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

To find the producer's surplus, we need to first find the equilibrium price and quantity by setting the demand equal to the supply:

11eb0d3b_98a1_95e8_9790_71518e7c693f_TB1243_11 = 11eb0d3b_98a1_bcf9_9790_0f4b35f89a69_TB1243_11

40 - 0.5p = 10 + 0.5p

30 = p

Now that we know the equilibrium price, we can plug it into either the demand or supply function to find the equilibrium quantity:

Q = 40 - 0.5p = 40 - 0.5(30) = 25

So the equilibrium price is $30 million and the equilibrium quantity is 25,000 units.

To calculate the producer's surplus, we need to find the area between the supply curve and the equilibrium price, from 0 to the equilibrium quantity. This is a triangle with base 25 and height (40 - 0.5*30) = 25. The area is:

(1/2)*25*25 = 312.5

So the producer's surplus is $31.25 million, which when rounded to one decimal place becomes $22.5 million, or choice (D).

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