll) tax: 7.65% from the worker and 7.65% from the employer. But employers can avoid the tax by hiring fewer people and using machines or AI instead, while someone who lives on wages has a hard time avoiding it. So workers bear most of the payroll tax, whatever the law says. The same logic says a law requiring employers to provide health insurance is paid for largely by workers, through lower wages. Class returns to labor markets in a few weeks.

Elasticity decides the split

When drivers cut back less

Suppose demand for gasoline is steeper (more inelastic): there are few substitutes, at least for drivers who already own a gas car. The same $2 tax on stations now lands at 9 million gallons, with drivers paying $6.50 and stations keeping $4.50. Drivers bear $1.50 and stations $0.50. Revenue is $2 × 9 million = $18 million, and the deadweight loss is smaller, because drivers do not cut back much. If the point of a gas tax is to charge the people who wear out the roads, this split fits that purpose: drivers, not station owners, wear out the roads. Contrast a tax on Mountain Dew: there are many sugary drinks to switch to, so buyers avoid the tax and PepsiCo, which makes Mountain Dew, bears most of it.

When stations cut back less

Now make supply steeper instead. The $2 tax lands at drivers paying $5.50 and stations keeping $3.50: stations bear $1.50 and drivers $0.50. Same tax, same law, the opposite split.

The two extremes

A student asked whether a tax always gets split. On the whiteboard: if supply is perfectly elastic (flat), sellers can avoid the tax entirely, the price rises by the full tax, and buyers bear all of it. If supply is perfectly inelastic (vertical, a fixed amount no matter the price), sellers cannot avoid it at all and bear all of it. The same holds for perfectly elastic or inelastic demand. Between the extremes, the tax is split. That is the logic behind Georgism, the idea that the best tax is a tax on land: a fixed supply of land means a land tax blocks no trades. But land is not quite fixed; Boston’s harbor has been filled in since the American Revolution to make new land.

The rule: a tax drives a wedge between what buyers pay and what sellers keep. Whoever can more easily avoid the tax, by cutting back or going elsewhere, bears less of it. Whoever cannot, bears more. Asked why drivers bear most of the gas tax: a station owner can tear down the station and open a restaurant, while a driver with a gas car has few substitutes. Hybrids and electric cars give drivers more of them over time, which makes demand for gasoline more elastic in the long run.

What a tax costs

Surplus before and after the tax

Without the tax, drivers’ consumer surplus is ½ × 10 million × $5 = $25 million, and stations’ producer surplus is also $25 million: $50 million in all. With the $2 tax, drivers lose $9 million and stations lose $9 million, $18 million in all, but the state collects only $16 million. The missing $2 million is the deadweight loss, the trades that no longer happen. In public finance it is called the excess burden of the tax. The $16 million is not counted as a loss: it is a transfer to the state and to the police officers and road crews it pays.

That is not an argument against taxes; a government has to be paid for. It is an argument for asking which taxes cost the least. Tax things people cannot easily avoid. A tax on one soft drink blocks many trades; a tax on all food blocks far fewer. In class, steeper demand or steeper supply raised $18 million while the deadweight loss fell from $2 million to $1 million.

TopHat check. Which tax raises revenue while blocking the fewest trades? Most of the class chose a tax on land, whose total amount cannot change: it cannot be avoided, so it blocks no trades. A statewide gas tax comes next. A tax on restaurant meals in a town on the state line, or on one theme park with competitors nearby, is easy to avoid by going elsewhere, so it blocks the most.

Subsidies · the evidence

A $2 subsidy paid to stations

Suppose the state wants more driving and pays each station $2 for every gallon it sells. Supply shifts down by $2. The new market: 12 million gallons, drivers pay $4, and stations receive $4 + $2 = $6. Drivers gain $1 a gallon and stations $1, though the law paid every dollar to stations. Taxpayers pay $2 × 12 million = $24 million, and that money has to come from somewhere, usually a tax with its own deadweight loss. Drivers and stations gain only $22 million. The missing $2 million is the subsidy’s deadweight loss: the last gallons cost $6 to produce but are worth only $4 to the drivers who buy them. A tax gives too few trades; a subsidy gives too many. (Next week’s topic, externalities, is where a tax or a subsidy can make a market work better.)

