Lecture: Government Intervention: Price Controls, Taxes & Subsidies
Lecture script · about 15–20 minutes spoken · Week 7
Opening
Think about a renter whose city limits how much the rent can rise each year. Think about a shift worker whose state sets the lowest hourly wage an employer may pay. Think about a small grocery owner who has to add a tax to every item sold. None of them picked the price. A rule picked it, or changed it.
This lecture asks what each of those rules does to a market. Who gains, who loses, and what disappears?
Here's where we are. In Week 1 you learned to separate positive statements, which evidence can check, from normative ones, which rest on values. In Week 4 you built the running market, where demand and supply cross at 6 dollars and 30 units a day. In Week 5 you measured how strongly buyers respond to price. And in Week 6 you measured the gains from that market as surplus: 45 dollars a day for buyers, 45 for sellers, 90 in all.
In this lecture we run government rules through that same market. I'll start with price ceilings and price floors and when they matter. Then two real cases, the minimum wage and rent control, where I'll separate what the model predicts from what economists still argue about. Then a tax, the question of who really pays it, and a subsidy. After the midterm the course turns to firms, so this is the last piece of the market story.
1. When a price rule matters
Picture a sign on a parking garage that says, "No more than this per hour." That's a top price. Now picture a rule that no worker may be paid less than a set wage. That's a bottom price.
Those have names. A price ceiling is a legal maximum price for a good. It binds only when it is set below the equilibrium price, and then the market has a shortage. A price floor is a legal minimum price for a good. It binds only when it is set above the equilibrium price, and then the market has a surplus.
Here's the key move. A rule only matters if the market price would break it. On the running market, the price settles at 6 dollars. A ceiling at 7 dollars says "no higher than 7." The market is already at 6, so nothing happens. A floor at 5 dollars says "no lower than 5," and again the market is already above it. Both rules are on paper only. We call them nonbinding.
Pause and try this. On the running market, is a ceiling at 4 dollars binding or nonbinding?
Compare 4 with the equilibrium price.
Here's the answer. It's binding, because a ceiling binds only below the equilibrium price, and 4 is below 6.
2. The ceiling at 4 dollars
So let's put that ceiling at 4 and see what happens. At 4 dollars, buyers want 50 units a day. Sellers, at that low price, offer only 10. The gap, 40 units, is a shortage. And since a sale needs a seller, only 10 units trade instead of 30.
That's a positive result of the model, and I'll say it plainly: a binding ceiling creates a shortage.
Now, what's lost? Remember from Week 6 that every unit up to the 30th was worth more to its buyer than it cost its seller. Under the ceiling, the units from the 10th to the 30th never get made. That lost value is the deadweight loss, the total surplus that disappears because a tax, a subsidy, or a price control moves the quantity traded away from the efficient quantity.
Here's how to see its size in words. At the 10th unit, a buyer values it at 8 dollars, and it costs a seller 4. Picture a triangle lying on its side. Its tall edge stands at 10 units, running from 4 dollars up to 8. Its point reaches right to the old equilibrium at 30 units and 6 dollars. Half of 20 units times 4 dollars is 40 dollars a day. So the ceiling wipes out 40 of the market's 90 dollars.
Pause and try this. Under the ceiling at 4 dollars, is the market left with extra units or with buyers who can't get one?
Think about which side wants more at the low price.
Here's the answer. Buyers who can't get one: buyers want 50 and sellers offer 10, so it's a shortage of 40, not a surplus.
3. The floor at 8 dollars
Flip it around. Put a floor at 8 dollars. Now sellers are eager: they offer 50 units a day. Buyers, facing the high price, want only 10. The gap, 40 units, is a surplus, unsold units sitting on the shelf. And a sale needs a buyer, so again only 10 units trade.
The deadweight loss is the same triangle, with the same corners: 10 units at 8 dollars, 10 units at 4 dollars, and the old equilibrium at 30 units and 6. It's 40 dollars a day again. They match here only because 4 and 8 sit the same distance from 6, on two lines that are equally steep.
One word of warning. In Week 6, consumer surplus and producer surplus meant gains. Here, a surplus means units nobody buys, the Week 4 meaning. Same word, two ideas.
Students sometimes swap ceilings and floors because one sounds "high" and the other "low." The names describe the rule, not the height. A ceiling is a cap that stops the price from rising. A floor is a base that stops it from falling.
