p = 12 − 2q1⁄3; p = 6

Question

Calculate the consumers' surplus (in dollars) at the indicated unit price p

 for the demand equation.

p = 12 − 2q^1⁄3;  p = 6

Answer 1

integrate 12-2q^(1/3)

= 12q -(3/2)q^4/3

evaluate from q = 0 to q = 27. 6=12-2q(^3)

-12 +6=-2q^(1/3)

q =3^3 =27

=12(27) -(3/2)(27^(4/3)

= 324- (3/2)(3^4)

=324-(3/2)(81)

=324-243/2

=648-243)/2

=405/2

= 202.50

subtract 6x27 =162

202.5-162

= $40.50 = consumer surplus

(12-2q^(1/3))-6

= 12-6-2q^(1/3)

-2q^(1/3) +6

integrate

= -(3/2)q(4/3) +6q

evaluate between q=0 and q= 27

-(3/2)(27^(4/3) +6(27)

=-(3/2)(3^4) +162

= -(3/2(81) +2(81)

=(81)/2

$40.50 = consumer surplus