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