{
  "id": "income-elasticity",
  "version": "43463fb850ea",
  "status": "published",
  "name": "Income Elasticity of Demand Calculator",
  "question": "What is income elasticity of demand?",
  "summary": "Finds the income elasticity of demand by the midpoint method from two incomes and the quantities demanded at each, and says whether the good is normal or inferior.",
  "category": "finance",
  "subcategory": "business",
  "url": "https://www.acalculator.org/finance/income-elasticity-calculator",
  "markdown": "https://www.acalculator.org/finance/income-elasticity-calculator.md",
  "kind": "function",
  "method": "Elasticity = (% change in quantity demanded) ÷ (% change in income), where each % change = (new − old) ÷ ((new + old) ÷ 2) × 100 (the midpoint method).",
  "assumptions": [
    "The midpoint (arc) method, so going from A to B gives the same elasticity as going from B to A.",
    "Everything else that affects demand stays the same between the two points.",
    "Incomes are at least $0.01; quantities are 0 or more, not both 0."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "i1": {
        "title": "Starting income",
        "description": "The income before the change.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0.01,
        "maximum": 1000000000000
      },
      "i2": {
        "title": "New income",
        "description": "The income after the change.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0.01,
        "maximum": 1000000000000
      },
      "q1": {
        "title": "Starting quantity",
        "description": "How many units buyers want at the starting income.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "q2": {
        "title": "New quantity",
        "description": "How many units buyers want at the new income.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "elasticity": {
      "label": "Income elasticity of demand",
      "description": "% change in quantity demanded ÷ % change in income (midpoint method), with its sign.",
      "format": "number"
    },
    "good": {
      "label": "The good is",
      "description": "A normal good when the elasticity is positive, an inferior good when it is negative.",
      "format": "text"
    },
    "quantityChange": {
      "label": "% change in quantity",
      "description": "(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) × 100.",
      "format": "percent"
    },
    "incomeChange": {
      "label": "% change in income",
      "description": "(I₂ − I₁) ÷ ((I₁ + I₂) ÷ 2) × 100.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "i1": 40000,
      "i2": 50000,
      "q1": 20,
      "q2": 24
    },
    "outputs": {
      "elasticity": 0.8181818181818182,
      "good": "a normal good",
      "quantityChange": 18.181818181818183,
      "incomeChange": 22.22222222222222
    },
    "text": "The income elasticity of demand is 0.8182: this is a normal good."
  },
  "examples": [
    {
      "given": {
        "i1": 40000,
        "i2": 50000,
        "q1": 20,
        "q2": 24
      },
      "expect": {
        "elasticity": 0.8181818181818182,
        "good": "a normal good",
        "quantityChange": 18.181818181818183,
        "incomeChange": 22.22222222222222
      },
      "source": "hand calculation in content.mdx; OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; normal good positive, inferior good negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)"
    },
    {
      "given": {
        "i1": 40000,
        "i2": 50000,
        "q1": 50,
        "q2": 45
      },
      "expect": {
        "elasticity": -0.47368421052631576,
        "good": "an inferior good",
        "quantityChange": -10.526315789473685
      },
      "source": "hand calculation in content.mdx; OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; normal good positive, inferior good negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)"
    },
    {
      "given": {
        "i1": 40000,
        "i2": 50000,
        "q1": 30,
        "q2": 30
      },
      "expect": {
        "elasticity": 0,
        "good": "neither: the quantity did not change"
      },
      "source": "hand calculation in content.mdx: no change in quantity; OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)"
    }
  ],
  "sources": [
    "OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; a normal good is positive, an inferior good negative). Retrieved 2026-11-01. https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price",
    "OpenStax, Principles of Economics 3e, section 5.1 Price Elasticity of Demand and Price Elasticity of Supply (the midpoint method). Retrieved 2026-11-01. https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply"
  ],
  "related": [
    "price-elasticity-of-demand",
    "cross-price-elasticity",
    "price-elasticity-of-supply"
  ],
  "changelog": []
}