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Question
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
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Solution
M.R = `20"e"^((-x)/10) (1 - x/10)`
M.R = `20"e"^((-1)/10^((x))) [1 + ((-1)/10) x]`
R = `int "MR" "d"x`
R = `int 20["e"^((-1)/10^((x))) (x)] "d"x`
R = `20x ["e"^((-1)/10^((x)))] + "c"`
When x = 0
R = 0
⇒ k = 0
∴ R = `(20x "e"^(- 1/10x))/x`
Demand function p = `"R"/x = (20x "e"^(- 1/10x))/x`
∴ p = `20 "e"^((-x)/10)`
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