Sum

If the demand function is D = 50 – 3p – p^{2}. Find the elasticity of demand at p = 2 comment on the result.

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#### Solution

Given, demand function is D = 50 - 3p - p^{2}.

∴ `"dD"/"dp" = 0 - 3 - 2"p" = - 3 - 2"p"`

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

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

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

When p = 2

`eta = (3(2) + 2(2)^2)/(50 - 3(2) - (2)^2) = (6 + 8)/(50 - 6 - 4) = 14/40`

∴ η = `7/20`

∴ elasticity of demand at p = 2 is `7/20`

Here, η > 0

∴ The demand is elastic.

Concept: Application of Derivatives to Economics

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