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How to Calculate the Effect of a Price Ceiling

A binding price ceiling creates a shortage equal to Qd − Qs at the ceiling price, and the quantity actually traded falls to the smaller amount, Qs.

The Price Ceiling formula

Shortage = Qd − Qs at the ceiling; quantity traded = Qs; DWL = ½ × (Q equilibrium − Q traded) × (demand price − supply price at Q traded)

Calculator

Enter the demand and supply equations and a cap to test whether it binds and size the shortage it creates.

The a in Qd = a − bP.

Enter b as a positive number.

Zero when supply is Qs = dP.

The legal maximum. It only bites when it sits below the equilibrium price.

Shortage at the ceiling
50

At the $10 cap buyers want 80 units while sellers offer only 30, a gap of 50 units.

Equilibrium price without the cap
$20

Where the market would clear if no ceiling existed.

Is the ceiling binding?
Binding
Quantity traded
30

Only 30 units change hands, because sellers are the short side of the market.

Deadweight loss
$375

Trades worth $375 disappear, the triangle between demand and supply from 30 units up to 60.

How to calculate Price Ceiling, step by step

  1. 1
    Check that the ceiling binds. A ceiling changes the market only when it is set below the equilibrium price; one set above equilibrium does nothing.
  2. 2
    Find quantity demanded at the ceiling. Substitute the ceiling price into the demand equation to get Qd.
  3. 3
    Find quantity supplied at the ceiling. Substitute the same price into the supply equation to get Qs.
  4. 4
    Compute the shortage and the quantity traded. Shortage = Qd − Qs, and only Qs units change hands because sellers are the short side of the market.
  5. 5
    Measure the deadweight loss. DWL = ½ × (equilibrium quantity − quantity traded) × (the price buyers would pay minus the price sellers would accept at the quantity traded).

Worked example: Price Ceiling

A market has Qd = 100 − 2P and Qs = 3P, so equilibrium is P = $20 with Q = 60. A ceiling of $10 binds. Qd = 100 − 2(10) = 80 and Qs = 3(10) = 30, so the shortage is 80 − 30 = 50 units and only 30 units trade. At 30 units buyers value the good at 50 − 0.5(30) = $35 while sellers need 30 ÷ 3 = $10, so deadweight loss = ½ × (60 − 30) × (35 − 10) = $375.

Price Ceiling questions

When is a price ceiling binding?

A ceiling binds only when it is set below the equilibrium price. A ceiling above equilibrium is non-binding, because the market already clears underneath it.

Does a price ceiling always help consumers?

No. Buyers who still get the good pay less, but buyers who are shut out by the shortage get nothing, so consumer surplus can rise or fall depending on how large the shortage is.

Why does a price ceiling cause deadweight loss?

Trades that buyers valued above the seller's cost no longer happen, and the value of those lost trades is the deadweight loss triangle between the two curves.

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