Practice
Price ceilings and price floors
The shortage or surplus a binding price control creates, its deadweight loss, and when a control does nothing.
The skill
A price control matters only if it binds. A ceiling binds when it is set below the equilibrium price and creates a shortage; a floor binds when it is set above the equilibrium price and creates a surplus. When one binds, the quantity traded is the smaller of quantity demanded and quantity supplied at the controlled price. Deadweight loss is the triangle between demand and supply from that quantity out to the equilibrium quantity. The trap is assuming every ceiling or floor changes the market.
A worked example
In a competitive market for concert tickets, demand is Qd = 53 − P and supply is Qs = −1 + P, where P is the price in dollars and Q is the number of tickets per week.
The government sets a price ceiling at $21.
What is the deadweight loss, in dollars? Round to two decimal places.
Solution
- Equilibrium: P = 27, Q = 26. The ceiling at $21 is below it, so it binds.
- At $21: Qd = 32 and Qs = 20, a shortage of 12. Only 20 are traded, the smaller of the two.
- At 20 units buyers would pay $33 and sellers would accept $21. Deadweight loss = ½ × (26 − 20) × (33 − 21) = $36.
Answer: 36