Pause and try this. A ceiling creates a shortage. What does a binding floor create?
Picture which side has too much at a high price.
Here's the answer. A surplus, because at a price above equilibrium sellers offer more than buyers want.
4. Who keeps what
A control doesn't only shrink the market. It also moves gains around. Under the ceiling, buyers who get the good pay less. Under the floor, sellers who make a sale earn more.
To measure the split, the model makes one assumption, and I want you to name it. Under the ceiling, it assumes the 10 units go to the buyers who value them most. If instead the good goes to whoever shows up first, some units reach buyers who value them less, and buyers keep less.
With that assumption, under the ceiling buyers keep 45 dollars a day, and sellers keep 5. Under the floor it flips: buyers keep 5, and sellers keep 45, if the lowest-cost sellers make the units. Either way, the total falls from 90 to 50 dollars a day.
Here's the part people miss. A ceiling helps the buyers who get the good. The buyers stuck in the shortage get nothing at all.
Pause and try this. Under the ceiling at 4 dollars, does every buyer come out ahead?
Think about the 40 units' worth of buyers in the shortage.
Here's the answer. No: the buyers who get a unit gain, but the ones left in the shortage get nothing.
5. The minimum wage
Now a floor you've seen. A job is a trade: a worker sells hours, and an employer buys them. The wage is the price. A minimum wage is a legal minimum hourly wage that an employer may pay a worker, which makes it a price floor in the labor market. The federal minimum wage is 7.25 dollars an hour, in effect since 2009, and many states and cities set higher minimums.
What does the model predict? This part is positive and plain. A binding minimum raises the wage of workers who keep their jobs and lowers the quantity of labor employed.
What do economists argue about? How big that effect is for moderate increases in real labor markets. In 1994, Card and Krueger compared fast-food jobs in New Jersey, which had raised its minimum in 1992, with neighboring Pennsylvania, and found no fall in New Jersey. In 2000, Neumark and Wascher reworked the question with payroll records and found a fall. That same year, Card and Krueger replied using Bureau of Labor Statistics employment records and again found no fall.
So one side has the model's logic and a careful reanalysis. The other side has two studies, on two kinds of data, finding no fall after a real increase. Those are claims about evidence, so the debate is positive, even though it's unsettled. Whether an increase is worth its costs is the normative part, and that rests on values.
Pause and try this. Do economists disagree about what a binding floor does in the model?
Separate the model from the size of the effect.
Here's the answer. No; they agree on the model's prediction and disagree about how large the effect is in real markets.
6. Rent control
Now a ceiling. Rent control is a legal limit on the rent a landlord may charge or on how fast rents may rise, which makes it a price ceiling in the market for rental housing. The simple model predicts that a binding rent ceiling creates a shortage of rental housing.
What does the evidence say? Diamond, McQuade, and Qian studied San Francisco's 1994 expansion of rent control in a 2019 study. They found two things. Tenants in covered buildings were more likely to stay in their homes. That's the protection the policy promises. And landlords of covered buildings reduced the supply of rental housing. That's the shortage side the model predicts.
So the strongest case for rent control points to people keeping their homes. The strongest case against points to fewer units for the renters who come later. Both come from the same study, and both are positive findings.
How a city should weigh those two is normative. It depends on how you value stability for people already housed against access for people still looking. I'm not going to answer that for you.
Pause and try this. "Rent control is unfair to future renters." Positive or normative?
Ask whether evidence alone could settle the word "unfair."
Here's the answer. Normative, because "unfair" rests on a value judgment, even though the drop in supply behind it is a positive finding.
7. A tax and its wedge
Now leave the price alone and add a tax. A per-unit tax is a fixed dollar amount collected by the government on each unit sold. Say it's 2 dollars on the running market, and sellers hand it over.
To keep supplying a unit, a seller now needs its old cost plus 2 dollars. So the supply curve shifts up by 2 dollars at every quantity. The new crossing is at 7 dollars. Buyers pay 7, sellers keep 5, and 20 units trade instead of 30.
The gap between what buyers pay and what sellers keep is the tax wedge, 2 dollars. The government collects 2 dollars on each of 20 units, so 40 dollars a day. And the deadweight loss is a small triangle: half of 2 dollars times the 10 lost units, 10 dollars a day. Buyers keep 20, sellers keep 20, the government gets 40, and that adds to 80, which is 90 minus the 10 that vanished.
