Average Product vs Average Variable Cost
Average Product and Average Variable 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 Variable Cost is the variable 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 calculated by dividing total variable cost by quantity of output. Average variable cost typically declines at first due to increasing efficiency, then rises due to diminishing marginal returns.
Average Product vs Average Variable Cost: The Same Fact With a Wage In Between
| Average Product | Average Variable Cost | |
|---|---|---|
| What is divided by what | Output divided by units of the variable input | Variable cost divided by units of output |
| Units of the answer | Units of output per worker | Dollars per unit of output |
| Does an input price appear | No, it is a purely physical relationship | Yes, the wage is built into every value |
| The link between them | Multiply it by average variable cost and you get the wage | Equals the wage divided by average product |
| Direction as the variable input rises | Rises, peaks, then falls | Falls, bottoms out, then rises, the mirror image |
| Effect of a wage increase | No effect at any output | Rises in the same proportion as the wage |
| Decision it feeds | Hiring and productivity comparisons | The short-run shutdown rule, price against minimum average variable cost |
Average variable cost is just the wage divided by average product
With labor as the only variable input, variable cost is the wage multiplied by the number of workers, so average variable cost is the wage times labor divided by output. Flip the last fraction: labor divided by output is the reciprocal of average product, which makes average variable cost equal to the wage divided by average product. The two are one fact read from opposite ends. Set the wage at 60 per worker and take output of 6, 20, 36, 48 and 50 as labor rises from one worker to five. Average product runs 6, 10, 12, 12 and 10. Average variable cost runs 10, 6, 5, 5 and 6, and each of those equals 60 divided by the matching average product. Average product peaks at 12 while average variable cost bottoms at 5 at the very same point, which is no coincidence, because dividing a constant by a number at its maximum returns a result at its minimum. Marginal product for the fourth worker is 12, equal to average product there, and marginal cost at that output is 60 divided by 12, or 5, equal to average variable cost. Every relationship on the cost side is a relabeled version of one on the production side.
Which table you are handed tells you which one is being tested
A question that gives a labor column and an output column with no dollar figures anywhere is testing the production side, and average product is output divided by labor. A question that gives output and a total variable cost column is testing the cost side, and average variable cost is variable cost divided by output. Confusing the denominators is the most common slip, since dividing output by output, or cost by workers, produces a number that looks reasonable and answers nothing. The second slip is applying the wrong rule. The shutdown decision compares price with minimum average variable cost and never with average product, because average product is measured in units of output while price is measured in dollars, so the comparison is not even dimensionally legal. When a free-response question walks a firm from a production table to a shutdown decision, the wage is the bridge you are expected to cross, and writing average variable cost as the wage divided by average product collapses two questions into one. Practice the mechanics separately at /calculate/average-product and /calculate/average-variable-cost.
Frequently asked questions
How is average variable cost related to average product?
Average variable cost equals the wage divided by average product when labor is the only variable input. The two curves are mirror images, so as average product rises average variable cost falls, and average product reaches its maximum at exactly the output where average variable cost reaches its minimum. Multiplying average product by average variable cost returns the wage itself.
Does a wage increase change average product?
Average product does not change when the wage changes, because average product counts physical output per worker and contains no prices. A higher wage raises average variable cost and marginal cost at every output, and it raises the minimum value of average variable cost, but it leaves the labor level and the output at which that minimum occurs exactly where they were.
Why does average variable cost hit its minimum where average product peaks?
Average variable cost equals a constant wage divided by average product, so the smallest value of the ratio occurs at the largest value of the denominator. When average product is at its maximum, each unit of output is absorbing the least labor possible, which means it carries the least wage cost. The same logic links marginal cost and marginal product, so marginal cost bottoms out where marginal product peaks.
Live Production Costs graph. Drag the curves, or open the full version.
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