question in description

Question

the marginal revenue for a product is given by r'(x)=-0.3x^2+50x+380 where x is the nuymber of units sold. find the demand function p(x)

Answer 1

r'(x) = -0.3x^2 +50x +380 = marginal revenue = MR

r(x) = total revenue = TR = px = -0.1x^3 +25x^2 + 380x

the constant term =0 as revenue =0 when x=0, there is no revenue when nothing is sold.

px = total revenue = TR = r(x) = price times output sold, price times x

price = average revenue, AR, per unit revenue = r/x

p =r/x = -0.1x^2 +25x +380. p=380, no one is buying anything

p(x) = -0.1x^2 +25x +380 = AR

the demand function is the average revenue function, p(x)