Why Marginal Cost Cuts Average Cost at Its Minimum

Think about adding a new score to a running average. If the new score is below your current average, it drags the average down. If it's above, it pulls the average up. If it equals the average, the average doesn't move at all. Marginal cost does exactly this to average total cost. Marginal cost is the cost of producing one more unit; average total cost is the cost per unit averaged over everything made so far. As long as the next unit costs less than the current average, making it lowers the average. Once the next unit costs more than the average, making it raises the average.

This means average total cost falls while marginal cost sits below it, and rises once marginal cost climbs above it. The only point where ATC is neither falling nor rising is where marginal cost equals it exactly — that's the bottom of the U-shaped ATC curve. The same logic links marginal cost to average variable cost, but AVC's minimum sits at a lower output than ATC's, because average fixed cost keeps declining as output grows and drags ATC's minimum further right.

This crossing point matters beyond cost curves alone. In a perfectly competitive market, price gets pushed toward the minimum of ATC as firms enter and exit chasing profit. The output where MC crosses ATC becomes the firm's break-even price — sell below it and every unit loses money on average, sell above it and economic profit is possible, at least until entry erodes it away.