A profit-maximizing firm in a competitive

market achieves maximum profit by producing at the quantity where marginal revenue equals marginal cost. To calculate this quantity, you can follow these steps:

1. Determine the firm's demand curve: In a competitive market, the firm is a price taker. Therefore, its demand curve is perfectly elastic and represents the market price. It means that for every quantity of output the firm produces, it can sell it at the same price.

2. Calculate the firm's marginal revenue (MR): Since the demand curve is perfectly elastic, the firm's marginal revenue is equal to the market price. In other words, MR = Price.

3. Determine the firm's marginal cost (MC): Marginal cost is the additional cost incurred by producing one more unit of output. To determine MC, you need to analyze the cost function of the firm, which includes both fixed costs (costs that do not change with the level of production) and variable costs (costs that vary with the level of production).

4. Set MR equal to MC: To maximize profit, the firm should produce at the quantity where MR equals MC. This is because, at this point, the additional revenue gained from producing one more unit (MR) is exactly balanced by the additional cost incurred (MC).

5. Identify the profit-maximizing quantity: Once you have found the quantity where MR equals MC, this is the level of output at which the firm should produce to maximize its profit.

It's important to note that profit-maximization also depends on the nature of the market, such as the ability to influence price or the presence of any barriers to entry.