# Math Help - Help with output problem

1. ## 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. 2. Originally Posted by wvmcanelly@cableone.net 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 3. Originally Posted by wvmcanelly@cableone.net 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