Final answer:
The firm maximizes profit when price equals marginal cost. Without knowing the price per unit, we can't definitively say if current output is optimized. If price per unit is inferred from total revenue, the firm is maximizing profit at 500 units as price exceeds both marginal and average cost.
Step-by-step explanation:
The question is asking whether a competitive firm is maximizing its profit with its current level of production, or if it should adjust its output to increase profit. Since the firm's marginal cost of producing the 500th unit of output is $5.75 and the average total cost is $4.00, while it produces and sells 500 units of output for a total revenue of $3,500, we need to assess the relationship between these costs and the revenue to determine if the firm is maximizing profits.
For profit maximization under perfect competition, the firm should produce up to the point where price equals marginal cost (P=MC). In this scenario, the firm has not disclosed the price per unit but only the total revenue and the cost of producing the 500th unit. Since marginal cost is the cost of producing one more unit, if the price (which equals marginal revenue in competitive markets) were higher than the marginal cost, the firm should continue to increase output. Conversely, if the marginal cost is higher than the price, it should decrease production.
Given that the average total cost of producing the 500th unit is less than the marginal cost, we can infer that the average total cost has been rising, which typically happens after the point of diminishing returns. Without the price per unit, we cannot definitively conclude whether the firm should increase or decrease production. However, if we assume that the price is constant and equal to the average total revenue ($3,500/500 units = $7 per unit), then the firm is currently making a profit per unit since price is above average total cost and should continue production as long as the price remains above the marginal cost. In this scenario, as the price of $7 is higher than both the marginal cost of $5.75 and the average total cost of $4, the firm is indeed maximizing profit at the production of 500 units.