Question

If the demand law is given by p = `10e^(- x/2)` then find the elasticity of demand.

Answer 1

p = `10e^(- x/2)`

Elasticity of demand: η_d = `- p/x * "dx"/"dp"`

p = `10e^(- x/2)`

`"dp"/"dx" = 10(e^(-x/2))(- 1/2)`

`= - 10/2 e^(-x/2)`

`= - 5e^(-x/2)`

Elasticity of demand: η_d = `- p/x * 1/("dp"/"dx")`

`= ((- 10e^(-x/2))/x)(1/(- 5e^(-x/2)))`

`= (-10)/(-5x) xx e^(-x/2)/e^(-x/2)`

η_d = `2/x`