The demand function for a product is where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars.
A) 114 million dollars
B) 149 million dollars
C) 83 million dollars
D) 88 million dollars
E) 174 million dollars

Question

The demand function for a product is  where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars. ​
A) 114 million dollars 
B) 149 million dollars 
C) 83 million dollars 
D) 88 million dollars 
E) 174 million dollars

Quizplus · Accepted Answer

To find the consumer's surplus, we need to first find the quantity demanded at the equilibrium price of $6 million. To do this, we set the demand function equal to 6:

11ea984b_b134_d420_9029_dd9aea0bd3f9_TB4005_11 = 6

Solving for x, we get:

x = (6 - 11ea984b_b134_d420_9029_dd9aea0bd3f9_TB4005_11) / 3

x ≈ 2,726

So, at a price of $6 million, 2.726 million units will be demanded.

To find the consumer's surplus, we need to find the area below the demand curve and above the equilibrium price. This can be done by integrating the demand function from x = 0 to x = 2.726:

∫0^2.726(11ea984b_b134_d420_9029_dd9aea0bd3f9_TB4005_11) dx

≈ 83 million dollars (rounded to the nearest million)

Therefore, the consumer's surplus is approximately 83 million dollars, so the best choice is (C).

The Demand Function for a Product Is Where P