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    Monopoly- output, price and profits

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    (Demand) P=$85Q-$0.2Q
    (Marginal Reveune) MR=$85-$0.4Q
    (Total Cost) TC=$900+$20Q+$0.8Q2
    (Marginal Cost) MC=$20+$1.6Q

    where P is price (in dollars), Q is output (in thousands of megawatt hours) and TC is total cost (in thousands of dollars).

    a) if the firm were operating as a pure monopolist, what would be its optimal price/output solution and level of economic profits?

    The way I worked it out:

    MR = MC
    $85-0.4Q = $20+1.6
    65 = 2.0Q
    32.5 = Q

    P = 85Q-0.2Q2
    = 85(32.5)-0.2(32.5)2
    = 276.25-0.2(1056.25)
    = 276.25-211.25
    = $65.00

    Could someone look over this to make sure that I am right.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:19 pm ad1c9bdddf
    https://brainmass.com/economics/general-equilibrium/monopoly-output-price-profits-39977

    Solution Preview

    There appears to be some mix up in the equations that you have written
    as
    P = 85Q-0.2Q2
    = 85(32.5)-0.2(32.5)2
    = 2762.50-0.2(1056.25) { as 85 x 32.5 is 2762.50 and not 276.25 as you have written)
    = 2762.50-211.25
    = $2511.25
    which is wrong

    The ...

    Solution Summary

    The solution calculates equilibrium quantity equilibrium price and profits for a monopoly. Pure monopolists for operating firms are discussed.

    $2.49

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