In long-run equilibrium, a perfectly competitive firm's short-run marginal cost curve crosses the long-run average cost curve at the lowest point on the long-run average cost curve.

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In long-run equilibrium, a perfectly competitive firm will produce at the minimum point on its long-run average cost curve, where the short-run marginal cost curve intersects the long-run average cost curve. This is because in the long run, firms can adjust their inputs and adopt more efficient production methods, leading to lower costs and shifting the long-run average cost curve downwards. The intersection of the short-run marginal cost curve and the long-run average cost curve at the minimum point of the long-run average cost curve ensures that the firm is producing at the most efficient scale and minimizing its average costs.

In Long-Run Equilibrium, a Perfectly Competitive Firm's Short-Run Marginal Cost