Why do short run average costs make a U shape in the long run?

The long-run average cost decline as output increases and after a certain point it start rising. The shape of the long run average cost is U-shape because of returns to scale. In the beginning, when there is increasing return to scale which is the increase in output is proportionally greater than the increase in inputs. The long run average cost curve becomes constant due to constant returns to scale which means increase in inputs will lead to proportionate increase in the output. After a certain level, there is decreasing returns to scale which means increase in inputs leads to proportionally less increase in output, this leads to long run average cost of production to rise.

Therefore, the long run average cost curve is U shaped.