If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is ______. - Mathematics and Statistics

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If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is ______.

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Solution

If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is 36.

Concept: Application of Derivatives to Economics
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Chapter 1.4: Applications of Derivatives - Q.2

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Differentiating w.r.t. x,

∴ `("dR")/("d"x) = square`

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∴ `("dR")/("d"x)` > 0

∴ Revenue is increasing for `square`


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Solution: Total cost C = 40 + 2x and Price p = 120 − x

Profit π = R – C

∴ π = `square`

Differentiating w.r.t. x,

`("d"pi)/("d"x)` = `square`

Since Profit is increasing,

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∴ Profit is increasing for `square`


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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`


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 Differentiating w.r.t. Q, we get

`(dpi)/(dQ) = square`

If profit is increasing , then `(dpi)/(dQ) >0`

∴ `Q < square` 

Hence, profit is increasing for `Q < square` 


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