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?

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.

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