Question

The market for plywood is characterized by the following demand and supply equations: QD = 800 – 10P and QS = 50P – 1,000, where P is the price per sheet of plywood and Q measures the quantity of plywood. What is the size of the deadweight loss if the government imposes a price ceiling of $25 per she

Answer 1

$3,750

Step-by-step explanation:

at $25 per sheet of plywood:

total demand = 800 - (10 x 25) = 800 - 250 = 550

total supply = (50 x 25) - 1,000 = 1,250 - 1,000 = 250

the equilibrium price is:

800 - 10P₁ = 50P₁ - 1,000

1,800 = 60P₁

P₁ = 1,800 / 60 = 30

the equilibrium quantity (Q₁) is:

Q₁ = 800 - (10 x 30) = 800 - 300 = 500

at 250 units, the price should be:

250 = 800 - 10P₂

10P₂ = 550

P₂ = $55

total deadweight loss = 0.5 x (P₂ - P₁) x (Q₂ - Q₁) = 0.5 x ($55 - $25) x (250 - 500) = 0.5 x $30 x -250 = -$3,750