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Question
For the demand function x = `25/"p"^4`, 1 ≤ p ≤ 5, determine the elasticity of demand.
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Solution
The demand function, x = `25/"p"^4`, 1 ≤ p ≤ 5
The elasticity demand, ηd = `- "p"/x * "dx"/"dp"`
x = `25/"p"^4`
x = 25 × p-4
`"dx"/"dp" = (25)(-4)"p"^(-4-1)`
`= 25 xx -4 xx "p"^(-5)`
`= 25 xx (-4)xx1/"p"^5`
Hint for differentiation
`"d"/"dx"(1/"x"^"n") = "-n"/("x"^("n + 1"))`
x = `25/"p"^4`
`"dx"/"dp" = 25((-4)/"p"^5)`
∴ ηd = `- "p"/x * "dx"/"dp"`
`= (-"p")/(25/"p"^4) xx 25 xx (-4)xx1/"p"^5`
`= (-"p"^5)/25 xx 25 xx (-4) xx 1/"p"^5` = 4
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