A perfectly competitive firm with the market price at $12, and cost functions AFC = 30/Q, AVC = 6 + 0.1Q, and MC = 6 + 0.2Q, will continue to operate in the short run by producing where P = MR = MC, which is at a quantity of 30 units, as the market price is above the AVC.
If the market price of a good is $12, a perfectly competitive firm will decide whether to operate or shut down in the short-run based on its cost functions and the market price. The firm's average variable cost (AVC) function is AVC = 6 + 0.1Q, and its marginal cost (MC) function is MC = 6 + 0.2Q. According to the short-run decision rule, a firm should continue to produce if the price is above the average variable cost.
To find the level of output where the firm maximizes profit or minimizes loss, we look for where marginal revenue (MR), which is equal to the market price (P) for a perfectly competitive firm, is equal to the marginal cost (MC). Thus, we solve P = MR = MC. Here, P = $12, so we solve $12 = 6 + 0.2Q, which gives us Q = 30. We then determine if this price is above the AVC at Q = 30.
Substituting Q = 30 into the AVC function gives us AVC = 6 + 0.1(30) = $9. Since $12 is greater than $9, the firm will continue operating and produce 30 units since it covers its variable costs and contributes to fixed costs, despite making economic losses in the short run.