Marginal-Average Rule
What is 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.
Marginal-Average Rule: a worked example
Track a bakery's cost table. At 4 cakes total cost is 80 dollars, so average total cost is 80 over 4, or 20 dollars. The fifth cake carries a marginal cost of 14 dollars. Total cost becomes 94 dollars and average total cost becomes 94 over 5, or 18.80 dollars. The average fell because the new cake cost less than the old average and dragged it down. Now the sixth cake costs 20 dollars at the margin. Total cost rises to 114 dollars and average total cost becomes 114 over 6, or 19 dollars. The average rose because 20 dollars sits above the 18.80 average. Notice that marginal cost never had to fall for the average to fall, and never had to rise for the average to rise. Only its position relative to the average mattered.
The mistake students make with marginal-average rule
Students assume a rising marginal cost curve must be dragging average total cost up with it. Marginal cost typically starts rising well before the minimum of ATC, and average total cost keeps falling the entire time marginal cost sits below it. The related drawing error is sketching the marginal cost curve so it cuts ATC on the downward slope, or at the minimum of MC itself. Force the crossing to land exactly at the lowest point of ATC, and remember that MC passes through minimum AVC first, at a smaller quantity, because AVC lies below ATC.
Marginal-Average Rule questions
Why does marginal cost cross ATC at its minimum point?
Marginal cost crosses average total cost exactly where ATC stops falling and starts rising, which is its minimum. While marginal cost sits below the average, each extra unit costs less than the running average and pulls it down. Once marginal cost climbs above the average, each extra unit pulls it up. The one quantity where the average is neither pulled down nor pushed up is where marginal equals average, so the curves have to meet there.
Does the marginal-average rule apply to average fixed cost?
Average fixed cost is the one average the rule never touches. Total fixed cost stays constant as output grows, so an extra unit adds nothing to it and there is no marginal fixed cost curve that could cross AFC. Average fixed cost simply falls toward zero as the same fixed cost is spread over more units. The rule governs average total cost and average variable cost, and marginal cost cuts each of those at its minimum point.
Does the marginal-average rule work for marginal product?
Marginal product and average product follow the identical pattern. When an extra worker produces more than the current average, average product rises, and when the extra worker produces less, average product falls, so the marginal product curve cuts average product at its maximum. Costs and products are mirror images here: marginal cost cuts an average cost curve at a minimum, while marginal product cuts average product at a maximum.
Formula / Example
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