A curve showing the average total cost for different levels of output when at least one input of production is fixed typically plant capacity is the -run average cost curve

The curve you're referring to is known as the Short-Run Average Total Cost (SRATC) curve. Here's a step-by-step explanation:

1. The Short-Run Average Total Cost (SRATC) curve is a graphical representation that displays the average total cost for different levels of output when at least one input of production is fixed, typically plant capacity.

2. In the short run, at least one factor of production is fixed. This could be capital, such as machinery or buildings. Because of this, if output increases, these fixed costs are spread over more units of output, which can decrease the average total cost.

3. The SRATC curve is typically U-shaped. This is because as output increases, initially, the average total cost falls. This is due to economies of scale and the spreading of fixed costs over a larger number of units.

4. However, after a certain point, the average total cost starts to rise again. This is due to diseconomies of scale. As production increases beyond this point, the fixed factor of production becomes a constraint, and additional units of the variable factor become less productive.

5. Therefore, the SRATC curve shows how the average total cost of production changes as the quantity of output produced changes, given that at least one factor of production is fixed in the short run.