The short-run average total cost curve (SATC):

The average total cost curve is U shaped due to the law of variable proportions. The average cost curve first declines with an increase in production reach its minimum at a certain level of production and it rises if the production is increased further.

In the short run, the fixed inputs of the firm remain constant and the firm can change its variable inputs such as raw materials and labor only. As the production increases, the average variable cost declines due to which average cost fall. When more output is produced, the fixed cost gets distributed over the entire range of production. Hence, the average cost curve declines.

The average cost reaches its minimum when the existing plant and machinery is operated to its optimal capacity. When the firm increases production on the existing fixed plant, there is more labor to work on the same plant, the average variable cost starts increasing. Thus, the average variable curve starts rising and due to which SATC curve slopes upwards.

The long-run average total cost curve (LATC):

In the long run, all the factors of the firm become variable. The shape of the LATC is defined due to the operation of returns to scale. The LATC falls in the beginning because of increasing returns to scale and remains constant at a specific level of output and starts rising because of decreasing returns to scale. The long-run average cost curve is derived from various short-run average cost curve which shows the different sizes of plants available to the firm.

In the beginning, the firm achieves economies of scale because of which average cost declines. The firms achieve economies of scale because of division and specialization of labor. Therefore the LATC declines at the beginning of the production.

At a certain level of production, the LATC is minimum and after that level of production, LATC starts rising because of decreasing returns to scale. It occurs because inefficiency arises in management and entrepreneurship.

Therefore, the LATC curve is U-shaped and also recognized as the envelope curve as it touches the various points of different SATC curves. In the beginning, LATC curve touches the left side of different SATC curves. At a certain level of production, the LATC touches the minimum point of a SATC curve. At a higher level of production, the LATC curve touches the rising portion of the SATC curves.