Question

Calculate the consumers' surplus at the indicated unit price p for the demand equation
p = 8−2q^1/3;p=6.

Answer 1

Answer:

consumer surplus = 0.5 cents

Explanation:

The unit price: p = 6 ,  demand equation = $p = 8 - 2q^{\frac{1}{3} }$

first find the value of q by equating the unit price and the demand equation

$8 - 2q^{\frac{1}{3} } = 6$

= 8 - 6 = 2q^1/3

hence q = 1

now the consumer surplus can be calculated by integrating and inputting all the values

   $Cs = \int\limits^1_0 {(8-2q^(1/3) )} \, dq - 6$

        = $[ 8q - 2(\frac{(q^(4/3))}{4/3}) ] - 6$     applying the limits of q = 1 , 0

Cs = 8 - 3/2 * ( 1 ) ^ 4/3  - 0 + 0 - 6

     = 8 - 3/2 - 6 =  1/2 = 0.5 cents