unit price p of some products is =-0.02x+400 where x number units produced up to 20.000 units find revenu function R and Marginal R’ what is marginal revenue for 2000 units

Question

unit price p of some products is =-0.02x+400 where x number units produced up to 20.000 units find revenu function R and Marginal R’ what is marginal revenue for 2000 units

Answer 1

p = 400 - .02x

Revenue = R = px = 400x - .02x^2

Marginal Revenue = MR = R' = 400 - .04x

R'(2,000)) = 400 - .04(2,000)

= 400 - 80 = 320 = Marginal Revenue when x=2,000

R(2,000) = 400(2,000)-.02(2,000)^2 =720,000

R(2001) = 400(2,001)-.02(2,001)^2 = 359.98(2,001) = 720319.98

close approximation to MR = R'(2000) = R(2001)-R(2000) = 319.98 = additional revenue from one more unit

R(2000)-R(1999) = 720,000 -719679.98 = 320.02 = additional revenue for one more unit

average of 319.98 and 320.02 = 320 = MR