Price controls — floors and ceilings — Economics

Before this

This leads to

Subsidies
Examples of government failure
Monopsony · coming soon

What if the law just sets the price?

Rents in a city have risen to $1 000 a month. Many families struggle to pay. The city council has an idea that sounds simple and kind: make it illegal to charge more than $800. Families will pay less. What could go wrong?

The earlier lectures showed that a market price is not chosen by anyone. It is the price where the plans of buyers and sellers match, and shortages and surpluses push the price there. A law that fixes the price does not stop those pushes. It only stops the price from moving. This lecture follows what happens next, for a maximum price (a price ceiling) and for a minimum price (a price floor).

A ceiling below the equilibrium

Here is an invented city's rental market. Rent $P$ is in dollars per month, and quantities are flats per month:

Q_{d} Q_{s} = 50000 - 20 P = 10000 + 20 P

Setting the plans equal gives $40000 = 40 P$ , so the equilibrium rent is $1 000 and 30 000 flats are rented. Now the council sets a ceiling of $800. At that rent, tenants want $50000 - 16000 = 34000$ flats. Landlords offer only $10000 + 16000 = 26000$ . There is a shortage of 8000 flats.

A rent ceiling of $800, below the equilibrium of $1 000. Tenants want 34 000 flats but landlords offer only 26 000, a shortage of 8000. Only 26 000 flats are rented. For the last of them, some tenant would pay up to $1 200. The grey triangle is the deadweight loss.

Notice the most important number on the diagram. Only 26 000 flats are rented, because nobody can rent a flat that is not offered. The quantity traded is always the smaller of the two plans. Fewer families now have flats than before the law, not more.

Read the demand curve upwards at 26 000 flats, as in the lecture on consumer surplus. Some tenant values that last flat at $(50000 - 26000) \div 20 = $1 200$ a month. So there are tenants without a flat who would happily pay $1 200, while the law says the rent is $800. That gap explains everything that follows.

Who gets the flats?

In a free market, the price decides who gets a flat: whoever will pay the market rent. A binding ceiling switches that off. Something else must decide, because 34 000 households want 26 000 flats.

Queues and waiting lists. The flats go to those who wait longest or applied first.
Connections and luck. Knowing a landlord, or hearing about a flat first, starts to matter.
Payments outside the law. With tenants willing to pay up to $1 200, some landlords ask for a "key fee" or a payment in cash. This is an illegal market, often called a black market, and its price can be above the old $1 000.
Lower quality. A landlord who can fill a flat at once has less reason to repair it, because a quality cut cannot be punished by losing tenants.

Tenants who do get a flat gain $200 a month each. With 26 000 such flats, that is $26000 \times 200 = $5 200000$ a month moved from landlords to tenants. That transfer is the point of the policy. But something is also lost completely: the 4000 flats between 26 000 and 30 000 that were worth more to tenants than they cost landlords to provide, and that are no longer rented. The lost surplus is the grey triangle:

\frac{1}{2} \times 4000 \times (1200 - 800) = $800 000 a month

That is it. That is the whole idea. A binding ceiling cannot make a good cheaper to supply. It moves money from sellers to the buyers who get the good, creates a shortage for everyone else, and destroys the trades that no longer happen.

Stop and think

The council sets the ceiling at $1 100 instead. What happens to rents and to the number of flats?

Show the answer

Nothing. The market rent is $1 000, which is already below the ceiling. Charging $1 000 is legal, and no landlord can charge more without losing tenants to cheaper flats. So the ceiling does not bind: it has no effect at all. A ceiling matters only when it is set below the equilibrium price. A floor matters only when it is set above it. Many students draw a ceiling above the equilibrium and then find a "surplus", which never happens.

A floor above the equilibrium

A price floor is a legal minimum price, set to protect sellers. Use the market from the last two lectures: $Q_{d} = 100 - 2 P$ and $Q_{s} = 20 + 3 P$ , with equilibrium $16 and 68 units. Suppose the government sets a floor of $20. Buyers now want $100 - 40 = 60$ units. Sellers offer $20 + 60 = 80$ . There is a surplus of 20 units that nobody buys.

Again, the quantity traded is the smaller plan: 60 units, fewer than the 68 before. Sellers who sell get more per unit, but they sell fewer units, and 20 units are left over. Governments that set floors for farm products have often had to buy the surplus to keep the floor in place. Here that would cost $20 \times $20 = $400$ per week, for goods nobody wanted at that price.

Explore both controls on the rental market below.

Graph builder — ceilings and floors

Choose a ceiling or a floor, then move the legal rent. Watch the gap between the two plans, the number of flats actually rented, and the deadweight loss. Find where each control stops binding.

