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Question
The demand curve of a commodity is given by p = `(50 - x)/5`, find the marginal revenue for any output x and also find marginal revenue at x = 0 and x = 25?
Solution
Given that p = `(50 - x)/5`
Revenue, R = px
`= ((50 - x)/5)`x
`= (50x - x^2)/5`
`= 1/5` (50x – x2)
Marginal Revenue (MR) = `"d"/"dx"`(R)
= `"d"/"dx" 1/5 (50x - x^2)`
= `1/5 "d"/"dx" (50x - x^2)`
= `1/5 (50 - 2x)`
Marginal revenue when x = 0 is, MR = `1/5` (50 – 2 × 0)
`= 1/5 xx 50`
= 10
When x = 25, marginal revenue is MR = `1/5` (50 – 2 × 25)
`= 1/5 (50 - 50)`
= 0
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