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Question
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)2
`= "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"`
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