Week 7 · Chapter

Chapter 7 — Government Intervention: Price Controls, Taxes & Subsidies

Principles of Microeconomics Free sample edition

The module's primary reading · ~45–55 minutes · 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), building on Objective 1 (use the tools of economic modeling — scarcity, opportunity cost, the production possibilities frontier, comparative advantage, and the gains from trade — and distinguish positive statements (what is) from normative statements (what ought to be)), Objective 2 (explain how demand and supply determine a market's equilibrium price and quantity, and predict how a shift in demand or supply changes them), and Objective 3 (compute and interpret price, income, and cross-price elasticities of demand by the midpoint formula, and relate price elasticity to total revenue) · 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

This week is about what happens when a government steps into a market and changes the price. Sometimes it sets a top price, called a price ceiling (a legal maximum price), and sometimes a bottom price, called a price floor (a legal minimum price). Sometimes it adds a per-unit tax (a fixed amount collected on each unit sold) or pays a per-unit subsidy (a fixed amount paid for each unit sold). Each rule changes how much gets bought and sold, and each one can shrink the total gain from the market. The model tells you who gains, who loses, and how much value disappears; whether a rule is worth it is a separate question about values.

Why you already care about this

Picture two people in one city. Lena rents a one-bedroom apartment, and her city limits how much her rent may rise each year. Tomás works weekend shifts at a hardware store, and his state sets the lowest hourly wage his employer may pay. Neither of them chose a price. A rule chose it.

Now picture a third person, Ama, who runs a small bakery. Suppose a tax of 1 dollar is added to every cake she sells. Who pays that dollar? Ama hands it to the government, so it looks like her cost. But if her price rises by 70 cents, her customers are paying 70 of those 100 cents. That is the puzzle this chapter solves.

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

tell a price ceiling from a price floor and say when each one binds;
compute the shortage, the surplus, the quantity traded, and the deadweight loss of a binding control;
describe the minimum wage and rent control as applied cases, with the model's prediction and the evidence on each side;
compute the buyer price, the seller price, the quantity, the revenue, and the deadweight loss of a per-unit tax;
explain why the side that responds less to price bears more of a tax, whoever writes the check;
compute what a per-unit subsidy costs taxpayers and the deadweight loss it creates.

Carry this sentence with you: a ceiling makes a shortage; the check is not the burden.

Where we are

Already covered: Week 1 separated positive statements from normative ones. Week 4 built the running market and its equilibrium. Week 5 measured how strongly buyers respond to price, and Week 6 measured the gains from trade as surplus.
This week: price ceilings and floors, binding and nonbinding; the minimum wage and rent control; a per-unit tax, its wedge, its revenue, and who bears it; a per-unit subsidy and its cost; and the deadweight loss of each.
How they connect: every rule this week is run through Week 4's market, and Week 6's triangles measure what each rule costs.
Where we're going next: Week 8 reviews the first seven weeks, adds the habit of thinking at the margin, and holds the midterm.

Recall the running market. Demand is Qd = 90 − 10P and supply is Qs = 10P − 30, where P is the price in dollars and quantities are in units per day. The curves cross at an equilibrium price of 6 dollars and an equilibrium quantity of 30 units a day. Read as values and costs, demand is P = 9 − Q ⁄ 10 and supply is P = 3 + Q ⁄ 10. At the equilibrium, consumer surplus is 45, producer surplus is 45, and total surplus is 90 dollars a day. Every rule this week is measured against that 90.

1. Name the two controls: ceilings, floors, and when they bind

A price control is a law about the price itself. Think of a sign on a parking garage that says "no more than this per hour." That is a top price. Think of a rule that says no one may be paid less than a certain hourly wage. That is a bottom price.

Price ceiling — a legal maximum price for a good. It binds only when it is set below the equilibrium price, and then quantity demanded exceeds quantity supplied, so the market has a shortage.
Price floor — a legal minimum price for a good. It binds only when it is set above the equilibrium price, and then quantity supplied exceeds quantity demanded, so the market has a surplus.
Binding price control — a ceiling or floor that stops the market from reaching its equilibrium price: a ceiling below the equilibrium price or a floor above it.

