The demand function for a certain commodity is $p ( x ) = \frac { 1800 } { ( x + 5 ) ^ { 2 } }$ . Find the consumer surplus when the selling price is $18?
A)135
B)30
C)45
D)360
E)270
F)40
G)90
H)180

Question

Quizplus · Accepted Answer

To find the consumer surplus, first determine the quantity demanded $x$ when the price $p(x) = 18$. Solve $\frac{1800}{(x+5)^2} = 18$ to find $x = 10$. The consumer surplus is the area between the demand curve and the price level up to this quantity. Calculate the integral of the demand function from 0 to 10 and subtract the total revenue (price times quantity). The consumer surplus is $\int_0^{10} \frac{1800}{(x+5)^2} \, dx - 18 \times 10 = 90$.

The Demand Function for a Certain Commodity Is p(x)=1800(x+5)2p ( x ) = \frac { 1800 } { ( x + 5 ) ^ { 2 } }p(x)=(x+5)21800​

The Demand Function for a Certain Commodity Is $p ( x ) = \frac { 1800 } { ( x + 5 ) ^ { 2 } }$