How to Calculate the Effect of a Price Floor
A binding price floor creates a surplus equal to Qs − Qd at the floor price, and the quantity actually traded falls to the smaller amount, Qd.
The Price Floor formula
Calculator
Enter the demand and supply equations and a floor to test whether it binds and size the surplus it creates.
The a in Qd = a − bP.
Enter b as a positive number.
Zero when supply is Qs = dP.
The legal minimum. It only bites when it sits above the equilibrium price.
At the $32 floor sellers offer 96 units while buyers take only 36, leaving 60 units unsold.
- Equilibrium price without the floor
- $20
- Is the floor binding?
- Binding
- Quantity traded
- 36
- Deadweight loss
- $240
- Cost to buy up the surplus
- $1,920
Where the market would clear if no floor existed.
Only 36 units change hands, because buyers are the short side of the market.
Trades worth $240 never happen, the triangle between demand and supply from 36 units up to 60.
A government that bought every unsold unit at the $32 floor would spend $1,920.
How to calculate Price Floor, step by step
- 1Check that the floor binds. A floor changes the market only when it is set above the equilibrium price; one set below equilibrium does nothing.
- 2Find quantity supplied at the floor. Substitute the floor price into the supply equation to get Qs.
- 3Find quantity demanded at the floor. Substitute the same price into the demand equation to get Qd.
- 4Compute the surplus and the quantity traded. Surplus = Qs − Qd, and only Qd units change hands because buyers are the short side of the market.
- 5Measure the deadweight loss. DWL = ½ × (equilibrium quantity − quantity traded) × (the floor price minus the price sellers would have accepted at the quantity traded).
Worked example: Price Floor
A market has Qd = 100 − 2P and Qs = 3P, so equilibrium is P = $20 with Q = 60. A floor of $32 binds. Qs = 3(32) = 96 and Qd = 100 − 2(32) = 36, so the surplus is 96 − 36 = 60 units and only 36 units trade. At 36 units sellers would have accepted 36 ÷ 3 = $12, so deadweight loss = ½ × (60 − 36) × (32 − 12) = $240.
Price Floor questions
When is a price floor binding?
A floor binds only when it sits above the equilibrium price. A floor below equilibrium is non-binding, because the market already trades above it.
What would it cost a government to buy up the surplus?
Multiply the floor price by the surplus quantity. In the example above that is $32 × 60 = $1,920.
Why is the minimum wage a price floor?
It sets a legal minimum price for labor, so a minimum wage above the equilibrium wage leaves quantity of labor supplied above quantity demanded, which shows up as unemployment.
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