Why does MC Curve intersect AC and AVC curve at their respective minimum points???Why not at any other points????

Marignal cost curve cuts both AC and AVC at their lowest points.

As long as MC is lower than AC/AVC it brings down the average. MC crosses AC when both are equal, i.e at the lowest point, then as MC tends to rise, the average cost also increases.

And since, AVC is less than AC. MC curve must first cut AVC, as it starts moving upwards and then AC.

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