Sum

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

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#### Solution

Given, demand function is

D = `(("p" + 6)/("p" - 3))`

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

`= (("p" - 3)(1 + 0) - ("p" + 6)(1 - 0))/("p" - 3)^2`

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

`= (-9)/("p" - 3)^2`

`eta = (-"p")/"D" * "dD"/"dp"`

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

∴ `eta = (9"p")/(("p" + 4)("p" - 3))`

Substituting p = 4, we get

`eta = (9 xx 4)/((4 + 6)(4 - 3)) = 36/(10(1))`

∴ η = 3.6

∴ elasticity of demand at p = 4 is 3.6

Concept: Application of Derivatives to Economics

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