Why is ATC a U-shaped curve?

Key Components:

In order to understand why the ATC i.e. the Average Total Cost Curve in U-shaped, we need to look at its key components.

Total Cost = Total Variable Cost + Total Fixed Cost

TC = TVC + TFC

Definitions:

Variable Cost refers to those costs which increase along with an increase in output. Example: Raw Materials, Labour i.e. if you want to produce more then you need more raw materials and labour.

Fixed Costs refer to those costs which do not change along with an increase in output.Example: Rent of Factory i.e. irrespective of how much you produce, the rent will stay the same.

Therefore:

Total Cost/Output = Total Variable Cost/Output + Total Fixed Cost/Output

Hence we get:

ATC= Average Fixed Costs(AFC) + Average Variable Costs(AVC)

Lets look at the Graph:
X-axis: Output
Y-Axis: Costs
graph{x^2 + 4 [-32.48, 32.46, -16.24, 16.24]}

Explanation:

As Output increases the total variable costs increases and hence the AVC is also increasing , BUT the total fixed costs remains the same, hence the AFC is falling.

Since the ATC = AFC+ AVC and one component is falling and the other is rising, the direction in which ATC moves will depend on which component is more dominant.

The downward slopping portion of the U-Shaped curve corresonds to the part where AFC is dominant and hence ATC is falling but eventually AVC becomes dominant and ATC starts to rise.

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