Question

a manufacturer estimates that D(p) = 3000e^-0.05p units of a particular good will be sold at market price of p cedis per unit. determine the market price that will result in marginal revenue of zero.

Answer 1

The market price that will result in marginal revenue of zero is:

$MR = TR'(p) = (p×D(p))' = -150e^{-0.05p} p^2 + 3000e^{-0.05p} = 0,$

$e^{-0.05p}×(20 - p^2) = 0,$

$e^{-0.05p} = 0$ (has no roots) or $p^2 = 20,$

p = 4.47.