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Math Help - profit maximising monoloys

  1. #1
    Junior Member
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    Mar 2009
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    profit maximising monoloys

    can anyone help?

    A monopoly firm has a total revenue function:
    R = 24Q – 2Q2
    and a total cost function:
    C = Q2 + 5
    where R, C and Q are total revenue, total cost and quantity respectively.

    (a)Calculate:
    i. The monopolist’s profit maximising output and price.
    ii. The value of total profit at the profit maximising price and output.
    iii. The co-efficient of price elasticity at the profit maximising price and output.
    iv. How will your calculations in i. and ii. above be affected by a lump sum tax of 30?
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  2. #2
    Junior Member
    Joined
    Jun 2009
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    arslan, maybe this'll help kick it off for you...

    Your profit function  \pi , for any Q, is just Revenue less Cost, or

     \pi(Q) = R(Q) - C(Q) = (24Q - 2Q^2) - (Q^2 + 5)

    When you put R and Q together, you'll end up with a single function / equation for profit:

     \pi = -3Q^2 + 24Q - 5

    Now you can see that your profit function is a quadratic, graphically represented by a downward-opening parabola (the leading term has a negative coefficient).

    Maximum profit is achieved at the vertex of that parabola. You can determine that vertex using your favorite weapon of choice: Either via algebra (rearrange the equation into "vertex" form), or calculus (find the Q at which the first derivative = 0).

    That'll get you running with ball, at least. Best of luck with it!
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