Results 1 to 3 of 3

Thread: Help with output problem

  1. #1
    Newbie
    Joined
    Jun 2007
    Posts
    24

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    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 $\displaystyle TFC$ be total fixed cost
    Let $\displaystyle TC$ be total cost
    Let $\displaystyle TVC$ be total variable cost
    Let $\displaystyle Q$ be quantity produced (output)
    Let $\displaystyle ATC$ be average total cost
    Let $\displaystyle AFC$ be average fixed cost
    Let $\displaystyle AVC$ be avereage variable cost

    We have the formula:

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

    if we divide everything by $\displaystyle Q$ we get,

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

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

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


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


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

    so $\displaystyle Q = \frac {TFC}{AFC}$

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

    $\displaystyle ATC = AFC + AVC$

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


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


    EDIT: Beaten by CaptainBlack...yet again! Plus his way is a lot shorter. He's not the Captain for nothing
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with Input and Output
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 3rd 2010, 06:34 PM
  2. LaTeX problem - with PDF output
    Posted in the LaTeX Help Forum
    Replies: 3
    Last Post: Feb 2nd 2010, 02:53 PM
  3. economics: output
    Posted in the Business Math Forum
    Replies: 0
    Last Post: Mar 11th 2009, 06:04 PM
  4. Multi Input Single Output Problem
    Posted in the Advanced Math Topics Forum
    Replies: 7
    Last Post: Jun 28th 2007, 10:17 PM
  5. input-output
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: Jul 20th 2006, 07:38 AM

Search Tags


/mathhelpforum @mathhelpforum