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Question
Solve the following example: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
Solution
Given, P = 175 + 9D + 25D2
Total revenue, R = P.D
= (175 + 9D + 25D2)D
= 175D + 9D2 + 25D3
Average revenue = P = 175 + 9D + 25D2
Marginal revenue = `("dR")/("dD")`
= `"d"/("dD") (175"D" + 9"D"^2 + 25"D"^3)`
=`175"d"/("dD")("D")+9"d"/"dD"("D"^2)+25"d"/("dD")("D"^3)`
=175(1) + 9(2D) + 25(3D2)
= 175 + 18D + 75D2
When D = 10,
Total revenue = 175(10) + 9(10)2 + 25(10)3
= 1750 + 900 + 25000
= 27650
Average revenue = 175 + 9(10) + 25(10)2
= 175 + 90 + 2500
= 2765
Marginal revenue = 175 + 18(10) + 75(10)2
= 175 + 180 + 7500
= 7855
∴ When Demand = 10,
Total revenue = 27650,
Average revenue = 2765
Marginal revenue = 7855.
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