Final answer:
The perfectly competitive firm in question is productively efficient in the short run because it produces where P = MC. However, since P > ATC, it is making economic profits, which suggests that the industry may not be in long-run productive efficiency until market adjustments lead to P = ATC.
Step-by-step explanation:
When analyzing whether a perfectly competitive firm's industry is productively efficient, we need to consider the firm's pricing in relation to its costs. Productive efficiency occurs when a firm is producing at the minimum point on its average total cost curve. In a perfectly competitive market, firms achieve productive efficiency because they produce where P = MC, which coincides with the minimum point on the ATC curve in long-run equilibrium.
In this scenario, the firm faces a market price (P) of $9, has an output of 4,000 units, an average total cost (ATC) of $8, an average variable cost (AVC) of $6, and a marginal cost (MC) of $9. Because P = MC, the firm is producing at the output level where marginal revenue is equal to marginal cost, which is the condition for productive efficiency in the short run.
However, for long-run productive efficiency, we look for P = ATC, which represents zero economic profit and indicates no incentive for new firms to enter or existing firms to exit the market. Since P > ATC in this case, the firm is making economic profits, which could lead to other firms entering the market in the long run, thus driving the price down until P = ATC. So, while this firm is productively efficient in the short run, the industry may not be in long-run productive efficiency until new firms enter, and the price adjusts to meet the minimum ATC.