When a perfectly competitive firm increases its output, its price remains the same as a perfectly competitive firm can sell all its outputs at the given market price. However, the marginal cost increases with an increase in production after a certain level. So, when the marginal cost is lower than the price, the firm can still earn a higher profit by increasing output to the point that marginal cost equals the price. Beyond this point, marginal cost will be higher than the price and each additional output would contribute loss and the total profit will come down. So, profit is maximized when the price equals the marginal cost.
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