The concept of consumers’ surplus

Question

For the price-demand equation p = 50 − 0.005x^2 , the consumers’ surplus at a price level of 32 is equal to the area of the region labeled CS in the figure. Find this area using integration. You’ll need to solve for x0 first.

Answer 1

p = 50 - 0.005x² = 32; x = - 18/(- 0.005) = 3600; x = 60

CS = ∫₀⁶⁰(50 - 0.005x² - 32)dx = (18x - 0.005x³/3)₀⁶⁰ = 720