economics

P=100-30+4a½
Tc=4q²+10q+a
find q,p,a values

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  1. I think this is what you want:
    A firm with monopoly power has the demand curve: P = 100 - 3Q + 4A^1/2
    And has the total cost function: C = 4Q^2 + 10Q + A where A is the level of advertising expenditures.
    P is price, Q is output. How do I find the values of A, Q, …

    You will get a family of curves. I would do this:
    from P, a=(P/4-7.5q)^2 and square that out.
    then insert the quadratic into the Tc equation for a, and combine like terms.

    You will have a function tc dependent on P and q. You can then plot that family, or use your analytical methods to maximize profit, if you have a profit function. With what you have given, demand, and cost, there is no profit function.

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