Price Ceilings, Price Floors and Quotas

A state caps gas at $3 a gallon to protect drivers. By noon the pumps are dry, and the line wraps around the block. How does a law meant to help buyers leave so many of them with nothing? This is Module 2.8B: price and quantity controls.

Sometimes the government sets a price or quantity by law. It has three tools: a price ceiling, a price floor, and a quota. Each one changes the incentives buyers and sellers face, in any kind of market. In a market already producing the efficient quantity, none of them can raise efficiency. At best, they change nothing.

A price ceiling is a legal maximum price. Sellers can't charge more than it. It only matters when it's set below the equilibrium price. Then we call it binding. A ceiling above the market price changes nothing, because the price was already lower. Here's our gas market. With no cap, the price is $4 a gallon, and drivers buy 10,000 gallons a day.

Quick refresher: to read a quantity at a price, go across from that price to a curve, then straight down to the quantity axis.

At the $3 cap, quantity demanded rises to 12,000 gallons, but quantity supplied slides down the supply curve to 7,000. 12,000 minus 7,000 is a shortage of 5,000 gallons a day. The price can't rise to close the gap, so the pumps run dry. Exam trap: the shortage is not the amount sold. Buyers can only buy what sellers supply, so the quantity traded is the smaller number: quantity supplied, 7,000 gallons. That's 3,000 gallons fewer than the 10,000 sold at equilibrium.

So what just happened at the pump? One: the $3 cap sits below the $4 equilibrium, so it binds. Two: quantity demanded hits 12,000, but quantity supplied is only 7,000: a shortage of 5,000. Three: only the 7,000 supplied get sold.

Quick refresher: consumer surplus is the area under the demand curve and above the price buyers pay. Producer surplus is the area above the supply curve and below the price sellers get. Both stop at the quantity actually sold.

Now follow the surplus. Drivers who still get gas pay $1 less on each of 7,000 gallons. That $7,000 a day moves from stations to drivers. But the 3,000 missing gallons were worth more to drivers than they cost stations to supply. That lost value is the deadweight loss.

Quick refresher: a triangle's area is one half, times its base, times its height. Read both off the graph: the base, or width, is a gap in quantity, and the height is a gap in price, the higher price minus the lower one.

Its width is those 3,000 gallons. Its height is not the $1 from $3 to $4. It runs from the $3 cap up to demand at 7,000 gallons: $5.50. Area equals one half, times 3,000, times $2.50. That's $3,750 a day in value that nobody gets. So producer surplus falls for sure. Consumer surplus can rise, as it does on this graph, but only for drivers who get gas.

So what just happened to the surplus? One: drivers who got gas gained $7,000 a day from stations. Two: 3,000 gallons stopped trading, and the value lost on them, $3,750 a day, is deadweight loss. Three: producer surplus falls for sure.

More waste: gas goes to whoever gets there first, not to the drivers who value it most. And hours spent in line are wasted resources. Stations have less reason to fix pumps, so quality drops. And since drivers would still buy all 7,000 gallons at $5.50, some gas gets resold illegally above the cap: a black market.

A price floor is the opposite: a legal minimum price. It binds only when it's set above equilibrium. A floor below the market price changes nothing. Say cheese sells for $6 a pound, 8,000 pounds a week. Then the government sets a $7 floor. At $7, quantity supplied is 10,000 pounds, but quantity demanded is only 6,000: a surplus of 4,000. Exam trap: don't say supply rose and demand fell. Neither curve moved.

Quick refresher: every sale needs a buyer and a seller, so the quantity that trades is the smaller of quantity demanded and quantity supplied. Here that's quantity demanded, 6,000, against quantity supplied, 10,000.

Purchases are limited to quantity demanded, the smaller number: 6,000 pounds. The 2,000 pounds that stop selling leave a deadweight loss triangle.

Quick refresher: consumer surplus sits under demand and above the price, and producer surplus sits above supply and below it. Raise the price from $6 to $7, and the strip between those two prices, on the 6,000 pounds still sold, switches sides.

Exam trap: watch which way the rectangle moves. Under a ceiling, it goes from sellers to buyers. Under a floor, buyers pay $1 more on 6,000 pounds, so $6,000 moves from buyers to sellers. So consumer surplus falls for sure. Producer surplus can go either way: dairies gain the rectangle but lose the sales that no longer happen. The triangle goes to nobody.

So what just happened with cheese? One: the $7 floor sits above the $6 equilibrium, so it binds. Two: quantity supplied is 10,000, quantity demanded 6,000: a 4,000 pound surplus, and only 6,000 sell. Three: $6,000 moves from buyers to sellers, and a deadweight loss appears.

Floors waste too. Unsold cheese spoils, unless the government buys the extra 4,000 pounds with tax money. Then dairies sell all 10,000. Sales don't go to the dairies with the lowest costs. Dairies may compete with fancy extras buyers wouldn't pay for. And some cheese gets sold illegally below $7.

The third tool limits quantity instead of price. A quota is a legal cap on how much can be sold, usually through permits. Say food trucks sell 5,000 lunches a day at $10 each. Then the city issues permits for only 4,000 lunches a day. With only 4,000 lunches, buyers will pay $12. That's the demand price, and it's what lunches now cost. Trucks would supply them for just $7, the supply price. The $5 gap on each lunch is the quota rent. It goes to whoever owns the permits. Across 4,000 lunches, that's $20,000 a day.

So what just happened with lunches? One: permits cut lunches from 5,000 to 4,000. Two: buyers now pay the demand price, $12, while trucks would supply them for $7. Three: the $5 gap times 4,000 lunches is $20,000 a day of quota rent for permit owners.

The 1,000 lunches that no longer happen leave a deadweight loss. Heads up: the AP exam won't ask you to draw a quota graph. But the idea is fair game: what a quota does to quantity, price and surplus.

Quick check, question 1. The equilibrium price of bike helmets is $30. The government sets a price ceiling of $40. What happens? A) A shortage B) A surplus C) Price and quantity don't change D) A deadweight loss triangle

C. The ceiling sits above the market price, so it isn't binding. It's not A, because only a ceiling below equilibrium causes a shortage, and not B, because the price stays at $30.

Question 2. At a binding price floor, buyers want 300 units and sellers want 500. How many units do buyers purchase? A) 500 B) 800 C) 200 D) 300

D, 300. Purchases are limited to quantity demanded, the smaller number. 200 is the surplus, and 500 is only what sellers wish they could sell.

Binding ceilings sit below equilibrium and cause shortages. Binding floors sit above it and cause surpluses. Either way, the smaller of quantity demanded and quantity supplied is what trades. Quotas cut quantity directly. In all three, the value lost on missing trades is deadweight loss. Next: Module 2.9, International Trade and Public Policy.