What is the profit maximising level of output for this firm in the short run ? At this quantity, what is the marginal revenue?
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Answer:
Short‐run profit maximization. A firm maximizes its profits by choosing to supply the level of output where its marginal revenue equals its marginal cost. When marginal revenue exceeds marginal cost, the firm can earn greater profits by increasing its output. When marginal revenue is below marginal cost, the firm is losing money, and consequently, it must reduce its output. Profits are therefore maximized when the firm chooses the level of output where its marginal revenue equals its marginal cost.
To illustrate the concept of profit maximization, consider again the example of the firm that produces a single good using only two inputs, labor and capital. In the short‐run, the amount of capital the firm uses is fixed at 1 unit. Assume that this firm is competing with many other firms in a perfectly competitive market. The price of the good sold in this market is $10 per unit. The firm's costs of production for different levels of output are the same as those considered in the numerical examples of the previous section, Theory of the Firm. These costs, along with the firm's total and marginal revenues and its profits for different levels of output, are reported in Table .

Because the price of the good is $10, the firm's total revenue is 10 × total product. The firm's marginal revenue is equal to the price of $10 per unit of total product. Notice that the marginal cost of the 29th unit produced is $10, while the marginal revenue from the 29th unit is also $10. Hence, the firm maximizes its profits by choosing to produce exactly 29 units of output. In choosing to produce 29 units of output, the firm earns $90 ($290 − 200) in profits.
Total revenue and marginal revenue. A firm's total revenue is

the dollar amount that the firm earns from sales of its output. If a firm decides to supply the amount Q of output and the price in the perfectly competitive market is P, the firm's total revenue is A firm's marginal revenue is the dollar amount by which its total revenue changes in response to a 1-unit change in the firm's output. If a firm in a perfectly competitive market increases its output by 1 unit, it increases its total revenue by P × 1 = P. Hence, in a perfectly competitive market, the firm's marginal revenue is just equal to the market price, P.