Question

Find the consumer's surplus for the following demand function at the given point. D(x)=(x-3)^2 ; x=3/2​

Answer 1

Step-by-step explanation:

given

D(x)=(x-3)^2; x=3/2

step 1

D(x)=(x-3)^2 Is to equation 1

subs x=3/2 in equation 1

D(3/2)= (3/2-3)^2

= ((3-6)/2)^2= (-3/2)^2= 9/4

D(x) = 9/4

x = 3/2

CS = integral 3/2 to 0 ( (D(x))dx- (x) )

= integral 3/2 to 0 (1/3(x-3)^3)-((3/2)(9/4))

= integral 3/2 to 0 (1/3(x-3)^3)-(27/8)

= ((1/3(3/2-3)^3))-(27/8)

= ((1/3(-3/2)^3))-(27/9) = ((1/3(-27/8))-(27/9))

= ((-9/8)-(27/9)) = (-81-216)/72 = -297/72

THEREFORE:- CS = 33/8