No,AVC and ATC can never be equal as they won't intersect each other at any point .It happens because the vertical distance between ATC and AVC is AFC which can never be zero..n so ATC n AVC curve won't intersect ...

Introduction:
The difference between average total cost (ATC) and average variable cost (AVC) is known as average fixed cost (AFC). As output increases, the AFC becomes smaller in relation to the total cost. This is because the fixed costs are spread over a larger number of units, leading to a decrease in the AFC. However, the AVC remains relatively constant as long as the variable costs per unit stay the same.

Explanation:
1. Average Total Cost (ATC):
- Average total cost (ATC) is the total cost per unit of output produced.
- It is calculated by dividing the total cost (TC) by the quantity of output (Q).
- ATC = TC / Q.

2. Average Variable Cost (AVC):
- Average variable cost (AVC) is the variable cost per unit of output produced.
- It is calculated by dividing the total variable cost (TVC) by the quantity of output (Q).
- AVC = TVC / Q.

3. Average Fixed Cost (AFC):
- Average fixed cost (AFC) is the fixed cost per unit of output produced.
- It is calculated by subtracting the average variable cost (AVC) from the average total cost (ATC).
- AFC = ATC - AVC.

Decrease in the Difference:
As the level of output increases, the fixed costs are spread over a larger number of units. This leads to a decrease in the average fixed cost (AFC) because the fixed costs are being distributed among more units of output. At the same time, the average variable cost (AVC) remains relatively constant as long as the variable costs per unit stay the same.

- The decrease in AFC contributes to a decrease in the difference between ATC and AVC because AFC is subtracted from ATC to calculate AVC.
- If AFC decreases, the difference between ATC and AVC decreases.

Equal at Some Level of Output:
- The ATC and AVC can be equal at a specific level of output when the average fixed cost (AFC) becomes zero.
- This happens when the fixed costs are spread so thinly over a large number of units that the fixed cost per unit becomes negligible.
- At this level of output, the ATC and AVC will be equal, as there is no fixed cost component left to be subtracted from the ATC to calculate the AVC.

Conclusion:
The difference between ATC and AVC decreases with an increase in the level of output due to the spreading of fixed costs over a larger number of units. The ATC and AVC can be equal at a specific level of output when the average fixed cost becomes zero.