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 calculated as the difference between the market price (equilibrium price) and the cost of production.

The demand function is given by:

p = 100 - 0.02x

The supply function is given by:

p = 30 + 0.03x

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

100 - 0.02x = 30 + 0.03x

Solving for x, we get:

x = 14000

Substituting x back into either the demand or supply function, we get the equilibrium price:

p = 100 - 0.02(14000) = 70

Therefore, the producer's surplus is:

PS = (70 - 30) × 14000 = 22.5 million dollars

Hence, the correct answer is D) 22.5 million dollars.

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