Question

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 5 comment on the result.

Answer 1

Given, demand function is D = 50 – 3p – p² 

∴ `(dD)/(dp) = 0 - 3 - 2p`

= `- 3 - 2p`

`eta = (-p)/D * (dD)/(dp)`

∴ `eta = (-p)/(50 - 3p - p^2) * (- 3 - 2p)`

∴ `eta = (3p + 2p^2)/(50 - 3p - p^2)`

When p = 5

`eta = (3(5) + 2(5)^2)/(50 - 3(5) - (5)^2)`

= `(15 + 50)/(50 - 15 - 25)`

= `65/10`

∴ η = 6.5

∴ elasticity of demand at p = 5 is 6.5

Here,  η > 0

∴ The demand is elastic.