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    Determining Profit Maximizing Price and Output Level

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    In a pure monopoly the company faces an inverse demand (price) for their product.

    p = 20-0.04q1

    marginal revenue is r= 20- 0.08q1

    and marginal cost is mc1= 0.1+ 0.5q1

    total costs is TC1= 5 + 0.1q + 0.25q1(squared)

    what is profit maximising level for
    a) price
    b) quantity
    c) monopoly profit

    If the company wants to produce some of the same product offshore with cheaper labour costs how much production should be undertaken in each factory to maximise total firm profit. Assume transport costs are the same.

    and for another factory is m2= 0.1 + 0.3q2

    Total costs for another factory are TC1=2 + 0.1q2 + 0.15q2(squared)

    © BrainMass Inc. brainmass.com October 9, 2019, 11:25 pm ad1c9bdddf
    https://brainmass.com/economics/price-levels/determining-profit-maximizing-price-and-output-level-256183

    Solution Preview

    Part 1

    P = 20-0.04q1
    Marginal revenue is MR1= 20- 0.08q1

    and Marginal cost is MC1= 0.1+ 0.5q1

    Total costs is TC1= 5 + 0.1q + 0.25q1^2

    A monopolist sets its output such that MR=MC to maximize its profit.
    Put MC=MR
    0.1+0.5q1=20-0.08q1
    0.5q1+0.08q1=20-0.1
    0.58q1=19.9
    q1=19.9/0.58 =34.31 units

    Price P=20-0.04*34.31=18.63

    TC1=5+0.1*34.31+0.25*34.31^2=302.725
    TR=P*q1=18.63*34.31=639.1953
    Profit=TR-TC1=639.1953-302.725=336.4703

    Part 2

    If the company wants to produce some of the same product ...

    Solution Summary

    Solution describes the steps to determine profit maximizing level of price, quantity and profit for a monopolist. It also calculates the profit maximizing level of price, quantity and profit if monopolist produces in two factories.

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