Q.Why does the Marginal Cost curve cut the Average Variable Cost and Average Total Cost curves at their minimum points? Also explain why it cuts AVC before it cuts AC.

It follows from how a marginal value moves an average: below the average it drags it down, above it pushes it up, so they meet at the average's lowest point; AFC falling keeps AC declining a little longer than AVC. …

The averaging principle: average variable cost and average total cost are running averages of the marginal costs of the units produced. Therefore:

• While $MC$ is below the average, each additional unit costs less than the current average, so it pulls the average down — the average curve is falling.
• While $MC$ is above the average, each additional unit costs more than the current average, so it pushes the average up — the average curve is rising.
• The average therefore stops falling and starts rising exactly when $MC$ crosses it, i.e. at the average's minimum point. This is why the U-shaped MC curve cuts both AVC and AC from below, precisely at their minimum points.

Why MC cuts AVC before AC: at every output, $AC = AVC + AFC$, so AC lies above AVC by the amount of AFC. Because AFC keeps falling as output rises, it continues to pull AC downward even after AVC has already bottomed out and begun to rise. As a result, AC reaches its minimum at a higher output than AVC does. Since MC passes through the minimum of each curve, it reaches (cuts) the minimum of AVC first and the minimum of AC afterwards. …

Saying MC cuts the averages at their maximum points, or from above — MC cuts the U-shaped AVC and AC curves from BELOW at their MINIMUM p …