The demand function for a certain brand of compact disc is given by
The supply function for the compact discs of is given by

Where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.

A) $16,907
B) $16,338
C) $16,667
D) $16,805

Question

The demand function for a certain brand of compact disc is given by ​  ​
The supply function for the compact discs of is given by
​  ​
Where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
​
A) $16,907 
B) $16,338 
C) $16,667 
D) $16,805

Quizplus · Accepted Answer

To find the equilibrium price, we need to set the demand equal to the supply:

11,000 – 50p = 2,000 + 30p

80p = 9,000

p = 112.50

So the equilibrium price is $112.50 per unit.

To find the equilibrium quantity, we can plug this price back into either the demand or supply function:

Qd = 11,000 – 50(112.50) = 5,250

Qs = 2,000 + 30(112.50) = 5,375

So the equilibrium quantity is approximately 5,313 units.

To find the producers' surplus, we first need to find the supply function at the equilibrium quantity:

Qs = 2,000 + 30p

Qs = 2,000 + 30(112.50)

Qs = 5,375

So at a price of $112.50 per unit, the producers are willing to supply 5,375 units per week.

The area of the triangle formed by the equilibrium price, the supply curve, and the x-axis represents the producers' surplus.

Producers' surplus = 0.5(112.50-40)(5,375)

Producers' surplus = $16,667

Therefore, the best choice is (C), $16,667.

The Demand Function for a Certain Brand of Compact Disc