why is the short-run average cost curve U- shaped ?

The short run AC curve is a U-shaped because as output increases, AC falls and reaches a minimum point and rises beyond that. The reason behind the U-shape of AC is attributed to the law of variable proportions. In the initial stages, due to the increasing returns to a factor, the average cost falls, as marginal product of labour (MP_L) is rising. However, at minimum point, owing to constant returns to labour, AC tends to stabilise and after the minimum point, as the firm is employing more units of labour with the constant unit of fixed input, the MP_L falls and consequently cost rises and therefore, AC starts rising up due to higher cost at the latter stages of production due to decreasing returns to labour. Therefore, AC is ‘U-shaped’ curve.