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Question
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which elasticity of demand for price ₹ 80.
Solution: Total cost C = 40 + 2x and Price p = 120 – x
p = 120 – x
∴ x = 120 – p
Differentiating w.r.t. p,
`("d"x)/("dp")` = `square`
∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`
∴ η = `square`
When p = 80, then elasticity of demand η = `square`
Solution
Total cost C = 40 + 2x and Price p = 120 – x
p = 120 – x
∴ x = 120 – p
Differentiating w.r.t. p,
`("d"x)/("dp")` = – 1
∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`
∴ η = `(-"P")/(120 - "P") (-1)`
= `"p"/(120 - "P")`
When p = 80, then elasticity of demand η = `80/(120 - 80)`
= `80/40`
= 2
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Differentiating w.r.t. x,
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