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Math Help - Costs question

  1. #1
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    Costs question

    I am given two equations:

    Min 5K + 15L

    and the constraint: 10= L^{.5}K^{.5}
    given that K=4 (then L=25)
    and am asked to find the:

    1. short run average cost
    2. short run variable cost
    3. short-run marginal cost

    And I'm a bit confused. What is the 10 actually represent in constraint? Is it total quantity produced?

    Is the answer to question 1 suppose to be:
    5(4) + 15(25)= 20+ 375= 395
    395/10 = 39.5?

    2. seems to be the cost of labor (wL), or in this case 15L, or w=15.

    3. I know that SRMC should be the change in SRTC/ change in quantity. I just don't understand where your find those values.
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  2. #2
    MHF Contributor
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    1. fine

    2. Not clear if you mean "short run total variable cost" or "short run average variable cost".
    SRTVC = 15L
    SRAVC = 15L / 10


    3.
    Compute the amount of labour needed to produce X units of output given that K is fixed at 4.
    Compute the SRTC = 15L + 4*5 [[note: it will be a function of x!!]]

    Differenciate SRTC with respect to X to obtain the SRMC
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  3. #3
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    My hero!
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