Q.Explain, with reasons, why the short-run Average Variable Cost (AVC) and Marginal Cost (MC) curves are both U-shaped.

AVC and MC are U-shaped because of how a variable factor interacts with a fixed plant — efficient at first, then increasingly crowded, exactly the pattern behind the 'law of variable proportions'.

In the short run, a firm's plant size (a fixed factor) stays constant while it adds more of a variable factor — say labour — to raise output. At low levels of employment, the fixed plant is under-used, so each additional worker can be combined with it very productively: output rises more than in proportion to the extra labour used, so the cost of producing extra output (MC) and the average variable cost per unit (AVC) both fall. This is the 'increasing returns to the variable factor' phase.

As more and more of the variable factor is added to the same fixed plant, however, the plant becomes crowded — there is only so much machinery and floor space for workers to share. Beyond a point, each extra unit of the variable factor adds less and less extra output than the one before it: this is 'diminishing returns to the variable factor'. When returns diminish, producing extra output costs progressively more, so both MC and AVC start rising.

The result, taken together, is a curve that falls, reaches a minimum, and then rises — the characteristic U-shape — for both AVC and MC. Because the whole effect stems from the fixed plant becoming a genuine constraint only in the later stages, MC (which reflects the cost of the very next unit) usually starts rising, and rises more steeply, before AVC (an average over all units produced so far) does.

A common mistake is attributing the U-shape to 'rising prices of inputs' — the standard short-run explanation has nothing to do with input prices changing; it is purely about the changing productivity of the variable factor as it is combined with a fixed plant in different proportions.