ECO 310100 i inter me u Your firm is in a perfectly competit

ECO 3101.00 i inter me u Your firm is in a perfectly competitive industry (i.e, you are a price taker). The engineering department estimated your cost function to be Your marginal cost is The market price in the industry is P 43. TC(Q) 30+30+Q2 MC(Q) 3+20 A) Is this a short-run or long-run cost function? B) What is the fixed cost (FC) of producing 10 units? C) What is the variable cost (VC) of producing 5 units? D) What is the average variable cost (A VC) of producing 20 units? E) What is the average total cost (AC) of producing 30 units? F) What is the marginal cost (MC) of producing the 15th unit? G) At the current market price, how many units should your firm produce? H) What is your profit if you produceO from part G)?

Solution

A) A short run cost function contains both variable cost and fixed cost(FC) but a long run cost function is only based on the variable costs. The figure 30 of the cost function depicts the fixed cost and thus it is a short run cost function.

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B) FC for producing 10 units is 30, since the FC is fixed and does not change with variable inputs.

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C) TC = 30 + 3Q + Q²

Variable Cost (VC) = 3Q + Q²

VC( for producing 5 units) = 3*5 + (5)^2

VC = 40

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D) AVC = VC / Q

VC = 3Q + Q²

VC = 3*20 + (20)^2

VC = 460

AVC = 460 / 20 = 23