Determine the consumers' surplus if the market price is set at $8/unit. (Round your answer to two decimal places.)

Question

Consumers' Surplus, It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is,

p=\sqrt(256-6x)

Determine the consumers' surplus if the market price is set at $8/unit. (Round your answer to two decimal places.)

Answer 1

Consumer surplus is the area above the market price and below the demand curve. Setting x=0, we get P = sqrt(256) = 16, so consumer surplus is equal to the integral from 8 to 16 of (sqrt(256-6x) - 8) dx, which when computed is 44.44.