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 sheet of plywood?

Answer: Dead weight loss- = $3750

Explanation:

QD = 800 - 10P

QS = 50P - 1,000,

At equilibrium, quantity demanded is equal to quantity supplied, so we have that, equating the two equations becomes

800 - 10p = 50p - 1000.

800 + 1000 = 50p + 10p

1800 = 60p

p = $30.

QD = QS = 800 - 10*30 = 500 units

QD = QS = 50x30 - 1000 = 500 units

Qd = Qs = 500 units.

When P = $25 by government putting a price ceiling, which is below the equilibrium price, it will lead to more demand than supply in the market

QD = 800 - 10P

QD = 800-10X25

QD=800-250 = 550units

QS = 50P - 1,000,

Qs = 50 X25 - 1000

= 1,250-1000

QS = 250 units.

When quantity demanded = 250units as a result of Quantity supplied at 250units. we will have our new price to be

QD = 800 - 10P

250 = 800 - 10p

10p = 800 - 250

10p = 550

p = $55.

To calculate Dead weight Loss, we use the formulae,

0.5 x (P2 - P1) x (Q1 - Q2) where P1 and P2 are old and new prices and Q1 AND Q2 are old and new quantities

DWL = 0.5 x (55-25) X (500-250)

= 0.5 x 30x 250

Dead weight loss = $3750.