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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?

Respuesta :

Answer:

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

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