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

Answer 1

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: η_d = `- "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))`

η_d = `("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"`