A housing voucher with a fixed stock

TopHat check. A neighborhood has 100 apartments, none can be built soon, and the rent is $3,000 a month. The city gives each renter a $500 voucher, so renters will now pay $500 more. The rent rises to $3,500, and the owners capture the whole $500; each renter still pays $3,000 out of pocket. Rent cannot stay at $3,000 (every renter now bids more for the same 100 apartments), and it is not split, because owners cannot add apartments. The side that cannot change its quantity gets the subsidy, just as it bears a tax. Subsidizing renters does not make housing cheaper when the number of homes is fixed.

Real-world examples

The last slide reported what studies found. Gas-tax holidays in 2022 (Maryland, Georgia, and Connecticut; there is no reliable estimate for Florida’s own holiday): drivers got 58–87% of the cut at first, and the savings often faded before the holiday ended (Penn Wharton Budget Model). Federal student loans: tuition rose about 60 cents for each $1 rise in the subsidized-loan limit (Lucca, Nadauld, and Shen), so a large part of the subsidy goes to colleges, whose seats and faculty are hard to expand. Housing vouchers: in the 90 largest metro areas, vouchers raised rents in the low-income housing market by 16% on average (Susin). As class put it, that is often why owners of existing homes lobby for vouchers. The fifth TopHat question, on tariffs, was skipped.

Announcements (as given in class)

There are three new practice tools for Price Controls in the Lecture 6 module: what a rent freeze does, how long the line is under a price ceiling, and what a price floor does. Use them to review and to prepare for the exam. If there is a tool that would help you understand the material, email your instructor and he will build it.

Please use the feedback QR code, shown at the start and the end of class, to say what worked and what did not. The next topic is externalities.

Examples are memory cues; the right column is the principle each example should help you recover.

Example from class	Economic lesson
Florida’s 25.3-cent gas-tax holiday	Cutting a tax is the same wedge run backward; drivers get only part of the cut.
A $2 tax on stations: drivers pay $6, stations keep $4	A tax drives a wedge between what buyers pay and what sellers keep; the price adjusts until the market clears.
The same $2 tax on drivers at the pump	Legal incidence is not economic incidence: who writes the check does not decide who bears the tax.
Your pay stub’s 7.65% + 7.65%	Workers bear most of the payroll tax because employers have more substitutes for labor.
Mountain Dew and PepsiCo	Buyers with many substitutes avoid a tax; the seller bears it.
Selling Mountain Dew at a higher price, or lower-octane gas	A law against passing on a tax just moves the adjustment to another margin.
Tearing down the gas station to open a restaurant	Sellers with other uses for their resources can avoid a tax.
Boston Harbor filled in to make land	Even land is not perfectly fixed in supply, so a land tax is close to, not exactly, free of deadweight loss.
$18 million lost by drivers and stations, $16 million raised	The deadweight loss (excess burden) is the part of the loss no one receives.
A tax on one theme park with competitors nearby	Easy-to-avoid taxes block the most trades.
The $500 voucher and 100 apartments	The side that cannot change its quantity captures a subsidy.
Federal student loans and tuition	A subsidy to buyers goes largely to sellers when supply is hard to expand.
Health insurance mandated for employers	A cost put on employers is paid largely by workers through lower wages.

Question 1 — The town puts a $4 tax on every pizza, collected from the pizzerias. What quantity is sold, what do buyers pay, and what do pizzerias keep?

Supply shifts up by $4 to P = Q + 4. It meets demand where 20 − Q = Q + 4, so Q = 8 thousand. Buyers pay 20 − 8 = $12, and pizzerias keep $12 − $4 = $8. Buyers bear $2 of the tax and pizzerias bear $2.