Legal rent: $800

The rental market (Qd = 50 000 − 20P, Qs = 10 000 + 20P, equilibrium $1 000 and 30 000 flats) under four legal rents:

Control	Wanted	Offered	Rented	Deadweight loss
Ceiling $800	34 000	26 000	26 000	$800 000
Ceiling $900	32 000	28 000	28 000	$200 000
Ceiling $1 100	30 000	30 000	30 000	$0 (does not bind)
Floor $1 200	26 000	34 000	26 000	$800 000

A binding control always reduces the number of flats rented to the smaller of the two plans. The further the legal rent is from $1 000, the bigger the loss.

Did you notice that the loss grows quickly as the control moves away from $1 000? A ceiling $100 below the equilibrium loses $200 000 a month. A ceiling $200 below loses $800 000, four times as much. Doubling the distance quadruples the triangle, because both its base and its height double.

The minimum wage: a floor in the labour market

The best-known price floor is a minimum wage. In the labour market, workers supply labour and employers demand it, and the price is the wage. The simple model makes a clear prediction: a minimum wage above the equilibrium wage raises pay for those who keep their jobs, but employers hire fewer workers, while more people look for work. The gap is unemployment.

Whether this happens in real labour markets is one of the most studied, and most argued over, questions in economics. Two well-known reviews point in different directions. David Neumark and William Wascher surveyed many studies (NBER working paper, 2006) and concluded that a sizable majority found negative effects on employment, with the clearest evidence for the least-skilled workers. Doruk Cengiz, Arindrajit Dube, Attila Lindner and Ben Zipperer (2019) studied 138 increases in US state minimum wages from 1979 to 2016. They found that the overall number of low-wage jobs stayed essentially unchanged over the five years after each increase.

Why might the evidence differ from the simple model? One reason economists give is that the size of the effect depends on how far the minimum is above the market wage. It also depends on how strongly employers and workers respond, just as in the tax lecture. Another is that some employers may have power to set wages below the competitive level, a case called monopsony, which a later lecture studies. In that case, a minimum wage need not reduce employment. The model tells you what to look for. The evidence tells you how large the effect is, and economists still disagree about that.

Before the real case, find the mistake in a student's working on a price floor.

Spot the error — what is sold under a floor?

A student analyses a $20 floor in the market Qd = 100 − 2P, Qs = 20 + 3P. Exactly one line is wrong. Tap it.

A student's working for a $20 price floor. Line 4 is wrong.

Line 1. Equilibrium: 100 − 2P = 20 + 3P gives P = 16 and Q = 68. Correct.
Line 2. The floor of $20 is above $16, so it binds. Correct.
Line 3. At $20, buyers want 60 and sellers offer 80, a surplus of 20. Correct.
Line 4. So 80 units are sold at $20. Wrong: buyers take only 60, so only 60 are sold.
Line 5. Sellers' revenue rises from 16 × 68 = $1 088 to 20 × 60 = $1 200. Correct for the 60 units actually sold.

A real case: rent control in San Francisco

Worked Example — Extending rent control (San Francisco, 1994)

The policy. In 1994, a change in San Francisco's law extended rent control to many smaller apartment buildings that had been exempt. In those buildings, rent increases for existing tenants became limited by law.

The prediction. Covered tenants should gain: lower rents give them a strong reason to stay. Landlords, earning less from controlled rental flats, have a reason to take flats out of the controlled rental market, for example by selling them as owner-occupied homes or redeveloping them. With fewer rental flats, rents for everyone else should rise.

What happened. Rebecca Diamond, Tim McQuade and Franklin Qian studied the change (American Economic Review, 2019). They found that rent control reduced tenants' moving by about 20%: covered tenants stayed in their homes. They also found that landlords of covered buildings reduced their rental housing supply by 15%, which caused a city-wide rent increase of 5.1%.

The verdict. Both predictions held. The policy gave large benefits to the tenants it covered, as it was meant to. But by reducing the supply of rental housing, it raised rents for future tenants across the city, which is the shortage logic of the ceiling diagram, spread over years. Economists differ on the right response. Some argue for building more housing instead; others argue for keeping protections for existing tenants and paying for them in ways that do not shrink supply. The diagram does not settle that choice. It shows what each choice costs.

Three classic mistakes

Trap 1 — A ceiling above the equilibrium

A ceiling is a maximum. It changes anything only when it is set below the equilibrium price. A floor changes anything only when it is set above it. Drawing them the other way round gives shortages and surpluses that do not exist.

