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Why does marginal cost curve cut average cost curve only at its minimum point?

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Marginal cost curve cuts average cost curve only at its minimum point because it is only here that MC = AC.
The marginal cost curve always intersects the average total cost curve at its lowest point because the marginal cost of making the next unit of output will always affect the average total cost. As a result, so long as marginal cost is less than average total cost, average total cost will fall.
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