Can there be a range of output in which MC rises while AC falls ? WHY ?

Dear Student,
Yes, for a certain range of output Marginal Cost (MC) rises when Average Cost (AC) is falling. This can be better understood with the help of a diagram.

As can be seen in the figure given above, MC rises beyond output Qx, while AC continues to fall. This continues for the entire range of output between Qx and Qz. This happens because though MC is rising, the magnitude of the rise is not enough to bring about a rise in AC. However, when the magnitude of the rise becomes large, AC and MC both rise simultaneously. This happens beyond output Qz.

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