Since marginal costs start out low, AVC starts out falling and continues to fall until MC is as large as AVC. Once the most recent cost is greater than the average the average begins to rise. This means that MC must cross the AVC curve where AVC is at its minimum.

   The reason the MC curve crosses the AVC curve at the minimum of AVC isn't an economic concept per se. It's just how average and marginal quantities are related, no matter what the quantities are.

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