The output Q3 of the lowest average cost is always greater than the lowest output Q2 of the average variable cost. In other words, when the output increases, the manufacturer always reaches the lowest point of the average variable cost first, and then reaches the lowest point of the average cost. This is because the average cost is equal to the average variable cost plus the average fixed cost. When the average variable cost reaches the lowest point, the average fixed cost is still falling, so the average cost will inevitably fall and reach the lowest point after the average variable cost. "

Now give the mathematical proof:

TC=FC+VC

Then: ATC=(FC+VC)/Q=AFC+AVC.

That is, the average cost (AFC) is equal to the average variable cost (AVC) plus the average fixed cost (AFC).

In the above formula, the average fixed cost decreases and the average variable cost decreases first and then increases.

Therefore, when the average cost is at the lowest point, its (ATC)'=0.

Then: (ATC)'=(AFC)'+(AVC)'=0.

Because the average cost is decreasing, namely: (AFC)'

Then: (ATC)'=0, (AVC)' >；; 0

Therefore, when the average cost reaches the lowest point, its variable cost will inevitably rise, so the minimum output of the average cost is greater than the minimum output of the average variable cost.