The market for plywood is characterized by the following demand and supply equations: Q^D = 800 - 10P and Q^S = 50P - 1,000, where P is the price per sheet of plywood and Q measures the quantity of plywood. If the government imposes a price ceiling of $25 per sheet of plywood, producer surplus: A) increases from $3,333 to $4,225. B) decreases from $5,000 to $1,250. C) decreases from $1,875 to $1,240. D) decreases from $2,500 to $625.

Question

Quizplus · Accepted Answer

To find producer surplus before the price ceiling, we need to find the equilibrium price and quantity of plywood. Setting the demand and supply equations equal to each other, we get 800 - 10P = 50P - 1,000, which simplifies to P = $20. Plugging in P = $20 into either the demand or supply equation gives us a quantity of 600 sheets of plywood. 
Before the price ceiling, producer surplus is the area above the supply curve and below the equilibrium price, which is (25-20)*600/2 = $1,500. 
After the price ceiling, the price is capped at $25 per sheet, which is above the previous equilibrium price. As a result, the quantity supplied is still 600 sheets, but the quantity demanded increases to 650 sheets (found by setting the demand equation equal to $25). This means that there is excess demand, or a shortage, of 50 sheets. 
Producer surplus is now the area above the supply curve and below the price ceiling, which is (25-20)*550/2 = $625. Therefore, producer surplus decreases from $2,500 to $625.

The Market for Plywood Is Characterized by the Following Demand