How much is the marginal product?
Enter the number of workers and the total output before and after a change. The marginal product calculator divides the change in output by the change in labor, and shows the average product at the new level.
- Marginal product of labor
- 2
With labor going from 2 to 3, total output changes by 2: a marginal product of 2 per unit of labor.
- Change in total output
- 2
- Change in labor
- 1
- Average product after the change
- 4
Marginal product of labor: 2. With labor going from 2 to 3, total output changes by 2: a marginal product of 2 per unit of labor.
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How to calculate
Computes the marginal product of labor, the change in total output divided by the change in labor, and the average product of labor.
Example with the default inputs (Workers at the start 2, Total output at the start 10, Workers after the change 3, Total output after the change 12): With labor going from 2 to 3, total output changes by 2: a marginal product of 2 per unit of labor.
Method: Marginal product of labor = (Q₂ − Q₁) ÷ (L₂ − L₁), where Q is total output with L units of labor. Average product = Q₂ ÷ L₂.
- Only labor changes; capital and other inputs stay fixed (the short run).
- Over more than one worker, the result is the average marginal product of each extra worker in that range.
- Arithmetic is exact on the typed decimals; results show up to 6 decimals (6 significant figures below 0.0001 in size).
Worked examples
Each example is checked against the calculator on every build.
- Workers at the start 2, Total output at the start 10, Workers after the change 3, Total output after the change 12 gives Marginal product of labor 2, Change in total output 2, Change in labor 1, Average product after the change 4.Source: OpenStax, Principles of Microeconomics 3e, 7.2 Production in the Short Run (MP = ΔTP ÷ ΔL; Table 7.2: 1 to 5 lumberjacks cut 4, 10, 12, 13 and 13 trees, marginal products 4, 6, 2, 1 and 0). https://openstax.org/books/principles-microeconomics-3e/pages/7-2-production-in-the-short-run: 12 − 10 = 2 trees; Principles of Economics v2.0 (Saylor Academy open textbook), 8.1 Production Choices and Costs: The Short Run (average product = output ÷ units of labor, Q ÷ L). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s11-01-production-choices-and-costs-t.html: 12 ÷ 3 = 4
- Workers at the start 1, Total output at the start 4, Workers after the change 2, Total output after the change 10 gives Marginal product of labor 6, Average product after the change 5.Source: OpenStax, Principles of Microeconomics 3e, 7.2 Production in the Short Run (MP = ΔTP ÷ ΔL; Table 7.2: 1 to 5 lumberjacks cut 4, 10, 12, 13 and 13 trees, marginal products 4, 6, 2, 1 and 0). https://openstax.org/books/principles-microeconomics-3e/pages/7-2-production-in-the-short-run: 10 − 4 = 6 trees; Principles of Economics v2.0 (Saylor Academy open textbook), 8.1 Production Choices and Costs: The Short Run (average product = output ÷ units of labor, Q ÷ L). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s11-01-production-choices-and-costs-t.html: 10 ÷ 2 = 5
- Workers at the start 4, Total output at the start 13, Workers after the change 5, Total output after the change 13 gives Marginal product of labor 0, Average product after the change 2.6.Source: OpenStax, Principles of Microeconomics 3e, 7.2 Production in the Short Run (MP = ΔTP ÷ ΔL; Table 7.2: 1 to 5 lumberjacks cut 4, 10, 12, 13 and 13 trees, marginal products 4, 6, 2, 1 and 0). https://openstax.org/books/principles-microeconomics-3e/pages/7-2-production-in-the-short-run: 13 − 13 = 0; Principles of Economics v2.0 (Saylor Academy open textbook), 8.1 Production Choices and Costs: The Short Run (average product = output ÷ units of labor, Q ÷ L). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s11-01-production-choices-and-costs-t.html: 13 ÷ 5 = 2.6
- Workers at the start 2.5, Total output at the start 17.5, Workers after the change 4, Total output after the change 25.3 gives Marginal product of labor 5.2, Change in total output 7.8, Change in labor 1.5, Average product after the change 6.325.Source: OpenStax, Principles of Microeconomics 3e, 7.2 Production in the Short Run (MP = ΔTP ÷ ΔL; Table 7.2: 1 to 5 lumberjacks cut 4, 10, 12, 13 and 13 trees, marginal products 4, 6, 2, 1 and 0). https://openstax.org/books/principles-microeconomics-3e/pages/7-2-production-in-the-short-run
How it works
- Change in total output = Q₂ − Q₁
- Change in labor = L₂ − L₁
- Marginal product of labor = (Q₂ − Q₁) ÷ (L₂ − L₁)
- Average product after the change = Q₂ ÷ L₂, shown when L₂ is more than 0
Rules:
- Labor and output are 0 or more, each at most 1 quadrillion. Labor may be in workers, hours or fractions of a worker.
- The two amounts of labor must differ; otherwise there is no answer.
- A result too large to show as a number gives no answer. So does a result that is not 0 but too small to show as a number.
- The arithmetic is exact on the decimals you type. Results show up to 6 decimals (6 significant figures below 0.0001 in size), rounded half away from 0.
Assumptions
- Only labor changes. Capital, land and the other inputs stay the same (the short run).
- Over a change of more than one worker, the result is the average marginal product of each extra worker in that range.
Worked examples by hand
The third lumberjack. From 2 to 3 workers, output rises from 10 to 12 trees: MP = (12 − 10) ÷ (3 − 2) = 2 trees. Average product = 12 ÷ 3 = 4 trees per worker.
The second lumberjack. MP = (10 − 4) ÷ (2 − 1) = 6; average product 10 ÷ 2 = 5.
The fifth lumberjack. Output stays at 13 trees: MP = (13 − 13) ÷ (5 − 4) = 0; average product 13 ÷ 5 = 2.6.
Part-time labor. From 2.5 to 4 workers, output rises from 17.5 to 25.3: MP = 7.8 ÷ 1.5 = 5.2; average product 25.3 ÷ 4 = 6.325.
Other questions people ask
What is marginal product?
The marginal product of labor is the extra output from one more worker (or one more hour of work), with machines, land and other inputs held fixed. It shows how much each added worker contributes.
How do I calculate the marginal product of labor?
Subtract the starting output from the new output and divide by the change in the number of workers. If 2 lumberjacks cut 10 trees and 3 cut 12, the third lumberjack’s marginal product is (12 − 10) ÷ (3 − 2) = 2 trees.
What is diminishing marginal productivity?
In the short run, with fixed equipment and space, each added worker eventually adds less output than the one before. The lumberjacks add 4, 6, 2, 1 and then 0 trees: after the second worker, marginal product falls.
What is the difference between marginal product and average product?
Average product is total output divided by the number of workers: 12 trees from 3 lumberjacks is 4 trees each. Marginal product is the output of the last worker added. While marginal product is above the average, it pulls the average up.
Can marginal product be zero or negative?
Yes. When workers crowd the fixed equipment, one more may add nothing (the fifth lumberjack adds 0 trees) or even get in the way, so output falls and marginal product is negative.
Why does marginal product matter for costs?
When each worker adds less output, each extra unit of output needs more labor, so the marginal cost of output rises. Diminishing marginal productivity is the reason marginal cost curves slope upward.