A control that does not bind changes nothing. On the running market, the price already settles at 6 dollars. A ceiling at 7 dollars says "no higher than 7," and the market is happy at 6, so nothing moves. A floor at 5 dollars says "no lower than 5," and the market is already above it. Both are nonbinding.

Worked example — testing two rules for whether they bind. Compare each rule's price with the equilibrium price of 6 dollars.

A ceiling at 7 dollars. A ceiling binds only below 6. Since 7 is above 6, it does not bind. The market stays at 6 dollars and 30 units a day.
A ceiling at 4 dollars. Since 4 is below 6, it binds. The price cannot rise to 6, so the market cannot clear.

In words: the ceiling at 7 is a rule on paper only, while the ceiling at 4 changes what buyers and sellers do.

Misconception check. Students often think a ceiling "binds" whenever it exists, or that a high ceiling is the strict one. It is tempting because "ceiling" sounds like a limit that always presses down. The cure: a ceiling only matters if it is below the price the market would reach anyway. Ask "would the market price break this rule?" If not, the rule is not binding.

2. Put a ceiling at 4 dollars: the shortage and the lost trades

Picture a popular food truck that is told it may not charge more than a set price, well below what customers would pay. The line gets long. The truck makes fewer meals at that low price than people want to buy. That gap is a shortage, and it is what the model predicts every time a ceiling binds.

On the running market, a ceiling at 4 dollars is binding, because 4 is below 6.

Worked example — the ceiling at 4 dollars on the running market. Read both sides of the market at the legal price.

Quantity demanded. Qd = 90 − 10 × 4 = 50 units a day.
Quantity supplied. Qs = 10 × 4 − 30 = 10 units a day.
The shortage. 50 − 10 = 40 units a day.
What trades. A sale needs a seller, so only 10 units trade.

In words: at 4 dollars, buyers want 50 units but sellers offer only 10, so 40 units' worth of buyers leave empty-handed and the market trades 10 units instead of 30. This shortage is a positive result of the model. It is not a matter of opinion.

Now measure what is lost. Week 6 showed that each unit is worth something to its buyer and costs something to its seller. The 20 units between the 10th and the 30th were all worth more to buyers than they cost sellers. Under the ceiling, those trades never happen.

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. It is the value of the trades that no longer happen, or the extra cost of trades that should not happen.

Worked example — the deadweight loss of the ceiling. Find the last unit's value and cost, then the triangle.

The last unit's value. At Q = 10, buyers value it at 9 − 10 ⁄ 10 = 8 dollars.
The last unit's cost. At Q = 10, it costs sellers 3 + 10 ⁄ 10 = 4 dollars.
The triangle. Its base is 30 − 10 = 20 units and its height is 8 − 4 = 4 dollars.
The loss. 1⁄2 × 20 × 4 = 40 dollars a day.

In words: the ceiling wipes out 40 dollars a day of gains that buyers and sellers would have made together. That is 40 of the market's 90 dollars, gone.

Here is the diagram in words. Price runs up the vertical axis and quantity runs along the horizontal axis. A horizontal line at 4 dollars marks the ceiling. It cuts the supply line at 10 units and the demand line at 50 units; the gap between those two points is the shortage. The deadweight loss is a triangle pointing right. Its left side is the vertical segment at 10 units from a price of 4 up to 8. Its tip sits at the old equilibrium, 30 units and 6 dollars.

In practice (your tools). In Desmos, type y = 9 - x/10 for demand and y = 3 + x/10 for supply, then y = 4 for the ceiling. Click where y = 4 meets each line: Desmos shows (10, 4) on supply and (50, 4) on demand. Type polygon((10,8),(10,4),(30,6)) to shade the deadweight-loss triangle.

Misconception check. Students often think a ceiling creates a surplus, because the price is "too low" and something must be left over. Nothing is left over: at a low price, sellers make less and buyers want more. The cure: at a ceiling, ask which side wants more. Buyers want more, so the market is short.

