Question

If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.

Answer 1

Given, demand function is D = `((p + 6)/(p − 3))`

Differentiating w.r.t. p, we get

∴ `(dD)/(dp) = ((p − 3) d/(dp) (p + 6) − (p + 6) d/(dp) (p − 3))/(p − 3)^2`

∴ `(dD)/(dp) = ((p − 3)(1 + 0) − (p + 6)(1 − 0))/(p − 3)^2`

∴ `(dD)/(dp) = (p − 3 − p − 6)/(p − 3)^2`

∴ `(dD)/(dp) = (-9)/(p − 3)^2`

Elasticity of demand, η = `(- p)/D * (dD)/(dp)`

∴ `eta = (− p)/(((p + 6)/(p − 3))) * (− 9)/(p − 3)^2`

∴ `eta = (9p)/((p + 6)(p - 3))`

Substituting p = 4, we get,

∴ `eta = (9 xx 4)/((4 + 6)(4 - 3))`

∴ `eta = 36/(10 × 1)`

∴ `eta = 36/10` 

∴ η = 3.6

∴ The elasticity of demand at p = 4 is 3.6.