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Question
Find the price, if the marginal revenue is 28 and elasticity of demand is 3.
Solution
Given, marginal revenue (Rm) = 28 and
elasticity of demand (η) = 3
`"R"_"m" = "P"(1 - 1/eta)`
∴ `28 = "P" (1 - 1/3)`
∴ 28 = `"P" (2/3)`
∴ `(28 xx 3)/2` = P
∴ P = 42
∴ price = ₹ 42
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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`
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Ec = (0.0003)I2 + (0.075)I2
when I = 1000
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