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    Marginal and average cost functions

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    Given that the total cost function is:

    TC = 100Q-Q^2+1/3 Q^3
    where Q = rate of output and TC = total cost

    a. Determine the marginal and average cost functions.
    b. Calculate the output level that minimizes average cost.
    c. Calculate the output level that minimizes marginal cost.

    © BrainMass Inc. brainmass.com October 10, 2019, 2:57 am ad1c9bdddf
    https://brainmass.com/economics/pricing-output-decisions/marginal-average-cost-functions-400863

    Solution Preview

    a. Determine the marginal and average cost functions. SHOW WORK

    TC = 100Q-Q^2 + 1/3 Q^3

    ATC=TC/Q=(100Q-Q^2+1/3Q^3)/Q=100-Q+1/3 Q^2

    MC=d(TC)/dQ= d(100Q-Q2 + 1/3 Q3)/dQ=100-2Q+Q^2 ...

    Solution Summary

    Solution determines the marginal and average cost functions. It also determines the output levels which minimize average and marginal costs.

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