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 calculate the area under the demand curve and above the price line up to the equilibrium quantity, which we can find by setting the demand equal to the quantity supplied (assuming perfect competition).

11ea984b_b057_6c75_9029_d5fecaf3f829_TB4005_11 = 6

Solving for x: 
x = (6/11ea984b_b057_6c75_9029_d5fecaf3f829_TB4005_11)*1000 = 81.39

So, the equilibrium quantity is 81,390 units.

The area under the demand curve and above the price line up to 81,390 units is:

(1/2)*(11ea984b_b057_6c75_9029_d5fecaf3f829_TB4005_11 - 6)*81.39 = 333.33

Multiplying by 1000 (to account for the fact that x is in thousands of units) and rounding to the nearest million, we get:

Consumer's surplus = $83 million.

The Demand Function for a Product Is Where P