3. Put a floor at 8 dollars: the surplus and the same loss

A floor works the other way. Imagine a rule that says a farmers' market vendor may not sell a crate of apples below a set price, above what most shoppers will pay. Vendors bring plenty of crates. Shoppers buy fewer. Crates are left over at closing time.

On the running market, a floor at 8 dollars is binding, because 8 is above 6.

Worked example — the floor at 8 dollars on the running market. Read both sides at the legal price.

Quantity supplied. Qs = 10 × 8 − 30 = 50 units a day.
Quantity demanded. Qd = 90 − 10 × 8 = 10 units a day.
The surplus. 50 − 10 = 40 units a day.
What trades. A sale needs a buyer, so only 10 units trade.
The loss. The same 20 units between the 10th and the 30th are lost, so the deadweight loss is 1⁄2 × (30 − 10) × (8 − 4) = 40 dollars a day.

In words: at 8 dollars, sellers offer 50 units but buyers take only 10, so 40 units a day go unsold and 40 dollars a day of gains disappear. The ceiling and the floor lose the same amount here only because they sit the same distance from 6 on two equally steep lines.

On the diagram, a horizontal line at 8 dollars marks the floor. It cuts the demand line at 10 units and the supply line at 50 units; the gap is the surplus. The deadweight-loss triangle has the same three corners as the ceiling's: 10 units at 8 dollars, 10 units at 4 dollars, and the old equilibrium at 30 units and 6 dollars.

A caveat about the word "surplus." In Week 6, consumer surplus and producer surplus meant gains. Here, a surplus means unsold units, the Week 4 meaning. Same word, two ideas, so read the words around it.

Misconception check. Students often swap the two controls: they call a floor a ceiling because it is "high," or a ceiling a floor because it is "low." The names describe the rule, not the height. The cure: a ceiling is a cap from above, so it stops the price from rising; a floor is a base from below, so it stops the price from falling.

4. Follow the surplus: who keeps what under each control

A control does not only shrink the market. It also moves gains from one side to the other. Ask who would want a ceiling: the buyers who still get the good, at a lower price. Ask who would want a floor: the sellers who still make a sale, at a higher price.

To measure the split, the model makes one assumption, and you should name it out loud. Under the ceiling, it assumes the 10 units go to the buyers who value them most. Under the floor, it assumes the 10 units are made by the lowest-cost sellers. If a shortage means the good goes to whoever arrives first instead, some units reach buyers who value them less, and consumer surplus is smaller than the figure below.

Worked example — the split under the ceiling at 4 dollars. Use the trapezoid and triangle areas from Week 6.

Consumer surplus. Between the demand line and the price of 4, from 0 to 10 units, the area is a trapezoid with sides 9 − 4 = 5 and 8 − 4 = 4: 1⁄2 × (5 + 4) × 10 = 45 dollars a day.
Producer surplus. Between the price of 4 and the supply line: 1⁄2 × 10 × (4 − 3) = 5 dollars a day.
Total. 45 + 5 = 50 dollars a day, which is 90 − 40.

Worked example — the split under the floor at 8 dollars. Use the same two shapes, now with the price at 8.

Consumer surplus. Between demand and the price of 8: 1⁄2 × 10 × (9 − 8) = 5 dollars a day.
Producer surplus. Between the price of 8 and supply, a trapezoid with sides 8 − 3 = 5 and 8 − 4 = 4: 1⁄2 × (5 + 4) × 10 = 45 dollars a day.
Total. 5 + 45 = 50 dollars a day.

In words: under the ceiling, buyers keep 45 dollars a day versus sellers' 5, a 9-to-1 split; under the floor the split flips. Either way the market's total falls from 90 to 50 dollars a day. Buyers as a group still keep 45 under the ceiling, the same as with no rule, while sellers fall from 45 to 5.

Misconception check. Students often think a ceiling must help every buyer, because the price is lower. It helps the buyers who get the good. The 40 units' worth of buyers in the shortage get nothing at all. The cure: before saying a rule "helps buyers," ask which buyers.

