Katie's Concrete Co. is the only producer of concrete in her town (a monopolist). The firm's total cost function is TC (Q) = Q^2-10Q+100 so marginal cost is MC = 2Q-10. What is the firm's fixed cost? What is the average total cost for the firm? For what quantity is average total cost at its minimum?

Fixed Cost = 100; Average Cost = Q - 10 + 100/Q

Average Cost Minimising Quantity = 10

Explanation:

Total Cost is the total production expenditure on all factors of productions, for all output quantities.

Total Cost (TC) is sum of Total Fixed Cost (TFC), Total Variable Cost (TVC)

Variable Cost is the cost incurred on variable factors of production. It varies directly with production quantity, is 0 at 0 production level. Fixed Cost is the cost incurred on fixed factors of production. It is constant at all production quantity, not 0 even at 0 production level.

So, TFC is the constant component of total cost function

TC Function = Q^2-10Q+100

TFC = Constant numeral = 100

Average Total Cost is the total cost per unit of output

ATC = TC / Q

(Q^2-10Q+100) / Q

= Q - 10 + 100/Q

ATC minimised : per first derivative rule

dTC / dQ = 1 - 100/Q^2

1 - 100/Q^2 = 0

1 = 100 / Q^2

Q^2 = 100

Q = 10