{
  "id": "marginal-utility",
  "version": "fc825d26831e",
  "status": "published",
  "name": "Marginal Utility Calculator",
  "question": "What is the marginal utility?",
  "summary": "Computes marginal utility, the change in total utility divided by the change in quantity, and marginal utility per dollar when a price is given.",
  "category": "finance",
  "subcategory": "business",
  "url": "https://www.acalculator.org/finance/marginal-utility-calculator",
  "markdown": "https://www.acalculator.org/finance/marginal-utility-calculator.md",
  "kind": "function",
  "method": "Marginal utility = (TU₂ − TU₁) ÷ (Q₂ − Q₁), where TU is total utility at quantity Q. Marginal utility per dollar = marginal utility ÷ price.",
  "assumptions": [
    "Total utility is measured in utils, a made-up unit of satisfaction; only the differences matter.",
    "Over more than one unit, the result is the average marginal utility of each extra unit in that range.",
    "Arithmetic is exact on the typed decimals; marginal utility shows up to 6 decimals (6 significant figures below 0.0001 in size) and per dollar up to 4."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "q1": {
        "title": "Starting quantity",
        "description": "Units consumed at the start.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "u1": {
        "title": "Total utility at the start",
        "description": "The total satisfaction (utils) from the starting quantity.",
        "type": "number",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "q2": {
        "title": "New quantity",
        "description": "Units consumed after the change.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "u2": {
        "title": "Total utility at the new quantity",
        "description": "The total satisfaction (utils) from the new quantity.",
        "type": "number",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "price": {
        "title": "Price of one unit",
        "description": "The price of the good, for marginal utility per dollar. Optional.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "mu": {
      "label": "Marginal utility",
      "description": "Change in total utility ÷ change in quantity: the utility of each extra unit.",
      "format": "number"
    },
    "dUtility": {
      "label": "Change in total utility",
      "description": "New total utility − starting total utility.",
      "format": "number"
    },
    "dQuantity": {
      "label": "Change in quantity",
      "description": "New quantity − starting quantity.",
      "format": "number"
    },
    "perDollar": {
      "label": "Marginal utility per dollar",
      "description": "Marginal utility ÷ price, when a price is given.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "q1": 3,
      "u1": 63,
      "q2": 4,
      "u2": 81,
      "price": 14
    },
    "outputs": {
      "mu": 18,
      "dUtility": 18,
      "dQuantity": 1,
      "perDollar": 1.2857142857142858
    },
    "text": "From a quantity of 3 to 4, total utility changes by 18: a marginal utility of 18 per unit."
  },
  "examples": [
    {
      "given": {
        "q1": 3,
        "u1": 63,
        "q2": 4,
        "u2": 81,
        "price": 14
      },
      "expect": {
        "mu": 18,
        "dUtility": 18,
        "dQuantity": 1,
        "perDollar": 1.2857142857142858
      },
      "source": "OpenStax, Principles of Microeconomics 3e, 6.1 Consumption Choices (MU = change in total utility ÷ change in quantity; Table 6.2: José’s T-shirts give total utility 22, 43, 63, 81 for 1 to 4 shirts and movies 16, 31, 45 for 1 to 3; Table 6.5: marginal utility per dollar at $14 a T-shirt and $7 a movie). https://openstax.org/books/principles-microeconomics-3e/pages/6-1-consumption-choices: 81 − 63 = 18; 18 ÷ 14 = 1.29 (OpenStax shows 1.3)"
    },
    {
      "given": {
        "q1": 1,
        "u1": 16,
        "q2": 2,
        "u2": 31,
        "price": 7
      },
      "expect": {
        "mu": 15,
        "perDollar": 2.142857142857143
      },
      "source": "OpenStax, Principles of Microeconomics 3e, 6.1 Consumption Choices (MU = change in total utility ÷ change in quantity; Table 6.2: José’s T-shirts give total utility 22, 43, 63, 81 for 1 to 4 shirts and movies 16, 31, 45 for 1 to 3; Table 6.5: marginal utility per dollar at $14 a T-shirt and $7 a movie). https://openstax.org/books/principles-microeconomics-3e/pages/6-1-consumption-choices: 31 − 16 = 15; 15 ÷ 7 = 2.14"
    },
    {
      "given": {
        "q1": 0,
        "u1": 0,
        "q2": 1,
        "u2": 22,
        "price": 14
      },
      "expect": {
        "mu": 22,
        "perDollar": 1.5714285714285714
      },
      "source": "OpenStax, Principles of Microeconomics 3e, 6.1 Consumption Choices (MU = change in total utility ÷ change in quantity; Table 6.2: José’s T-shirts give total utility 22, 43, 63, 81 for 1 to 4 shirts and movies 16, 31, 45 for 1 to 3; Table 6.5: marginal utility per dollar at $14 a T-shirt and $7 a movie). https://openstax.org/books/principles-microeconomics-3e/pages/6-1-consumption-choices: 22 − 0 = 22; 22 ÷ 14 = 1.57 (OpenStax shows 1.6)"
    },
    {
      "given": {
        "q1": 2.5,
        "u1": 40.25,
        "q2": 4,
        "u2": 52
      },
      "expect": {
        "mu": 7.833333333333333,
        "dUtility": 11.75,
        "dQuantity": 1.5
      },
      "source": "OpenStax, Principles of Microeconomics 3e, 6.1 Consumption Choices (MU = change in total utility ÷ change in quantity; Table 6.2: José’s T-shirts give total utility 22, 43, 63, 81 for 1 to 4 shirts and movies 16, 31, 45 for 1 to 3; Table 6.5: marginal utility per dollar at $14 a T-shirt and $7 a movie). https://openstax.org/books/principles-microeconomics-3e/pages/6-1-consumption-choices; hand calculation in content.mdx: (52 − 40.25) ÷ (4 − 2.5) = 11.75 ÷ 1.5 = 7.8333…"
    }
  ],
  "sources": [
    "OpenStax, Principles of Microeconomics 3e, 6.1 Consumption Choices: marginal utility is the additional utility provided by one additional unit of consumption, MU = change in total utility ÷ change in quantity; the law of diminishing marginal utility; Table 6.2 total and marginal utility of José’s T-shirts (22, 43, 63, 81, …) and movies (16, 31, 45, …); Table 6.5 marginal utility per dollar with T-shirts at $14 and movies at $7. https://openstax.org/books/principles-microeconomics-3e/pages/6-1-consumption-choices (retrieved 2026-10-19)"
  ],
  "related": [
    "marginal-benefit",
    "consumer-surplus",
    "price-elasticity-of-demand",
    "marginal-revenue"
  ],
  "changelog": []
}