Average cost is the sum of average fixed cost and average variable cost.
Hence
ATC (AC) = AFC + AVC
So, ATC - AVC = AFC
This shows that difference between ATC and AVC is equal to AFC.
AFC is obtained by dividing total fixed cost by output, i.e. AFC=TFC / Q
And total fixed cost (TFC) is constant.
Therefore, with the increase in the level of output, AFC falls.
Thus, the difference between ATC and AVC decreases with increase in output.
No, ATC and AVC cannot be equal at any level of output as gap between them i.e.
AFC can never be zero because TFC is constant and positive.