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
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
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