Why is a slope zero when its average cost is equal to its marginal cost?

The average cost is the per-unit production cost which is also sometimes referred to as the average total cost. It is calculated by dividing the total cost (sum of fixed and variable costs) by the total quantity produced. Marginal cost is the change (increase or decrease) in the total cost when an incremental unit of the product is produced.

The point where the average total cost curve crosses the marginal cost curve is called the minimum efficient scale. At this level of production, the average total cost is minimized. By calculus, the slope of a curve is zero at the minimum point. Hence, the slope of the average total cost is zero when the average cost is equal to the marginal cost.