How to Use the Marginal-Average Rule
The marginal-average rule says an average falls when the marginal value is below it and rises when the marginal value is above it, so MC cuts ATC and AVC at their minimum points.
The Marginal-Average Rule formula
Calculator
Enter total cost, quantity and the next unit's marginal cost to see which way the average moves.
Everything the firm spends at the output level you are starting from.
Units produced at that starting point, before the next one is made.
What that one extra unit adds to total cost.
Adding the next unit moves the average to $19, which is the rule stated as a number.
- Average total cost now
- $20
- Change in ATC
- −$1
- Which way the average moves
- ATC falls
- Marginal cost that leaves ATC unchanged
- $20
Total cost spread over the units made so far is $20 each.
One more unit moves average total cost by −$1, and the gap between MC and ATC is what sets that size.
Marginal cost of $10 against an average of $20 pulls the average in that direction, whatever MC is doing on its own.
Only a marginal cost of exactly $20 holds the average flat, which is the output where MC crosses ATC at its minimum.
How to calculate Marginal-Average Rule, step by step
- 1Find the average you are starting from. Divide total cost by quantity: ATC = TC ÷ Q. This is the average the next unit is about to pull on.
- 2Read the marginal cost of the next unit. Marginal cost is what that one unit alone adds to total cost, taken from the cost table or from MC = ΔTC ÷ ΔQ.
- 3Compare the marginal with the average. A marginal cost below the current ATC drags the average down, and a marginal cost above it pushes the average up. The size of the gap sets how far the average moves.
- 4Recompute the average one unit later. New ATC = (TC + MC) ÷ (Q + 1), which confirms the direction with a number instead of a rule of thumb.
- 5Locate the minimum of the average curve. The average stops falling only where MC equals ATC, which is exactly why the MC curve cuts ATC and AVC at their lowest points.
Worked example: Marginal-Average Rule
Total cost is $180 at 9 units, so ATC = 180 ÷ 9 = $20. The 10th unit costs $10 to make, and since that marginal cost sits below the $20 average, ATC has to fall. Checking it: new total cost = 180 + 10 = $190, so new ATC = 190 ÷ 10 = $19, a fall of $1. Had the 10th unit cost $20, exactly the old average, ATC would have stayed at $20, the flat bottom of the curve where MC crosses ATC.
Marginal-Average Rule questions
Why does marginal cost cross ATC at its minimum?
Average total cost keeps falling while MC is below it and starts rising once MC is above it. The turning point is the single output where MC equals ATC, so the crossing has to sit at the lowest point of the average curve.
Does the marginal-average rule apply to average variable cost too?
Yes. MC pulls AVC down while it is below AVC and pushes it up once it is above, so MC also cuts AVC at its minimum. AVC reaches its minimum at a smaller output than ATC does, because ATC still has falling average fixed cost working on it.
Can average total cost fall while marginal cost is rising?
Yes, and it usually does. What matters is whether MC is below ATC, not whether MC is heading up. A marginal cost of $10 that is climbing still pulls a $20 average down.
Is this the same rule that links marginal product to average product?
The arithmetic is identical, only the direction flips. Marginal product pulls average product up while it is above it and down once it is below, so MP cuts AP at its highest point rather than its lowest.
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