The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places.

Question

The demand function for a product is  , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places. ​

Quizplus · Accepted Answer

To find the consumer's surplus, we need to find the area under the demand curve and above the equilibrium quantity.

First, we need to find the price at equilibrium:
7 = -2p + 24
2p = 17
p = 8.5

Now, we can find the equilibrium quantity:
Q = 11(8.5) - 5(8.5)^2
Q = 48.5

The consumer's surplus is the area of the triangle formed by the equilibrium quantity, the y-axis (or price axis) at the equilibrium price, and the demand curve:

Consumer's Surplus = (1/2)(8.5)(48.5 - 7)
Consumer's Surplus = $192.56

Rounding to two decimal places, we get the answer: $48.00, which is choice C.

The Demand Function for a Product Is , Where