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 first need to find the equilibrium price. Setting x = 7 and solving for p, we get:

p = 11eb0d3b_98a0_f999_9790_3ff63df31a48_TB1243_12

p = 11 - 0.5(7)

p = $7.50

Now we can find the area of the triangle formed by the demand curve, the x-axis (quantity), and a vertical line drawn from the equilibrium price ($7.50).

The base of this triangle is (7 - 0) = 7, and the height is (11 - 0.5(7)) = 7.5.

So the area of the triangle (consumer's surplus) is:

(0.5) * 7 * 7.5 = $26.25

Rounding to two decimal places gives us $26.25, which is closest to answer choice C ($48.00)

The Demand Function for a Product Is , Where