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

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

#### 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]