Question

Demand function of a commodity given by p =100-8x find consumer surplus p=4

Answer 1

Answer:

Demand function of Commodity , p =100 - 8 x

The curve will touch ,both p axis and p axis ,at

8 x + p=100

When, p=4,

8 x +4=100

8 x=100-4

8 x=96

x=12

$\frac{8 x}{100}+\frac{p}{100}=1\\\\ \frac{x}{12.5}+\frac{p}{100}=1$

at, (12.5,0) and (0,100).

So, we will find area from , p=4 to , p=100, under y axis.

Consumer Surplus = Maximum Price that Consumer can pay - Actual Price

Required Area   =

                       $=\int\limits^{100}_4 {\frac{100-p}{8}} \, dp \\\\=\int\limits^{100}_4\frac{100 p -\frac{p^2}{2}}{8}\\\\=(12.5 p - \frac{p^2}{16})\left \{ {{p=100} \atop {p=4}} \right. \\\\=1250 - 50-625+1\\\\=576$

So, Consumer Surplus=576

Or

You can find consumer surplus Directly by calculating area of right Triangle

      $=\frac{1}{2}\times 12 \times (100-4)\\\\=6 \times 96\\\\=576$