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28 June, 14:04

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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  1. 28 June, 14:19
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    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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