Determine the consumers' surplus if the market price is set at $9/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=square root of 169-4x

Answer 1

Let find corresponding demand: 9 = (169 - 4x)^1/2; 81 = 169 - 4x; 4x = 88; x = 22.

CS = ∫₀²²[(169 - 4x)^1/2 - 9]dx = [2/3(169 - 4x)^3/2/(- 4) - 9x]₀²² = - 1/6(81^3/2 - 169^3/2) - 198 = $49.67