QUESTION: Practice Problem 1 Suppose a firm has fixed costs in the short run of 100. Also, its variable costs are given by VC = 4q². The firm's marginal cost is MC = 8q. What is the break-even price for the firm?

Check the answer.

ANSWER: The break-even price for the firm is the minimum of Average Total Cost. This occurs where marginal cost equals average cost. Average Total Cost is TC/q where q is the quantity of output. Total Cost = TFC + TVC, so average cost equals (100 + 4q²) / (q) Setting this equal to 8q and solving for q, q = 5. Therefore, marginal cost equals average cost = 40. So 40 is the break-even price. So if the price is above 40, the firm will make a profit. If it is below 40, the firm will make a loss.

I understand that the answer if q = 5, but there's a lot of math missing.