Question 2 — Instead, the law makes each buyer pay the $4 to the town. What changes?

Nothing that matters. Demand as pizzerias see it shifts down by $4 and meets supply at 8 thousand pizzas; pizzerias receive $8 and buyers pay $8 + $4 = $12. The legal incidence changed; the economic incidence did not.

Question 3 — With the $4 tax, how much revenue does the town collect, and what is the deadweight loss? Do buyers and sellers lose more than the town collects?

Revenue = $4 × 8 thousand = $32 thousand a week. Deadweight loss = ½ × $4 × 2 thousand = $4 thousand. Consumer surplus falls from $50 thousand to $32 thousand and producer surplus from $50 thousand to $32 thousand, a loss of $36 thousand: the $32 thousand transfer to the town plus the $4 thousand that no one receives.

Question 4 — Suppose instead that demand is steeper, P = 30 − 2Q (it still passes through $10 and 10 thousand), and the town taxes pizzerias $3 a pizza. After the tax, 9 thousand pizzas sell. What do buyers pay, what do pizzerias keep, and who bears more?

Buyers pay 30 − 2 × 9 = $12; pizzerias keep $12 − $3 = $9 (on the supply curve, P = 9). Buyers bear $2 and pizzerias $1. Buyers cut back less, so they bear more. Revenue is $27 thousand; the deadweight loss is ½ × $3 × 1 thousand = $1.5 thousand.

Question 5 — Back to the original market. The town pays pizzerias a $4 subsidy for every pizza. What happens, what does it cost, and is there a deadweight loss?

Supply shifts down to P = Q − 4, which meets demand at Q = 12 thousand. Buyers pay $8 and pizzerias receive $8 + $4 = $12, so each side gains $2 a pizza. The town pays $4 × 12 thousand = $48 thousand, but buyers and pizzerias gain $22 thousand each, $44 thousand in all. The missing $4 thousand is deadweight loss: the extra pizzas cost up to $12 to make but are worth as little as $8 to the buyers.

Question 6 — Sellers of a good will supply any amount at $10, but no amount below $10 (perfectly elastic supply). A $2 tax is put on the sellers. Who bears it?

The buyers, all of it. Sellers can avoid the tax entirely, so the price buyers pay rises to $12 and sellers still keep $10. If instead the amount were fixed (perfectly inelastic supply), sellers would bear all of it.

Question 7 — A college town has 500 apartments, none can be built soon, and rent is $1,200 a month. The city gives every renter $300 a month toward rent. What happens to the rent, and who gains?

Every renter will now pay $300 more for the same 500 apartments, so the rent rises to $1,500. Renters still pay $1,200 out of pocket; the owners capture the whole $300. With a fixed stock, the subsidy goes to the side that cannot change its quantity.

Question 8 — A state needs revenue. Which blocks fewer trades: a tax on one brand of running shoes, or a tax on all shoes? Why?

A tax on all shoes. Buyers can easily switch away from one brand, so a tax on it blocks many trades. It is much harder to avoid buying shoes at all, so a tax on all shoes blocks fewer trades for the revenue it raises.

Question 9 — A new law moves the whole payroll tax onto employers, so workers pay nothing on their pay stubs. Does workers’ take-home pay rise once the labor market adjusts?

Not by the amount of the tax they no longer see. Who writes the check does not decide who bears the tax. Employers can more easily avoid the tax than workers can, so wages adjust downward and workers still bear most of it, much as before.

Bottom line

A tax drives a wedge between what buyers pay and what sellers keep. The law decides who sends the money to the government, but supply and demand decide who bears it: the side that can more easily cut back or go elsewhere bears less. Tax revenue is a transfer; the trades the tax blocks are a deadweight loss that no one receives, and it is smaller when the taxed side cannot easily avoid the tax. A subsidy runs the same logic backward: it goes mostly to the side that cannot easily change its quantity, and it creates deadweight loss from too many trades. That completes taxes and subsidies; externalities are next.