AP MicroeconomicsProduction & Costs
Marginal-Average Rule
The marginal-average rule explains that an average curve falls when marginal is below it and rises when marginal is above it, so MC cuts ATC and AVC at their minimum points.
Whenever the marginal value is below the average, it drags the average down; when marginal is above the average, it pulls the average up. This is why the marginal cost curve always intersects average total cost and average variable cost at their lowest points. It is a purely arithmetic relationship (like how a low test score pulls your GPA down) and is the reason cost curves take their characteristic shapes. The same logic links marginal product to average product.
Formula / Example
If MC < ATC, ATC falls; if MC > ATC, ATC rises; MC = ATC at min ATC (same for AVC).