5. Weigh the minimum wage: a real floor and a live debate

Here is a price floor you have 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, so it is a price floor in the labor market.

Minimum wage — 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 of their own. That is a real, dated figure from the Department of Labor, not an illustration.

The model's prediction (positive). The simple competitive model treats a binding minimum like the floor in Section 3. It predicts that a binding minimum raises the wage of workers who keep their jobs and lowers the quantity of labor employed. That prediction follows from the model, and it is stated plainly.

The evidence about size (positive, and debated). The question economists argue about is how large that job effect is for moderate increases in real labor markets. Three studies the course cites mark the debate:

Card and Krueger (1994) compared fast-food employment in New Jersey, which raised its minimum wage in 1992, with neighboring Pennsylvania. They found no fall in fast-food jobs in New Jersey after the increase.
Neumark and Wascher (2000) reworked the same question with payroll records from restaurants and found a fall in employment.
Card and Krueger's reply (2000) used Bureau of Labor Statistics employment records and again found no fall.

The strongest case on one side is the model's own logic plus the payroll-record finding: a higher price for labor should mean less labor bought, and one careful reanalysis found exactly that. The strongest case on the other side is two studies, using two different sources of employment data, that found no fall after a real increase. Both sides make testable claims about evidence. That is what makes this a positive debate, even though it is unsettled.

The judgment (normative). Suppose you knew the job effect exactly. You would still have to decide whether higher pay for some workers is worth fewer hours or jobs for others. That weighing rests on values. The model and the studies inform it; they cannot make it for you.

An honesty note on scope: the course does not grade you on the size of the minimum wage's job effect, because economists have not settled it. It does grade you on what a binding floor does in the model, because that part is settled.

Misconception check. Students often hear that economists disagree about the minimum wage and conclude that economists disagree about what a binding floor does in the model. They do not. The disagreement is about how large the effect is in real markets. The cure: separate "what the model predicts" from "how big the effect is in the data."

Pause and reflect. Choose one: (a) Write one positive sentence and one normative sentence about the minimum wage, and label each. (b) Write two sentences, each giving the strongest evidence one side of the minimum-wage debate would cite, without saying which side you favor.

6. Weigh rent control: a real ceiling and its evidence

Back to Lena and her apartment. A limit on rent, or on how fast rent may rise, is a price ceiling in the market for rental housing.

Rent control — 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 model's prediction (positive). The simple model predicts that a binding rent ceiling creates a shortage of rental housing. That is Section 2's result applied to apartments.

The evidence (positive). Diamond, McQuade, and Qian (2019) studied San Francisco's 1994 expansion of rent control. They found two things at once:

Tenants in covered buildings were more likely to stay in their homes. That is the protection rent control promises.
Landlords of covered buildings reduced the supply of rental housing. That is the shortage side the model predicts.

So one study found a real benefit for current tenants and a real cost for the supply of rentals. The strongest case for rent control points to the first finding: people kept their homes. The strongest case against points to the second: fewer units for the renters who come later.

The judgment (normative). How should a city weigh protection for current tenants against fewer units for future renters? That is a normative question. It depends on how you value stability for people already housed against access for people still looking. The course does not answer it for you.

Misconception check. Students often think that because rent control helped tenants stay put, it cannot have created a shortage, or that because supply fell, no one was helped. Both happened in the same study. The cure: a policy can have a benefit and a cost at once, and the positive work is to measure both.

7. Add a tax: the wedge, the revenue, and the loss

Now leave the price alone and add a tax. Suppose a government collects 2 dollars on every unit sold on the running market, and sellers hand it over.

Per-unit tax — a fixed dollar amount collected by the government on each unit sold. When sellers pay it, it shifts supply up by the amount of the tax.

Why up? To keep supplying a unit, a seller now needs its old cost plus 2 dollars. Every point on the supply line rises by 2 dollars. The new supply is Qs = 10 × (P − 2) − 30 = 10P − 50.

