A bicycle repair shop with one mechanic services 8 bikes per day. Adding a second mechanic raises output to 18 bikes — the second mechanic added 10 bikes (marginal product = 10), and average output per mechanic is now 9. Add a third: total output is 25, the third mechanic added 7 (marginal product = 7), average output is 8.3. The marginal product is falling — diminishing returns are setting in — and as it falls below the average, the average also falls. This relationship between the margin and the average is one of the most reliable patterns in production economics.
The formula
Marginal Product of Labor (MPL) = ΔTotal Product ÷ ΔLabor
Average Product of Labor (APL) = Total Product ÷ Labor
For the bicycle shop:
| Workers | Total Output | MPL | APL |
|---|---|---|---|
| 1 | 8 | — | 8.0 |
| 2 | 18 | 10 | 9.0 |
| 3 | 25 | 7 | 8.3 |
| 4 | 29 | 4 | 7.3 |
MPL is falling after worker 2. Once MPL falls below APL (between workers 2 and 3), APL begins to fall.
Reading the result
The relationship between marginal and average is a mathematical identity: the marginal pulls the average toward it. When MPL > APL, each new hire raises the average (they contribute more than the average worker). When MPL < APL, each new hire lowers the average. The crossover is the maximum of APL.
This relationship governs the shape of cost curves. Because MPL typically first rises then falls (as workers specialize and then experience diminishing returns), marginal cost first falls then rises — producing the U-shaped cost curve that underpins firm output decisions.
Worked example
A firm is deciding whether to hire a fifth assembly worker at $200 per shift. The fifth worker would produce 12 additional units per shift (MPL = 12). Each unit sells for $25. The value of the marginal product (VMP = MPL × Price = 12 × $25 = $300) exceeds the wage ($200). Hire the worker — the additional revenue exceeds the additional cost.
The sixth worker would produce only 8 additional units (MPL = 8 after diminishing returns). VMP = 8 × $25 = $200 = wage. Hire or don't hire — it's exactly break-even. A seventh worker (MPL = 5) yields VMP = $125 < $200 wage. Don't hire.
The Bureau of Labor Statistics Productivity and Costs data tracks output per worker-hour — the aggregate expression of average product across the U.S. economy. Quarterly productivity releases showing whether output per worker hour is rising or falling are one of the most closely watched economic indicators because they directly track the average product of labor economy-wide.
Where it's used
Marginal product analysis determines the demand for labor in competitive markets. Firms hire until VMP = wage — the labor demand condition. When MPL is high (skilled, productive workers), firms can afford to pay high wages. When MPL is low, wages are constrained. The entire relationship between education, productivity, and wages runs through marginal product: higher education increases MPL, which raises VMP, which supports higher wages in a competitive labor market.
