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

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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"`

Elasticity of demand is given by

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

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

∴ `eta = (p(3 + 2p))/(50 - 3p - p^2)`

(i) When p = 5

`eta = (5(3 + 2xx 5))/(50 - 3(5) - (5)^2) = (5xx13)/(50 - 15 - 25)`

= `65/10 = 6.5`

Since η > 1 the demand is elastic

(ii) When p = 2 then,

`eta = (2(3 + 2 xx 2))/(50 - 3(2) - (2)^2) = (2xx7)/(50 -6 - 4)`

 = `14/40 = 7/20`

Since, < η < 1, the demand is inelastic.

Concept: Application of Derivatives to Economics
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Chapter 1.4: Applications of Derivatives - Q.4

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