Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# 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 – bx)2 - Business Mathematics and Statistics

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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 – bx)2

#### Solution

p = (a – bx)

= "dp"/"dx" = 2("a" - "b"x)^(2-1) "d"/"dx" ("a" - "b"x)

= 2(a – bx) (0 – b(1))

= -2b(a – bx)

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

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

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

ηd = ("a" - "b"x)/(2"b"x)

When the elasticity of demand is equals to unity,

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

a – bx = 2bx

2bx = a – bx

2bx + bx = a

3bx = a

x = "a"/"3b"

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

Concept: Applications of Differentiation in Business and Economics
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#### APPEARS IN

Chapter 6 Applications of Differentiation
Exercise 6.1 | Q 5. (i) | Page 139
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