The market for plywood (a sheet of wood used in construction) 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 sheet of plywood?

$3750

Explanation:

From the question,

Qd = 800 - 10p

Qs = 50p - 1000.

To attain equilibrium, Qd = Qs

800 - 10p = 50p - 1000.

Collect like terms

800 + 1000 = 50p + 10p

60p = 1800

p = 1800/60

p = $30.

Equilibrium price = $30

Equilibrium quantity:

= 800 - 10p

= 800 - (10 × 30)

= 800 - 300

= 500 units.

When the government has imposed a price ceiling of $25, this will lead to excess demand in the market as buyers will want to buy more plywood.

When P = $25,

Qd = 800 - 10p

Qd = 800 - (10 × 25)

Qd = 800 - 250

Qd = 550 units.

Qs = 50p - 1000

Qs = (50 × 25) - 1000

Qs = 1250 - 1000

Qs = 250 units.

When quantity demanded Qd = 250,

Qd = 800 - 10p

250 = 800 - 10p

Collect like terms

10p = 800 -250

10p = 550

p = 550/10

p = $55.

Deadweight loss is shown by the shaded area in the attached file.

Size of the dead weight triangle will be:

= 1/2 × base × height.

= 1/2× (55-25) × (500-250)

= 1/2 × 30 × 250

Dead weight loss = $3750.

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