Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

Find the elasticity of demand in terms of x for the following demand laws and also find the value of x where elasticity is equal to unity. p = a – bx2 - Business Mathematics and Statistics

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Sum

Find the elasticity of demand in terms of x for the following demand laws and also find the value of x where elasticity is equal to unity.

p = a – bx2

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Solution

p = a – bx

`= "dp"/"dx" = 0 - "b" "d"/"dx" (x^2)`

= - b(2x)

= - 2bx

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

`= (- p)/x xx 1/("dp"/"dx")`

`= (- ("a" - "b"x)^2)/x xx 1/(- 2"b"x)`

ηd = `("a" - "b"x^2)/(2"b"x^2)`

When elasticity is equals to unit,

`("a" - "b"x^2)/(2"b"x^2)` = 1

a – bx2 = 2bx2

2bx2 = a – bx2

2bx2 + bx2 = a

3bx2 = a

`x^2 = "a"/"3b"`

x = `sqrt("a"/"3b")`

∴ The value of x when elasticity is equal to unity is `sqrt("a"/"3b")`

Concept: Applications of Differentiation in Business and Economics
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Chapter 6: Applications of Differentiation - Exercise 6.1 [Page 139]

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Tamil Nadu Board Samacheer Kalvi Class 11th Business Mathematics and Statistics Answers Guide
Chapter 6 Applications of Differentiation
Exercise 6.1 | Q 5. (ii) | Page 139
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