Worked example — the 2-dollar tax on sellers. Solve the new market, then read every piece.

New equilibrium. 90 − 10P = 10P − 50, so 20P = 140 and P = 7.
The buyer price. Buyers pay 7 dollars.
The seller price. Sellers keep 7 − 2 = 5 dollars.
The quantity. Q = 90 − 70 = 20 units a day.
The revenue. 2 × 20 = 40 dollars a day.
The loss. 1⁄2 × 2 × (30 − 20) = 10 dollars a day.
The surplus check. Consumer surplus is 1⁄2 × 20 × (9 − 7) = 20, producer surplus is 1⁄2 × 20 × (5 − 3) = 20, and 20 + 20 + 40 = 80 = 90 − 10.

In words: the tax raises the buyer price from 6 to 7 dollars, cuts the seller's take from 6 to 5, and shrinks the market from 30 to 20 units a day. The government collects 40 dollars a day, and 10 dollars a day of gains vanish for everyone. A per-unit tax shrinks the quantity traded; that is a positive result of the model.

Tax wedge — the gap, equal to a per-unit tax, between the price buyers pay and the price sellers keep after paying the tax.
Tax revenue — the money a government collects from a per-unit tax: the tax per unit times the number of units still traded. It is a transfer, not part of the deadweight loss.

Here is the diagram in words. The supply line moves up by 2 dollars at every quantity, from P = 3 + Q ⁄ 10 to P = 5 + Q ⁄ 10. The new line meets demand at 20 units and 7 dollars. Below that point, at 20 units, the old supply line sits at 5 dollars. The vertical gap from 5 to 7 at 20 units is the wedge. The revenue is a rectangle 20 units wide and 2 dollars tall, between prices 5 and 7. The deadweight loss is a small triangle to its right, with corners at 20 units and 7 dollars, 20 units and 5 dollars, and the old equilibrium at 30 units and 6 dollars.

In practice (your tools). In Desmos, keep y = 9 - x/10 and y = 3 + x/10, then add y = 5 + x/10 for supply with the tax. Click the crossing of the new line and demand: Desmos shows (20, 7). Type polygon((20,7),(20,5),(30,6)) to shade the deadweight loss. In Google Sheets, type =2*20 for the revenue and =0.5*2*(30-20) for the loss.

Does it matter which side writes the check? Collect the same 2 dollars from buyers instead. Demand shifts down by 2: Qd = 90 − 10 × (P + 2) = 70 − 10P. Then 70 − 10P = 10P − 30, so the seller price is 5, buyers pay 5 + 2 = 7, and 20 units trade. The outcome is the same.

Misconception check. Students often count tax revenue as part of the deadweight loss, or compute the loss as tax × quantity. The 40 dollars of revenue is not lost; it moves from buyers and sellers to the government, which can spend it. The cure: the loss is only the triangle, 10 dollars a day, the trades that no longer happen. The rectangle, 2 × 20 = 40, is the revenue.

8. Find who bears a tax: the check versus the burden

Back to Ama's bakery. She writes the check to the government. But who carries the cost depends on how much the price moves. Two words help.

Economic incidence — how the burden of a tax is actually shared between buyers and sellers, measured by how much the buyer price rises and the seller price falls. The side that is less responsive to price bears more, whichever side writes the check to the government.

The legal rule about who hands over the money is sometimes called the statutory incidence. Economic incidence is about who ends up poorer.

On the running market, the 2-dollar tax raised the buyer price from 6 to 7 and lowered the seller price from 6 to 5. Buyers bear 7 − 6 = 1 dollar and sellers bear 6 − 5 = 1 dollar. That even split happens only because quantity demanded and quantity supplied each change by 10 units per dollar. The two lines are equally steep.

Now take a market where they are not. Think of a good buyers find hard to do without, such as the fuel a delivery driver needs to keep working. This market is constructed for this course: demand is Qd = 60 − 5P and supply is Qs = 15P − 40.

Worked example — a 4-dollar tax on sellers in the who-bears-it market. Solve before and after the tax, then compare the prices.

