# How much is the marginal product?

Computes the marginal product of labor, the change in total output divided by the change in labor, and the average product of labor.

- Page: https://www.acalculator.org/finance/marginal-product-calculator
- JSON spec: https://www.acalculator.org/finance/marginal-product-calculator.json
- Version: 6b114aa52033

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| l1 | Workers at the start | Units of labor at the start: workers, or hours of work. |
| q1 | Total output at the start | Units produced with the starting labor. |
| l2 | Workers after the change | Units of labor after adding or removing workers. |
| q2 | Total output after the change | Units produced with the new labor. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mp | Marginal product of labor | Change in total output ÷ change in labor: the output of each extra worker. |
| dOutput | Change in total output | New output − starting output. |
| dLabor | Change in labor | New labor − starting labor. |
| average | Average product after the change | New total output ÷ new labor, when labor is more than 0. |

## Method

Marginal product of labor = (Q₂ − Q₁) ÷ (L₂ − L₁), where Q is total output with L units of labor. Average product = Q₂ ÷ L₂.

## Assumptions

- 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

1. l1 = 2, q1 = 10, l2 = 3, q2 = 12 gives mp = 2, dOutput = 2, dLabor = 1, average = 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.
2. l1 = 1, q1 = 4, l2 = 2, q2 = 10 gives mp = 6, average = 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.
3. l1 = 4, q1 = 13, l2 = 5, q2 = 13 gives mp = 0, average = 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.
4. l1 = 2.5, q1 = 17.5, l2 = 4, q2 = 25.3 gives mp = 5.2, dOutput = 7.8, dLabor = 1.5, average = 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.

## FAQ

### 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.

## Sources

- OpenStax, Principles of Microeconomics 3e, 7.2 Production in the Short Run: marginal product is the additional output of one more worker, MP = ΔTP ÷ ΔL; Table 7.2 short run production function for trees (1 to 5 lumberjacks: 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 (retrieved 2026-10-19)
- Principles of Economics v2.0 (Saylor Academy open textbook, CC BY-NC-SA 3.0), 8.1 Production Choices and Costs: The Short Run: the marginal product of a variable factor is the amount by which output rises with an additional unit of it, MP = ΔQ ÷ ΔL; the average product of labor is the ratio of output to the number of units of labor, Q ÷ L. https://saylordotorg.github.io/text_principles-of-economics-v2.0/s11-01-production-choices-and-costs-t.html (retrieved 2026-10-19)