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6 October, 18:33

A firms total cost function is: TC = 500 + 150q - 20q2 + q3 what is the dollar value at the minimum of the average variable cost (avc) curve? $50?

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  1. 6 October, 18:37
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    the correct answer is $150

    Explanation:

    TC=500 + 150q - 20q^2 + q^3

    AVC = (150Q-20Q^2+Q^3) / Q

    =150-20Q+Q^2

    When AVC is at its minimum means that the marginal cost (CM) is igual to AVC, so we could consider this analysis:

    CM = d (TC) / dq = 150-40Q+3Q^2

    CM=AVC

    150-40Q+3Q^2=150-20Q+Q^2

    Join similar terms:

    150-150-40Q+20Q+3Q^2-Q^2=0

    0-20Q+2Q^2=0

    Q (-20+2Q) = 0

    Q_1=0 y Q_2=20/2=10

    with q_1 with q_2

    150-40*0+3*0=150-20*0+0 150-40*10+3*10^2=150-20*10+10^2

    $150=$150 150-400+300 = 150-200+100

    $50 = $ 50

    We have two solution if we assume that q=0 like the minimum then the results is $150.

    f we assume that q=10 like the minimum then the results is $50.
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