Before the tax. 60 − 5P = 15P − 40, so 20P = 100 and P = 5 dollars; Q = 60 − 25 = 35 units a day.
Supply with the tax. Qs = 15 × (P − 4) − 40 = 15P − 100.
After the tax. 60 − 5P = 15P − 100, so 20P = 160 and P = 8; buyers pay 8 dollars, sellers keep 8 − 4 = 4 dollars, and Q = 60 − 40 = 20 units a day.
Each side's burden. Buyers bear 8 − 5 = 3 dollars and sellers bear 5 − 4 = 1 dollar.
Revenue and loss. Revenue is 4 × 20 = 80 dollars a day; the deadweight loss is 1⁄2 × 4 × (35 − 20) = 1⁄2 × 4 × 15 = 30 dollars a day.

In words: the sellers write the whole 4-dollar check, but buyers carry 3 dollars of it versus sellers' 1, three times as much. The reason is responsiveness, the Week 5 idea. Quantity demanded changes by only 5 units per dollar, while quantity supplied changes by 15. Buyers have few ways to dodge the price rise, so they absorb most of it. Sellers can cut back more easily, so the price they keep falls less.

Misconception check. Students often assume whoever writes the check bears the whole tax. It is tempting because the check is the visible part. The cure: compare the prices before and after. The buyer's share is the rise in the buyer price; the seller's share is the fall in the seller price. The side that responds less to price bears more.

Pause and reflect. Choose one: (a) Name a good you would keep buying even if its price rose a lot. If it were taxed, explain in two sentences which side would bear more. (b) Name a good you would drop quickly if its price rose. If it were taxed, explain in two sentences which side would bear more.

9. Run a subsidy: more trades at a cost

A subsidy is a tax turned upside down. Instead of collecting money on each unit, the government pays it. Suppose it pays sellers 2 dollars for every unit sold on the running market.

Per-unit subsidy — a fixed dollar amount the government pays for each unit sold; it works like a negative tax, lowering the price buyers pay, raising the price sellers receive, and raising the quantity traded, at a cost to taxpayers.

With 2 dollars from the government, a seller needs 2 dollars less from the buyer, so supply shifts down by 2 at every quantity: Qs = 10 × (P + 2) − 30 = 10P − 10.

Worked example — the 2-dollar subsidy to sellers. Solve the new market, then count every group, taxpayers included.

New equilibrium. 90 − 10P = 10P − 10, so 20P = 100 and P = 5.
The prices. Buyers pay 5 dollars, and sellers receive 5 + 2 = 7 dollars.
The quantity. Q = 90 − 50 = 40 units a day.
The cost to taxpayers. 2 × 40 = 80 dollars a day.
The gains. Consumer surplus is 1⁄2 × 40 × (9 − 5) = 80, and producer surplus is 1⁄2 × 40 × (7 − 3) = 80.
The net. 80 + 80 − 80 = 80 dollars a day, so total surplus falls from 90 to 80, a deadweight loss of 10 dollars a day.

In words: buyers and sellers both gain, but taxpayers pay 80 dollars a day for it, and the net gain to society shrinks by 10 dollars a day. The ten extra units, from the 31st to the 40th, cost sellers more to make than buyers value them. The 40th unit, for example, is worth 5 dollars to a buyer and costs a seller 7.

On the diagram, the supply line drops 2 dollars, to P = 1 + Q ⁄ 10, and meets demand at 40 units and 5 dollars. The deadweight loss is a triangle to the right of the old equilibrium. Its corners are the old equilibrium at 30 units and 6 dollars, the point at 40 units and 7 dollars on the old supply line, and the point at 40 units and 5 dollars on the demand line. The loss is 1⁄2 × 2 × (40 − 30) = 10.

A limitation to state plainly: this result holds in a market with no costs or benefits falling on people outside the trade. Week 14 adds such effects and shows when a subsidy can raise total surplus instead. This week's market has none, so here the subsidy loses value.

