{
  "id": "marginal-product",
  "version": "6b114aa52033",
  "status": "published",
  "name": "Marginal Product Calculator",
  "question": "How much is the marginal product?",
  "summary": "Computes the marginal product of labor, the change in total output divided by the change in labor, and the average product of labor.",
  "category": "finance",
  "subcategory": "business",
  "url": "https://www.acalculator.org/finance/marginal-product-calculator",
  "markdown": "https://www.acalculator.org/finance/marginal-product-calculator.md",
  "kind": "function",
  "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)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "l1": {
        "title": "Workers at the start",
        "description": "Units of labor at the start: workers, or hours of work.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "q1": {
        "title": "Total output at the start",
        "description": "Units produced with the starting labor.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "l2": {
        "title": "Workers after the change",
        "description": "Units of labor after adding or removing workers.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "q2": {
        "title": "Total output after the change",
        "description": "Units produced with the new labor.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "mp": {
      "label": "Marginal product of labor",
      "description": "Change in total output ÷ change in labor: the output of each extra worker.",
      "format": "number"
    },
    "dOutput": {
      "label": "Change in total output",
      "description": "New output − starting output.",
      "format": "number"
    },
    "dLabor": {
      "label": "Change in labor",
      "description": "New labor − starting labor.",
      "format": "number"
    },
    "average": {
      "label": "Average product after the change",
      "description": "New total output ÷ new labor, when labor is more than 0.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "l1": 2,
      "q1": 10,
      "l2": 3,
      "q2": 12
    },
    "outputs": {
      "mp": 2,
      "dOutput": 2,
      "dLabor": 1,
      "average": 4
    },
    "text": "With labor going from 2 to 3, total output changes by 2: a marginal product of 2 per unit of labor."
  },
  "examples": [
    {
      "given": {
        "l1": 2,
        "q1": 10,
        "l2": 3,
        "q2": 12
      },
      "expect": {
        "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"
    },
    {
      "given": {
        "l1": 1,
        "q1": 4,
        "l2": 2,
        "q2": 10
      },
      "expect": {
        "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"
    },
    {
      "given": {
        "l1": 4,
        "q1": 13,
        "l2": 5,
        "q2": 13
      },
      "expect": {
        "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"
    },
    {
      "given": {
        "l1": 2.5,
        "q1": 17.5,
        "l2": 4,
        "q2": 25.3
      },
      "expect": {
        "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; hand calculation in content.mdx: (25.3 − 17.5) ÷ (4 − 2.5) = 7.8 ÷ 1.5 = 5.2; 25.3 ÷ 4 = 6.325"
    }
  ],
  "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)"
  ],
  "related": [
    "marginal-cost",
    "marginal-revenue",
    "variable-cost",
    "marginal-benefit"
  ],
  "changelog": []
}