In the short-run marginal cost curve cuts which of the following curves at their minimum points ?

Question

Accepted Answer

The correct option is 2: AVC and AC.

In short-run cost analysis, the Marginal Cost (MC) curve represents the change in total cost resulting from producing one additional unit of output. The relationship between MC and average costs—specifically Average Variable Cost (AVC) and Average Total Cost (AC)—is a fundamental principle derived from the law of variable proportions. When marginal cost is below the average cost (either AVC or AC), the average cost must be falling. Conversely, when marginal cost is above the average cost, the average cost must be rising. Logically, for the average cost to switch from falling to rising, the marginal cost curve must intersect the average cost curve precisely at its lowest point, which represents the point of maximum productive efficiency for that cost measure. Therefore, the short-run MC curve always intersects both the AVC curve and the AC curve at their respective minimum points.

The incorrect option is 1: AFC and AVC.
While the MC curve cuts the AVC curve at its minimum point, it does not cut the Average Fixed Cost (AFC) curve at its minimum point. The AFC curve is continuously declining as output increases (since fixed cost is spread over more units) and thus does not have a minimum point from which it rises.

The incorrect option is 3: AFC and AC.
The MC curve cuts the Average Total Cost (AC) curve at its minimum point. However, as explained above, the MC curve never cuts the Average Fixed Cost (AFC) curve at a minimum point, because the AFC curve continually falls and approaches zero but never increases.

The incorrect option is 4: TC and AC.
The MC curve cuts the Average Total Cost (AC) curve at its minimum point. However, the Marginal Cost (MC) is derived from Total Cost (TC), but the MC curve does not intersect the Total Cost (TC) curve at its minimum point, as the TC curve continually rises with output. The minimum point of the TC curve occurs at zero output, where TC equals Total Fixed Cost.