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    Detailed Optimization Calculations

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    Please help with the following problem.

    Optimization:
    Giant Screen TV, Inc, is a manufacturer and distributor of high-resolution 50-inch television monitors and consoles for individual and commercial customers. Revenue and cost relations are:
    TR = $4,500Q - 0.1Q^2
    MR = $4,500 - 0.2Q
    TC = $2,000,000 + $1,500Q + 0.5Q^2
    MC = $1,500 + $Q
    A. Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level.
    B. Calculate these values at the profit-maximizing activity level.
    C. Compare and discuss your answers to part A and B.

    © BrainMass Inc. brainmass.com October 10, 2019, 4:16 am ad1c9bdddf
    https://brainmass.com/economics/output-and-costs/detailed-optimization-calculations-454076

    Solution Preview

    a) Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level.

    At the cost-minimization point, MC = ATC
    ATC = TC/Q = 2000000/Q + 1500 + 0.5Q
    Let MC = ATC
    1500 + Q = 2000000/Q + 1500 + 0.5Q
    0.5Q = 2000000/Q
    0.5Q^2 = 2000000
    Q^2 = ...

    Solution Summary

    Given a firm's cost and revenue functions, this solution shows the precise, detailed mathematical calculations necessary to maximize a firm's revenues and minimize its costs.

    $2.19