Find the producer's surplus for a product if its demand function is and its supply function is where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars.
A) 53 million dollars
B) 44 million dollars
C) 40 million dollars
D) 36 million dollars
E) 47 million dollars

Question

Find the producer's surplus for a product if its demand function is  and its supply function is  where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars. ​
A) 53 million dollars 
B) 44 million dollars 
C) 40 million dollars 
D) 36 million dollars 
E) 47 million dollars

Quizplus · Accepted Answer

To find the producer's surplus, we need to first find the equilibrium price and quantity. This occurs where the demand and supply functions intersect:

11ea984b_b136_a8ef_9029_67e8c6d11c10_TB4005_11 = 11ea984b_b136_d000_9029_8980abed1c2f_TB4005_11
50 - 0.5p = 5 + 0.5p
50 = p + 10
p = 40

Substituting this into either the demand or supply function gives the equilibrium quantity:

Q = 50 - 0.5(40) = 30

The producer's surplus is then the area between the supply curve and the equilibrium price, from zero to the equilibrium quantity:

PS = 0.5(40-5)(30) = 625

Rounding to the nearest million gives $40 million. Therefore, the correct answer is C.

Find the Producer's Surplus for a Product If Its Demand