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Question
A monopolist's demand function is `x = 60 - p/5`. At what level of output will marginal revenue be zero?
Solution
Demand function, `x = 60 - p/5` ...(i)
Total revenue function, R(x) = px
= 5(60 – x)x ...[From (i)]
= 5x(60 – x)
= 300x – 5x2
Then, MR = `d/dx(R(x))`
= `d/dx(300x - 5x^2)`
= 300 – 10x
Put MR = 0
`\implies` 300 – 10x = 0
`\implies` 10x = 300
`\implies` x = 30
Hence, the value of output is 30.
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