Question

Calculate the consumer surplus for the demand function P = 25/Q+2 when the market price P = 5.

Answer 1

We use the equilibrium price provided to solve for Q.

Therefore,

$5=\frac{25}{Q+2}$

$Q=3$ when we simplify the equation.

In order to calculate the Consumer Surplus, we need to integrate the demand function at Q=3 and Q=0 range. We would get 25−Q²dQ−(5)(3)

$25Q-\frac{Q^3}{3}-15$

we substitute Q with 3 from the equation.

$(25\times3)-\frac{3^3}{3}-15$

51

Therefore Consumer Surplus will be $51