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If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 2 comment on the result. - Mathematics and Statistics

Sum

If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 2 comment on the result.

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Solution

Given, demand function is D = 50 - 3p - p2.

∴ `"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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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 10.2 | Page 113
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