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Question
The demand function of a monopoly is given by x = 100 − 4p. Find the quantity at which the MR will be zero.
Sum
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Solution
Given, x = 100 − 4p
⇒ 4p = 100 − x
⇒ p = `(100 - x)/4`
∴ R(x) = px
= `((100 - x)/4)x`
= `(100x - x^2)/4`
⇒ MR = `d/dx((100x - x^2)/4)`
= `1/4 (100 - 2x)`
= `(100 - 2x)/4`
∵ MR = 0
100 − 2x = 0
2x = 100
∴ x = 50
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Application of Calculus in Commerce and Economics in the Marginal Revenue Function and Its Interpretation
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