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24-06-2017
Mathematics

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determine the price and quantity for which revenue is maximised given a firm demand function of a particular commodity to be (12-q)^1/2

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mathmate mathmate

25-06-2017

Demand
D(q)=(12-q)^(1/2)
Revenue,
R(q)=q*D(q)=q*sqrt(12-q)
At maximum revenue,
R'(q)=0
where
R'(q)=sqrt(12-q)-q/[2(sqrt(12-q))]=0
Solve for q=8.
Hence, quantity=8, price=sqrt(12-q)=sqrt(12-8)=sqrt(4)=2

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