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  1. #1
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    Help with output problem

    A firm's average total cost is $100, its average variable cost is $90, and its total fixed cost is $1000. What is the output?

    I'm not sure how to figure this one out. Any help appreciated.
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  2. #2
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    Quote Originally Posted by wvmcanelly@cableone.net View Post
    A firm's average total cost is $100, its average variable cost is $90, and its total fixed cost is $1000. What is the output?

    I'm not sure how to figure this one out. Any help appreciated.
    Let the output be N units, then the variable cost is $90 per unit, so the
    total costs are:

    TC = 90*N+1000

    and so the average cost is:

    AC = TC/N = 90 + 1000/N = 100

    So:

    1000/N = 10,

    or N=100.

    RonL
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by wvmcanelly@cableone.net View Post
    A firm's average total cost is $100, its average variable cost is $90, and its total fixed cost is $1000. What is the output?

    I'm not sure how to figure this one out. Any help appreciated.

    Do you know the formulas?

    Let TFC be total fixed cost
    Let TC be total cost
    Let TVC be total variable cost
    Let Q be quantity produced (output)
    Let ATC be average total cost
    Let AFC be average fixed cost
    Let AVC be avereage variable cost

    We have the formula:

    TC = TFC + TVC \mbox {  } ....................(1)

    if we divide everything by Q we get,

    \frac {TC}{Q} = \frac {TFC}{Q} + \frac {TVC}{Q} \mbox {  } ........................(2)

    but when we divide by Q, what we are actually finding are the average costs, so

    \Rightarrow ATC = AFC + AVC \mbox {  } ....................(3)


    we are given the ATC \mbox { , } AVC \mbox { , and } TFC and we want to find Q


    Now, as i said before AFC = \frac {TFC}{Q}

    so Q = \frac {TFC}{AFC}

    But we don't know the AFC, so let's use formula (3) to find it

    ATC = AFC + AVC

    \Rightarrow AFC = ATC - AVC = 100 - 90 = 10


    So finally, Q = \frac {TFC}{AFC} = \frac {1000}{10} = 100


    EDIT: Beaten by CaptainBlack...yet again! Plus his way is a lot shorter. He's not the Captain for nothing
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