What accounts for the ‘U-shaped’ of the short run average cost (AC) curve?

The 'U-shaped' of the short run average cost (AC) curve is due to the law of variable proportions. The law of variable proportions, also known as the law of diminishing marginal returns, states that as more and more units of a variable input are added to a fixed input, the marginal product of the variable input will eventually decrease. In the short run, at the beginning of the production process, as more variable inputs are added, the marginal product of these inputs will increase. As a result, the average cost of production will decrease, since the total cost will be spread over a greater output. This is the downward-sloping portion of the 'U-shaped' AC curve. However, at a certain point, adding more variable inputs will lead to diminishing marginal returns. This means that the marginal product of the additional variable inputs will start to decrease, causing the average cost of production to increase. This is the upward-sloping portion of the 'U-shaped' AC curve. At the minimum point of the 'U-shaped' AC curve, the marginal product of the variable input is equal to the average product, and the average cost is at its minimum. Beyond this point, the marginal product of the variable input continues to decrease, causing the average cost to increase. In summary, the 'U-shaped' of the short run average cost (AC) curve is due to the law of variable proportions, which causes the average cost of production to decrease at first as more variable inputs are added, and then increase as the marginal product of the variable input diminishes.