determine the price and quantity for which revenue is maximised given a firm demand function of a particular commodity to be (12

Question

il63 [147K]

3 years ago

12

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

Mathematics

1 answer:

DerKrebs [107] · Answer 1 · 2022-03-25T10:45:18+03:00

DerKrebs [107]3 years ago

7 0

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