Misconception check. Students often think a subsidy cannot create a loss, because both buyers and sellers gain. The cure: count the taxpayers too. Buyers and sellers gain 70 dollars a day more than before, from 90 to 160, but taxpayers pay 80, so society comes out 10 dollars a day behind.

10. Check the classic wrong turns

Most errors this week are a flipped label or a missing step, not a deep confusion. Here are the five to watch for, each tied to the running market.

A ceiling above 6 dollars called binding. A ceiling at 7 does nothing. Only a ceiling below 6 binds.
A ceiling said to create a surplus. A ceiling at 4 creates a shortage of 40 units. A floor at 8 creates a surplus.
The check confused with the burden. In the who-bears-it market, sellers write the check, yet buyers bear 3 of the 4 dollars.
Revenue counted as loss. The 2-dollar tax raises 40 dollars of revenue and causes 10 dollars of deadweight loss. Tax × quantity gives the revenue, never the loss.
A debate about size read as a debate about direction. Economists disagree about how large the minimum wage's job effect is. They do not disagree about what a binding floor does in the model.

Worked example — checking a classmate's tax work. A classmate writes: "With the 2-dollar tax on the running market, sellers pay the tax, so sellers lose 2 dollars a unit, and the deadweight loss is 2 × 20 = 40."

The burden. Sellers keep 5 dollars, down from 6, so they bear 1 dollar, not 2. Buyers pay 7, up from 6, and bear the other dollar.
The loss. 2 × 20 = 40 is the revenue. The deadweight loss is 1⁄2 × 2 × (30 − 20) = 10 dollars a day.

In words: the classmate made two of this week's classic slips at once, assigning the tax to whoever writes the check and counting revenue as loss.

Misconception check. Students often think they need to memorize five separate rules. There are really two habits. First, compare the rule's price with the equilibrium before you say anything. Second, measure losses as triangles of trades that no longer happen, and keep money that changes hands separate.

Key terms

Price ceiling — A legal maximum price for a good that binds only when it is set below the equilibrium price, where it creates a shortage. (first used: 1. Name the two controls: ceilings, floors, and when they bind)
Price floor — A legal minimum price for a good that binds only when it is set above the equilibrium price, where it creates a surplus. (first used: 1. Name the two controls: ceilings, floors, and when they bind)
Binding price control — A ceiling or floor that stops the market from reaching its equilibrium price: a ceiling below it or a floor above it. (first used: 1. Name the two controls: ceilings, floors, and when they bind)
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, shown as a triangle on straight-line curves. (first used: 2. Put a ceiling at 4 dollars: the shortage and the lost trades)
Minimum wage — A legal minimum hourly wage that an employer may pay a worker, which makes it a price floor in the labor market. (first used: 5. Weigh the minimum wage: a real floor and a live debate)
Rent control — 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. (first used: 6. Weigh rent control: a real ceiling and its evidence)
Per-unit tax — A fixed dollar amount collected by the government on each unit sold, drawn as supply shifting up by the tax when sellers pay it. (first used: 7. Add a tax: the wedge, the revenue, and the loss)
Tax wedge — The gap, equal to a per-unit tax, between the price buyers pay and the price sellers keep after paying the tax. (first used: 7. Add a tax: the wedge, the revenue, and the loss)
Tax revenue — The tax per unit times the number of units still traded, a transfer to the government rather than part of the deadweight loss. (first used: 7. Add a tax: the wedge, the revenue, and the loss)
Economic incidence — How a tax's burden is actually shared between buyers and sellers, with the less price-responsive side bearing more, whichever side writes the check. (first used: 8. Find who bears a tax: the check versus the burden)
Per-unit subsidy — A fixed dollar amount the government pays for each unit sold, which lowers the buyer price, raises the seller price, and raises the quantity traded at a cost to taxpayers. (first used: 9. Run a subsidy: more trades at a cost)

Summary

A ceiling is a legal top price; it binds only below the equilibrium price.
A floor is a legal bottom price; it binds only above the equilibrium price.
A binding ceiling creates a shortage; a binding floor creates a surplus.
A binding control shrinks the quantity traded and causes a deadweight loss.
The minimum wage is a real floor; economists debate the size of its job effect.
Rent control is a real ceiling; the evidence shows a benefit and a cost.
A per-unit tax drives a wedge between the buyer price and the seller price.
Tax revenue is a transfer; the deadweight loss is only the lost-trades triangle.
The side less responsive to price bears more of a tax, whoever writes the check.
A subsidy raises the quantity traded, costs taxpayers, and here causes a loss.

