Question

Find the elasticity of supply when the supply function is given by x = 2p² + 5 at p = 1.

Answer 1

Given x = 2p² + 5

Differentiating with respect to 'p' we get,

${\displaystyle \frac{\text{dx}}{\text{dp}}}$ = 4p 

Elasticity of Supply

${\displaystyle {\eta }_s=\frac{\text{p}}{x}\cdot \frac{\text{dx}}{\text{dp}}}$

${\displaystyle \Rightarrow {\eta }_s=\frac{\text{p}}{2{\text{p}}^2+5}}$(4p)

${\displaystyle =\frac{4{\text{p}}^2}{2{\text{p}}^2+5}}$

when p = 1, ${\displaystyle {\eta }_s=\frac{4{\left(1\right)}^2}{2\left(1^2\right)+5}=\frac{4}{2+5}=\frac{4}{7}}$