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 calculate consumer surplus, first find the equilibrium quantity by setting the demand function equal to the price:

11ea984b_b0e7_9ed7_9029_13da263aa106_TB4005_01

11,000 - 800p = 6

5,200 = 800p

p = 6.5

So, the equilibrium quantity is:

Q = 11ea984b_b0e7_9ed7_9029_13da263aa106_TB4005_02

11,000 - 800(6) = 5,200

Next, find the area under the demand curve and above the equilibrium price:

11ea984b_b0e7_9ed7_9029_13da263aa106_TB4005_03

11,000x - 400x^2

Plugging in the equilibrium quantity, we get:

11ea984b_b0e7_9ed7_9029_13da263aa106_TB4005_04

11,000(5.2) - 400(5.2)^2

= 28,600

Consumer surplus is half of this area, since it is a triangle:

11ea984b_b0e7_9ed7_9029_13da263aa106_TB4005_05

= 14,300

Rounding to the nearest million, the answer is 83 million dollars.

The Demand Function for a Product Is Where P