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Math Help - profit maximisation using calculous

  1. #1
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    Unhappy profit maximisation using calculous

    Q1. The demand and cost functions of a monopolist are p=100-3q+4A^1^/^2 and C=4q^2+10q+A(A is the level of advertising expenditure). Find the values of A,q and p that maximise profit.

    Since here, profit is a function of q and A, I want to find the value of q and A at maximum profit, by using "total derivative". Will that be correct?
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  2. #2
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    Re: profit maximisation using calculous

    Firm will maximize profits (pi)
    pi=pq-C
    max (100-3q+4A^(1/2))q-(4q^2+10q+A)
    Take the first order conditions with respect to A, q,p (i.e partial derivative w/ respect to each set to zero)
    next make sure second order condition is satisified.
    Then solve for the A,q,p that maximize profits. Hope this helps
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  3. #3
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    Talking Re: profit maximisation using calculous

    Thank you so much!
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