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Question
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
Solution
Marginal Revenue function MR = 9 – 4x2
Revenue function R = `int "MR" "d"x`
R = `int (9 - 4x^2) "d"x`
R = `9x - 4(x^3/3) + "k"`
When x = 0
R = 0
⇒ k = 0
∴ R = `9x - (4x^3)/3`
⇒ px = `9x - (4x^3)/3` .......`("p" = (4x^2)/x)`
p = `((9x - (4x^3)/3))/x`
= `9 - (4x^3)/3`
∴Demand function = `9 - (4x^2)/3`
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