Answer to Question #292843 in Microeconomics for kilfer

Question #292843

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


1
Expert's answer
2022-02-02T12:34:40-0500

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)×P)(D(p)\times P)

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

TR(p)=ddp(3000e0.05p)=150ez/20TR'(p)=\frac{d}{dp}(3000e^{-0.05p})=\frac{150}{-e^{z/20}}

Marginal revenue (MR=0)(MR=0)

equating to zero we get;

MR=150e0.05pP2+3000e0.05p=0MR=-150e^{-0.05p}P^2 +3000e^{-0.05p}=0

substituting,

e0.05p×(20P2)=0e^{-0.05p}\times(20-P^2)=0

e1/20p=0e^{1/20p}=0

P2=20P^2=20

P=4.47P=4.47

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


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