Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.
A) 37.5 million dollars
B) 26.5 million dollars
C) 21.0 million dollars
D) 22.5 million dollars
E) 23.5 million dollars

Question

Find the producer's surplus for a product with demand function  and supply function  where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​
A) 37.5 million dollars 
B) 26.5 million dollars 
C) 21.0 million dollars 
D) 22.5 million dollars 
E) 23.5 million dollars

Quizplus · Accepted Answer

The producer's surplus is the area above the supply curve and below the market price.

The demand function is:

p = 100 - 0.01x

The supply function is:

p = 40 + 0.02x

Setting the two equations equal to each other, we can find the equilibrium quantity and price:

100 - 0.01x = 40 + 0.02x

0.03x = 60

x = 2000

p = 100 - 0.01(2000) = 80

Therefore, the market equilibrium is 2000 thousand units at a price of 80 million dollars.

To find the producer's surplus, we need to integrate the supply function from 0 to 2000:

∫(40 + 0.02x) dx = 40x + 0.01x^2

Substituting x = 2000:

40(2000) + 0.01(2000)^2 = 80000

Therefore, the producer's surplus is 80 - 80,000 = 22.5 million dollars.

The correct choice is (D).

Find the Producer's Surplus for a Product with Demand Function