Question

The demand for a product, in dollars, is P=2000-0.2x-0.01x^2. Find the consumer surplus when the sales level is 250

Answer 1

$P(250)=2000-0.2*(250)-0.01*(250)^2=1325$

The consumer surplus is as follows

$\int_0^{250}(p(x)-P)dx=\int_0^{250}(2000-0.2x-0.01x^2-1325)dx=[675x-0.1x^2-\frac{0.01x^3}{3}]|_0^{250}=675*250-0.01*(250)^2-\frac{0.01*(250)^3}{3}=110416.67$