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    Fixed proportion production function Q = min(5K, 10L)

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    Suppose that a firm's fixed proportion production function is given by Q = min(5k,10L)

    The firm's Total Cost (TC) function is given by TC = vK + wL,
    where v is the cost of K and w is the cost of L.

    v = 1
    w = 3
    TC = K + 3L

    a) Calculate the firm's long-run total, average and marginal functions.

    b) Suppose that K is fixed at 10 in the short run. Calculate the firm's short-run total, average and marginal cost functions, and state the domain of the functions.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:18 am ad1c9bdddf
    https://brainmass.com/economics/production/fixed-proportion-production-function-q-min-5k-10l-500485

    Solution Preview

    a) Calculate the firm's long-run total, average and marginal cost functions.

    To make one unit of q requires (1/5 =) 0.2 units of K and (1/10 =) 0.1 units of L
    The cost of K is v and the cost of L is w, so:
    LRAC = 0.2v + ...

    Solution Summary

    Given a firm's fixed production function:

    Q = min(5k,10L)

    And its total cost function:

    TC = vK + wL
    where v = 1 and w = 3

    This solution shows how to calculate the firm's long-run total, average and marginal functions, and, if K is fixed at 10 in the short run, the firm's short-run total, average and marginal cost functions. All calculations are given in detail.

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