Here's the classic slip. The 40 dollars of revenue is not lost. It moves from buyers and sellers to the government, which can spend it. Only the triangle, 10 dollars, is the trades that no longer happen.
Pause and try this. Someone says the tax's deadweight loss is 2 times 20, or 40. What did they compute?
Think about what tax times quantity measures.
Here's the answer. They computed the revenue, which is a transfer, not the loss; the deadweight loss is 10 dollars a day.
8. Who really pays
Back to that grocery owner. The owner writes the check to the government. But who ends up poorer depends on how much the prices move. That's economic incidence: how the burden of a tax is actually shared between buyers and sellers, with the less price-responsive side bearing more.
On the running market, buyers' price went from 6 to 7, and sellers' from 6 to 5. Each side bears 1 dollar. That even split happens only because the two curves are equally steep.
Now take a good buyers find hard to do without. In this course's who-bears-it market, demand and supply meet at 5 dollars and 35 units. Put a 4-dollar tax on sellers. Buyers now pay 8, sellers keep 4, and 20 units trade. Buyers bear 3 of the 4 dollars, and sellers bear 1, even though the sellers write the whole check. Why? Quantity demanded changes by only 5 units per dollar, while quantity supplied changes by 15. Buyers can't dodge the price rise, so they absorb most of it. Revenue is 80 dollars a day, and the deadweight loss is 30.
Pause and try this. In the who-bears-it market, which side is less responsive to price?
Compare 5 units per dollar with 15.
Here's the answer. Buyers, because their quantity changes by only 5 units per dollar, and that's why they bear 3 of the 4 dollars.
9. A subsidy
A subsidy is a tax turned upside down. A per-unit subsidy is a fixed dollar amount the government pays for each unit sold. Say it's 2 dollars per unit, paid to sellers on the running market.
Now a seller needs 2 dollars less from the buyer, so supply shifts down by 2. Buyers pay 5 dollars, sellers receive 7, and 40 units trade. Buyers keep 80 dollars a day in surplus, and sellers keep 80. Sounds like a win.
But count the taxpayers. The subsidy costs 2 dollars on each of 40 units, 80 dollars a day. So 80 plus 80 minus 80 is 80, and total surplus falls from 90 to 80. That's a deadweight loss of 10. The extra units past the 30th cost more to make than buyers value them. The 40th unit is worth 5 dollars to a buyer and costs a seller 7.
A limitation worth saying: this holds in a market where no one outside the trade is affected. In Week 14, Externalities, Public Goods & Market Failure, you'll see when that changes.
Pause and try this. Buyers and sellers both gain from the subsidy. Why does society still come out behind?
Remember who pays the 80 dollars.
Here's the answer. Taxpayers pay 80 dollars a day, more than the gain to buyers and sellers, so total surplus falls by 10.
10. The classic wrong turns
Let's pull the slips together. A ceiling above 6 dollars isn't binding. A ceiling makes a shortage; a floor makes a surplus. Whoever writes the check doesn't have to bear the tax. Tax revenue isn't deadweight loss, and the loss isn't tax times quantity. And a debate about the size of the minimum wage's job effect isn't a debate about what a binding floor does in the model.
Most of those come down to two habits. First, compare the rule's price with the equilibrium before you say anything else. Second, measure a loss as the triangle of trades that no longer happen, and keep money that only changes hands separate.
Pause and try this. With the 2-dollar tax on the running market, a classmate says sellers bear the whole 2 dollars. What's the fix?
Compare the seller's price before and after.
Here's the answer. Sellers keep 5 instead of 6, so they bear 1 dollar, and buyers, paying 7 instead of 6, bear the other.
Closing
Let me pull it together. A price ceiling binds only below the equilibrium price, and then it makes a shortage, like the 40 units at 4 dollars. A floor binds only above it and makes a surplus. Either control shrinks the market and costs 40 dollars a day here. The minimum wage and rent control are real versions, where the model's prediction is plain and the size of the effects is debated with evidence on both sides. A tax drives a wedge, raises revenue, and costs a smaller triangle. The less responsive side bears more of it. And a subsidy buys extra trades at a cost to taxpayers.
Next in this module, read through the slide deck, then the Readings and Resources page, and then work the lecture tutorial, the practice set, and the quiz. Next week, in Week 8, Midterm Review & Exam, we review all seven weeks and add the habit of thinking at the margin.
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