Governments sometimes set a legal price limit. Whether the limit changes anything depends on where it sits relative to equilibrium; when it does, it creates the shortages and surpluses of Shortages and Surpluses and the deadweight loss of Total Surplus and Deadweight Loss.
Key idea
A price ceiling is a legal maximum price. It is binding only if it is below the equilibrium price; then quantity demanded exceeds quantity supplied (a shortage), and only the quantity sellers offer is traded. A price floor is a legal minimum. It is binding only if it is above equilibrium; then there is a surplus, and only the quantity buyers want is traded. A binding control creates a deadweight loss.
Why it works
A ceiling above the equilibrium price allows the market price, so it changes nothing. A ceiling below it forbids the equilibrium; at the legal price, sellers move down their supply curve and offer less, while buyers want more. The smaller side of the market decides how much changes hands, so trades that would benefit both sides don't happen. A floor works the same way from above.
Worked example: A binding ceiling
$Q_d = 20 - 2P$ and $Q_s = -4 + 2P$ (equilibrium \$6, 8 units). The government sets a price ceiling of \$4. Find the shortage, the quantity traded and the deadweight loss.
- \$4 is below \$6, so the ceiling binds.
- At \$4: $Q_d = 12$, $Q_s = 4$. Shortage: $12 - 4 = 8$. Only 4 are traded.
- At 4 units, buyers would pay $10 - 4/2 = \$8$; sellers' cost is \$4.
- $DWL = \tfrac{1}{2} \times (\$8 - \$4) \times (8 - 4) = \$8$.
Answer: Shortage 8, quantity traded 4, DWL \$8.
Worked example: A floor that does nothing
In the same market, a price floor of \$5 is set. What happens?
- A floor is a minimum. The market price, \$6, is already above \$5.
- The floor doesn't bind: the market stays at \$6 and 8 units.
Answer: Nothing changes.
Common mistake
Placing a binding ceiling above the equilibrium because "ceiling" sounds high, or thinking a ceiling above equilibrium changes the market. A ceiling is a lid: it only matters if it pushes the price down. Check: a binding ceiling is below $P^*$ and a binding floor is above it.
Economists broadly agree that binding rent ceilings reduce the quantity and quality of rental housing over time. The minimum wage is a price floor in the labor market; in the competitive model it creates a surplus of labor, but the model in Monopsony predicts it can raise employment, and the measured effects of particular minimum wages are studied and debated.