Question

Given a total cost function, 

TC(Q) = Q

2 + 10Q + 100

where Q represents quantity of output produced. 

(i) Find the expressions for the variable cost, fixed cost, average cost, average variable cost, 

and average fixed cost. 5

(ii) At what output level (Q) is the average cost lowest? Also find the minimum average cost.

Answer 1

$TC = Q^2 + 10Q +100$

1) $TC = TVC + TFC;$ $TVC = Q^2 +10Q;$ $TFC = 100$;

$AC = TC/Q = Q+10 +\frac{100}{Q}$

$AVC= TVC/Q = Q+10$

2)$AC' = 1 - 100\times \frac{1}{Q^2} =0$ => $\frac{1}{Q^2} = \frac{1}{100} => Q = 10$

$AC_{min} = 10 + 10 + \frac{100}{10}=30$