{
  "id": "mpc",
  "version": "e8590e1f28e3",
  "status": "published",
  "name": "MPC Calculator",
  "question": "What is the MPC?",
  "summary": "Computes the marginal propensity to consume (MPC) from changes in consumption and income, with the marginal propensity to save and the spending multiplier.",
  "category": "finance",
  "subcategory": "business",
  "url": "https://www.acalculator.org/finance/mpc-calculator",
  "markdown": "https://www.acalculator.org/finance/mpc-calculator.md",
  "kind": "function",
  "method": "MPC = change in consumption ÷ change in income. MPS = 1 − MPC. Spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)), shown when the denominator is more than 0. Change in GDP = multiplier × change in spending.",
  "assumptions": [
    "Consumption and income change over the same period; income is disposable (after-tax) income for the MPC.",
    "An empty tax rate or MPI counts as 0, which gives the simple multiplier 1 ÷ (1 − MPC) = 1 ÷ MPS.",
    "Arithmetic is exact on the typed decimals; the MPC and MPS show up to 6 decimals (6 significant figures below 0.0001 in size), the multiplier to 2 and money to the cent."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "dc": {
        "title": "Change in consumption",
        "description": "How much consumer spending rose (or fell, as a negative number).",
        "type": "number",
        "x-unit": "USD",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "dy": {
        "title": "Change in income",
        "description": "How much disposable income rose (or fell, as a negative number) at the same time.",
        "type": "number",
        "x-unit": "USD",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "tax": {
        "title": "Tax rate",
        "description": "The share of extra income taken in taxes, for the multiplier. Optional; empty means 0%.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "mpi": {
        "title": "Marginal propensity to import (MPI)",
        "description": "The share of extra income spent on imports, from 0 to 1, for the multiplier. Optional; empty means 0.",
        "type": "number",
        "minimum": 0,
        "maximum": 1
      },
      "spend": {
        "title": "Change in spending",
        "description": "A change in government spending or investment, to see its effect on GDP through the multiplier. Optional.",
        "type": "number",
        "x-unit": "USD",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "mpc": {
      "label": "Marginal propensity to consume (MPC)",
      "description": "Change in consumption ÷ change in income.",
      "format": "number"
    },
    "mps": {
      "label": "Marginal propensity to save (MPS)",
      "description": "1 − MPC.",
      "format": "number"
    },
    "multiplier": {
      "label": "Spending multiplier",
      "description": "1 ÷ (1 − (MPC × (1 − tax rate) − MPI)); with no taxes or imports, 1 ÷ (1 − MPC).",
      "format": "number"
    },
    "gdp": {
      "label": "Change in GDP",
      "description": "Spending multiplier × change in spending.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "dc": 800,
      "dy": 1000
    },
    "outputs": {
      "mpc": 0.8,
      "mps": 0.2,
      "multiplier": 5
    },
    "text": "Consumption changes by $800.00 when income changes by $1,000.00: an MPC of 0.8 and an MPS of 0.2."
  },
  "examples": [
    {
      "given": {
        "dc": 800,
        "dy": 1000
      },
      "expect": {
        "mpc": 0.8,
        "mps": 0.2,
        "multiplier": 5
      },
      "source": "OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model: 800 ÷ 1,000 = 0.8; 1 − 0.8 = 0.2; hand calculation in content.mdx: 1 ÷ (1 − 0.8) = 5"
    },
    {
      "given": {
        "dc": 700,
        "dy": 1000,
        "tax": 10,
        "mpi": 0.1,
        "spend": 100
      },
      "expect": {
        "mpc": 0.7,
        "mps": 0.3,
        "multiplier": 2.127659574468085,
        "gdp": 212.7659574468085
      },
      "source": "OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model: 1 ÷ (1 − (0.7 × 0.9 − 0.1)) = 1 ÷ 0.47 = 2.13 (exact 100/47); 100 ÷ 0.47 = 212.77"
    },
    {
      "given": {
        "dc": -450,
        "dy": -600
      },
      "expect": {
        "mpc": 0.75,
        "mps": 0.25,
        "multiplier": 4
      },
      "source": "OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model; hand calculation in content.mdx: −450 ÷ −600 = 0.75; 1 ÷ 0.25 = 4"
    },
    {
      "given": {
        "dc": 2345.67,
        "dy": 3000,
        "tax": 22.5,
        "mpi": 0.15,
        "spend": 1000000
      },
      "expect": {
        "mpc": 0.78189,
        "mps": 0.21811,
        "multiplier": 1.838116188243317,
        "gdp": 1838116.188243317
      },
      "source": "OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model (MPC is the share of an additional dollar of income spent on consumption; MPC + MPS = 1; when income rises by $1,000 and the MPC is 0.8, consumption rises by $800; spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)): MPS 30%, tax rate 10% and MPI 10% give 1 ÷ 0.47 = 2.13, and $100 of spending raises GDP by $213). https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model; hand calculation in content.mdx: 2,345.67 ÷ 3,000 = 0.78189; 1 − (0.78189 × 0.775 − 0.15) = 0.54403525; 1 ÷ 0.54403525 = 1.8381 (Python Fraction)"
    }
  ],
  "sources": [
    "OpenStax, Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model: the marginal propensity to consume is the share of the additional dollar of income devoted to consumption, the marginal propensity to save the share saved, MPC + MPS = 1 (when income rises by $1,000 with an MPC of 0.8, consumption rises by $800); spending multiplier = 1 ÷ (1 − (MPC × (1 − tax rate) − MPI)), with MPS 30%, a 10% tax rate and an MPI of 10% giving 1 ÷ 0.47 = 2.13, so $100 of spending raises GDP by $213. https://openstax.org/books/principles-macroeconomics-3e/pages/b-the-expenditure-output-model (retrieved 2026-10-19)"
  ],
  "related": [
    "gdp",
    "real-interest-rate",
    "inflation",
    "marginal-benefit"
  ],
  "changelog": []
}