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.

An illustrative market for weekly permits in a downtown parking garage has demand Qd = 80 − 4P and supply Qs = 4P − 16, with P in dollars and Q in permits. Its equilibrium is 32 permits at 12 dollars. The city sets a ceiling of 10 dollars. Find the shortage, the number of permits sold, and the deadweight loss.
An illustrative beach-town market for bottles of sunscreen has demand Qd = 50 − 2P and supply Qs = 6P − 30, with an equilibrium of 30 bottles at 10 dollars. A 4-dollar tax is collected from sellers. Find the buyer price, the seller price, the quantity, each side's burden, the revenue, and the deadweight loss.
An illustrative market for bicycle helmets has demand Qd = 120 − 4P and supply Qs = 4P − 40, with an equilibrium of 40 helmets at 20 dollars. The government pays sellers 4 dollars per helmet. Find the buyer price, the seller price, the quantity, the cost to taxpayers, and the deadweight loss.
A friend says: "Economists can't even agree whether a binding minimum wage creates a surplus of labor in the model." Explain what is wrong with the claim, then label this sentence positive or normative: "A higher minimum wage is worth some lost jobs."

Answers (worked reasoning — read after attempting)

At 10 dollars, Qd = 80 − 4 × 10 = 40 and Qs = 4 × 10 − 16 = 24, so the shortage is 40 − 24 = 16 permits and 24 permits sell. Read as values and costs, demand is P = 20 − Q ⁄ 4 and supply is P = 4 + Q ⁄ 4. At 24 permits a driver values the last one at 20 − 24 ⁄ 4 = 14 dollars and it costs the garage 4 + 24 ⁄ 4 = 10 dollars. The deadweight loss is 1⁄2 × (32 − 24) × (14 − 10) = 16 dollars a week. The ceiling binds because 10 is below 12, so 16 drivers who want a permit cannot get one.
Supply with the tax is Qs = 6 × (P − 4) − 30 = 6P − 54. Then 50 − 2P = 6P − 54, so 8P = 104 and P = 13. Buyers pay 13 dollars, sellers keep 13 − 4 = 9, and Q = 50 − 26 = 24 bottles. Buyers bear 13 − 10 = 3 dollars and sellers bear 10 − 9 = 1 dollar. Revenue is 4 × 24 = 96 dollars, and the deadweight loss is 1⁄2 × 4 × (30 − 24) = 12 dollars. Buyers bear more because quantity demanded changes by only 2 bottles per dollar, while quantity supplied changes by 6.
Supply with the subsidy is Qs = 4 × (P + 4) − 40 = 4P − 24. Then 120 − 4P = 4P − 24, so 8P = 144 and P = 18. Buyers pay 18 dollars, sellers receive 18 + 4 = 22, and Q = 120 − 72 = 48 helmets. Taxpayers pay 4 × 48 = 192 dollars. The deadweight loss is 1⁄2 × 4 × (48 − 40) = 16 dollars, from the 8 extra helmets that cost more to make than buyers value them.
The claim mixes up two questions. In the model, a binding minimum wage is a floor above the equilibrium wage, so it creates a surplus of labor: more hours offered than employers want. Economists agree on that. What they debate is how large the job effect is in real markets, with Card and Krueger finding no fall and Neumark and Wascher finding one. The sentence "A higher minimum wage is worth some lost jobs" is normative, because "worth it" rests on how you weigh higher pay against lost work.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the midterm review adds the marginal-benefit and marginal-cost rule, the habit that carries the course into the firm weeks.

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