In economics why does a marginal cost curve intersect an average total cost curve at its lowest point?
When marginal cost is less than average total cost, then the cost of producing an additional widget is less than the average cost of the widgets produced so far. This means by producing an extra widget, we are lowering the average cost of a widget. Therefore if MC < ATC, ATC must be decreasing.
The exact opposite holds, ie. if MC > ATC, ATC must be increasing.
Thus ATC is decreasing while MC < ATC, and increasing when MC > ATC. This means when MC = ATC, ATC must be at a minimum (because ATC was decreasing up to that point and increasing after that point).
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