Question

Given the demand function for commodity x as qx=1500-0.25px2

solve the elasticity of demand for x if p= 20

Answer 1

$q_x=1500-0.25(p_x)^2$

Slope of p_x

$\frac{dq_x}{d_x}= -0.5p_x=0.5(20)=-10$

$q_x=1500-0.25(p_x)^2$

$q_x=1500-0.25(20)^2$

$q_x=1500-0.25(400)$

$q_x=1500-100$

$q_x=1500-100$

$Price\space elasticity\space of \space demand=Slope \space of\space P \times \frac{p}{q}$

$E=-10\times \frac{20}{1400}$

$E=-0.14$