Question

4. The engineering department has estimated your firm's cost function to be TC(O) = 5,000 + Q-Q? + Q: 13 This cost function has a marginal cost function MC(Q) = 1 -2Q+Q? a. Is this your long run or short run cost function? b. How much will it cost to produce 100 units? c. What is the average cost of 100 units? d. What is the marginal cost of the 100th unit? e. At what quantity is minimum average variable cost reached? f. What is the shutdown price? g. This firm is a price taker, and the market price is $2,401. How many units should the firm produce? h. What is the profit in part g above?

Answer 1

a. This is a short run cost function because 5000 in the TC is the fixed cost which is only present in the short run. In the long run, there is no fixed cost.

b. TC(100) = 5000 + 100 - (100)² + (100)³/3 = 5100 - 10,000 + 333,333.33 = 328,433.33

c. AC = TC/Q = 328,433.33/100 = 3,284.33

d. MC(100) = 1 - 2(100) + (100)² = 1- 200 + 10,000 = 9,801

(Note: Post 4 subparts at a time.)

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