Average Product vs Average Total Cost
Average Product and Average Total Cost are two Production & Costs concepts in AP Economics that students often mix up. Average Product is the total output produced per unit of a variable input, typically labor. Average Total Cost is the total cost per unit of output produced. Here is how they compare side by side.
It is found by dividing total product by the quantity of the variable input used. Average product rises when marginal product is above it and falls when marginal product is below it.
It is found by dividing total cost by the quantity of output. Average total cost includes both average fixed and average variable costs and typically forms a U-shaped curve due to spreading fixed costs and diminishing returns.
Average Product vs ATC: Output per Worker and Cost per Unit
| Average Product | Average Total Cost | |
|---|---|---|
| Direction of the ratio | Output on top, input on the bottom | Dollars on top, output on the bottom |
| Units | Units of output per worker | Dollars per unit of output |
| Shape as the firm expands | Rises, then falls | Falls, then rises |
| Plotted against | The number of workers | Output |
| Fixed costs | Absent; only the variable input appears | Included, through average fixed cost |
| Exact link between them | The wage divided by average product gives average variable cost | That average variable cost plus average fixed cost |
| Effect of a wage increase | Unchanged; technology did not change | Shifts up at every output |
Average product is the flipped version of average variable cost, not of ATC
Turn average product upside down, multiply by the wage, and average variable cost appears, which is why those two curves mirror each other while average total cost does not. Take a bakery paying 30 per worker with fixed costs of 48. One worker produces 6 loaves, two produce 16, three produce 21 and four produce 24, so average product runs 6, 8, 7 and 6. Average variable cost is the wage divided by average product: 5, then 3.75, then about 4.29, then 5 again. Average product peaks with the second worker at 16 loaves, and average variable cost bottoms at that same output. Average total cost does not. At 16 loaves it is 108 divided by 16, or 6.75; at 21 loaves it is 138 divided by 21, or about 6.57. Cost per loaf is still falling after productivity has turned down, because average fixed cost dropped from 3 to about 2.29 across that stretch. The ratio is worked at /calculate/average-product and its flipped partner at /calculate/average-variable-cost.
A wage rise moves average total cost and leaves average product untouched
Average product is a fact about technology and average total cost is a fact about dollars, so a change in prices alone moves one and not the other. Keep the bakery's output figures and raise the wage from 30 to 45. Two workers still produce 16 loaves, so average product is still 8. Variable cost becomes 90, average variable cost becomes 5.625, and average total cost climbs from 6.75 to 8.625. Not one entry in the production table moved. The reverse works too: a better oven that lifts output per worker cuts average variable cost with no wage changing at all. Exam questions exploit this by describing a change and asking which curves shift. Higher input prices shift the cost curves and leave the product curves alone, while better technology or better trained workers shift the product curves up and pull the cost curves down. Watch the axes as well, since average product is plotted against workers and average total cost against output, so the hump and the dip do not line up on the page even when they correspond.
Frequently asked questions
Why is average variable cost the wage divided by average product?
Average product is output divided by workers, and average variable cost is the wage bill divided by output. Write the wage bill as the wage times the number of workers, and the worker count cancels, leaving the wage divided by average product. A wage of 30 with average product of 8 therefore gives average variable cost of 3.75. The result holds only when labor is the sole variable input and every worker earns the same wage.
Does average product peak where average total cost is lowest?
No. Peak average product lines up with the minimum of average variable cost, not average total cost. Average total cost keeps falling past that point because average fixed cost is still dropping fast enough to offset the rise in average variable cost, so its minimum sits at a larger output. In the bakery figures above, average product peaks at 16 loaves while average total cost is still falling at 21.
Does a higher wage lower average product?
No. Average product measures physical output per worker and knows nothing about what workers are paid. A wage increase raises average variable cost and average total cost at every output while leaving the production table, marginal product and average product exactly where they were. Mixing the two up is how students end up claiming that a pay rise makes workers less productive, when the model says only that labor became more expensive.
Live Production Costs graph. Drag the curves, or open the full version.
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