Working with Numbers
When the marginal cost curve is below the average total cost curve, the average total cost must be .
When the marginal cost curve is above the average total cost curve, the average total cost must be .
Therefore, the marginal cost curve intersects the average total cost curve .

Explanation: When marginal cost falls, it drops to a minimum value and then increases again. This is because the marginal cost curve intersects both the average variable cost curve (AVC) and the (short-run) average total cost curve at their minimal points. So whenever marginal cost curve is above an average cost curve this implies that the average curve is on the rise or increase.

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Working with Numbers When the marginal cost curve is below the average total cost curve, the average total cost must be . When the marginal cost curve is above the average total cost curve, the average total cost must be . Therefore, the marginal cost curve intersects the average total cost curve .

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Working with Numbers
When the marginal cost curve is below the average total cost curve, the average total cost must be .
When the marginal cost curve is above the average total cost curve, the average total cost must be .
Therefore, the marginal cost curve intersects the average total cost curve .