Final Answer:
If a purely competitive firm is producing at the P = MC output and realizing an economic profit, at that output, total revenue equals total cost. In a perfectly competitive market, the profit-maximizing condition is P = MC. With economic profit, P > ATC. Given the equality of P = MC and the economic profit condition, total revenue (P * Q) equals total cost (ATC * Q), affirming the economic profit scenario.
Step-by-step explanation:
In a perfectly competitive market, a firm maximizes profit by producing where marginal cost (MC) equals marginal revenue (MR), and this is also equal to the market price (P). Therefore, in this scenario, P = MC, and the firm is operating at the profit-maximizing level of output. Economic profit occurs when the price (P) exceeds average total cost (ATC). Given that the firm is making an economic profit, it implies that P > ATC.
Now, let's consider the relationship between total revenue (TR) and total cost (TC). TR is calculated as the product of price (P) and quantity (Q), while TC is the product of average total cost (ATC) and quantity (Q). Since P > ATC and Q is the same for TR and TC, it follows that TR > TC, resulting in an economic profit. Therefore, at the P = MC output with economic profit, total revenue equals total cost.
In summary, the firm is producing where P = MC, indicating profit maximization, and realizing an economic profit where P > ATC. Consequently, total revenue (P * Q) equals total cost (ATC * Q), affirming the economic profit condition.