Trap 2 — Counting the larger quantity as sold

Under a ceiling, the amount bought is limited by sellers. Under a floor, it is limited by buyers. In both cases the quantity traded is the smaller of $Q_{d}$ and $Q_{s}$ , and it is less than the equilibrium quantity.

Trap 3 — "The ceiling makes the good cheaper for everyone"

It makes the good cheaper for those who get it. Others get nothing at the legal price, and some end up paying more through queues, fees or an illegal market, where the price can be above the old equilibrium.

Try it yourself

Use the rental market $Q_{d} = 50000 - 20 P$ , $Q_{s} = 10000 + 20 P$ unless told otherwise.

The council sets a rent ceiling of $900. Find the shortage, the number of flats rented, and the most that some tenant would pay for the last flat rented.

Hint 1
Work out $Q_{d}$ and $Q_{s}$ at $900.

Hint 2
For the last flat, read the demand curve at the quantity rented: $P = (50000 - Q) \div 20$ .

Full answer
$Q_{d} = 50000 - 18000 = 32000$ and $Q_{s} = 10000 + 18000 = 28000$ . Shortage: 4000 flats. Only 28 000 are rented. For the last of them, some tenant would pay $(50000 - 28000) \div 20 = $1 100$ .
Explain why a ceiling of $1 100 has no effect on this market.

Hint 1
Find the equilibrium rent first.

Hint 2
Is the market rent already below the ceiling?

Full answer
The equilibrium rent is $1 000 (from $40000 = 40 P$ ). That is already allowed under a $1 100 ceiling, and no landlord can charge more than $1 000 without losing tenants. So rents stay at $1 000 and 30 000 flats are rented: the ceiling does not bind.
In the market $Q_{d} = 100 - 2 P$ , $Q_{s} = 20 + 3 P$ , the government sets a floor of $18 and promises to buy any surplus at that price. Find the quantity bought by consumers, the surplus, and the cost to the government.

Hint 1
Work out $Q_{d}$ and $Q_{s}$ at $18.

Hint 2
The government pays $18 for each surplus unit.

Full answer
$Q_{d} = 100 - 36 = 64$ and $Q_{s} = 20 + 54 = 74$ . Consumers buy 64 units; the surplus is 10 units. The government pays $10 \times 18 = $180$ per week. Check: $64 + 10 = 74$ , everything sellers offer is sold, which is how the floor is kept in place.
An invented labour market has demand for workers $L_{d} = 1000 - 50 W$ and supply $L_{s} = 100 + 40 W$ , with the wage $W$ in dollars per hour. Find the equilibrium. A minimum wage of $12 is introduced. According to this simple model, how many workers are employed, and how many want a job but cannot find one? Then give one reason why real evidence on minimum wages may differ from this model's answer.

Hint 1
Set $1000 - 50 W = 100 + 40 W$ .

Hint 2
At $12, employment is the smaller of $L_{d}$ and $L_{s}$ .

Full answer
$900 = 90 W$ , so the equilibrium wage is $10 and 500 workers are employed. At $12, $L_{d} = 1000 - 600 = 400$ and $L_{s} = 100 + 480 = 580$ . The model predicts 400 employed and 180 unemployed: 100 who lost jobs and 80 newly attracted to look for work. Real evidence may differ for several reasons. The size of the effect depends on how strongly employers respond, which these straight lines fix in advance. And if employers have power to set wages (monopsony), a minimum wage need not reduce employment. Studies disagree on how large the effect is in practice.

The bigger idea

A price does two jobs at once. It moves money between buyers and sellers, and it carries information: a high rent tells builders and landlords that flats are scarce and worth providing. A price control can change the first job by law. It cannot stop the second job from mattering. When the signal is held down, the scarcity it was reporting does not go away. It shows up somewhere else: in queues, in quality, in fewer flats years later.

That is why economists judge price controls by asking who gains, who loses and what is destroyed, using the same welfare diagram as for taxes. A government may decide that helping today's tenants or today's low-paid workers is worth the cost. The economics does not make that choice. It makes the cost visible. The next lecture looks at a tool that pushes prices the other way without forbidding any price: a subsidy.

Key concepts in this lesson

A price ceiling is a legal maximum price, and it binds only when set below the equilibrium price, creating a shortage.
A price floor is a legal minimum price, and it binds only when set above the equilibrium price, creating a surplus.
Under any binding control, the quantity traded is the smaller of quantity demanded and quantity supplied, so fewer trades happen.
A binding ceiling transfers surplus to the buyers who get the good, but leads to rationing, illegal markets and a deadweight loss.
The minimum wage is a price floor in the labour market, and economists still disagree about how large its effect on employment is.