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    imperfectly competitive firm

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    1) An imperfectly competitive firm has the following demand and cost functions:
    P=230-20Q
    C=50+30Q

    a. What is optimum output?
    b. What is equilibrium price of this output per unit?
    c. What is optimal revenue?
    d. What is total profit?

    2) A firm in a perfectly-competitive industry where market price of output prevailing is $50 per unit has a cost function where:
    C=40+5Q2
    a. What is marginal cost in dollars?
    b. What is marginal revenue in dollars?
    c. What is optimal output in units?
    d. What is maximal profit?

    3) A monopolist facing a demand curve and cost function like the following:
    P=72-6Q
    C=15+6Q2
    a. has what equation for marginal revenue?
    b. What is the equation for marginal cost?
    c. What is optimal output?
    d. What is price per unit?
    What is profit?

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    Solution Preview

    <br>1) An imperfectly competitive firm has the following demand and cost functions:
    <br>P=230-20Q
    <br>C=50+30Q
    <br>
    <br>a. What is optimum output?
    <br>b. What is equilibrium price of this output per unit?
    <br>c. What is optimal revenue?
    <br>d. What is total profit?
    <br>
    <br>For optimum in an imperfectly competitive firm, MR = MC
    <br>
    <br>Total Revenue = TR = Price * Quantity = P*Q
    <br> = (230-20Q)*Q = 230Q - 20Q^2
    <br>MR = d(TR)/dQ = d(230Q - 20Q^2)/dQ = 230 - 40Q
    <br>MC = dC/dQ = 30
    <br>MR = MC ==> 230-40Q = 30 ==> ...

    Solution Summary

    Characterize an imperfectly competitive firm.

    $2.19

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