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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- Jun 17th 2007, 12:53 PMwvmcanelly@cableone.netHelp 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. - Jun 17th 2007, 01:13 PMCaptainBlack
- Jun 17th 2007, 01:24 PMJhevon

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