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Why does the SMC curve cut the AVC curve...

Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?

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It is because when AVC falls, SMC is less than AVC. When AVC starts rising, SMC is more than AVC. So, it is only when AVC is constant and at its minimum point, that SMC is equal to AVC. Therefore, SMC curve cuts AVC curve when it is minimum.
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