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

Market Price with Zero MR

Marginal Revenue is given as the change in total revenue divided by the change in total quantity.

Total revenue= $(D(p)\times P)$

change in total revenue $TR'(p)$ on the other hand is given as;

$TR'(p)=\frac{d}{dp}(3000e^{-0.05p})=\frac{150}{-e^{z/20}}$

Marginal revenue $(MR=0)$

equating to zero we get;

$MR=-150e^{-0.05p}P^2 +3000e^{-0.05p}=0$

substituting,

$e^{-0.05p}\times(20-P^2)=0$

$e^{1/20p}=0$

$P^2=20$

$P=4.47$

therefore, market price at zero MR is given as P=4.47