{
  "id": "cross-price-elasticity",
  "version": "71626c65ea01",
  "status": "published",
  "name": "Cross Price Elasticity Calculator",
  "question": "What is the cross price elasticity?",
  "summary": "Finds the cross price elasticity of demand by the midpoint method from two prices of one good and the quantities of another, and says whether the goods are substitutes or complements.",
  "category": "finance",
  "subcategory": "business",
  "url": "https://www.acalculator.org/finance/cross-price-elasticity-calculator",
  "markdown": "https://www.acalculator.org/finance/cross-price-elasticity-calculator.md",
  "kind": "function",
  "method": "Elasticity = (% change in quantity of good A) ÷ (% change in price of good B), 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 for good A stays the same between the two points.",
    "Prices 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": {
      "p1": {
        "title": "Starting price of good B",
        "description": "The price of the other good before the change.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0.01,
        "maximum": 1000000000000
      },
      "p2": {
        "title": "New price of good B",
        "description": "The price of the other good after the change.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0.01,
        "maximum": 1000000000000
      },
      "q1": {
        "title": "Starting quantity of good A",
        "description": "How many units of good A buyers want before the change.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      },
      "q2": {
        "title": "New quantity of good A",
        "description": "How many units of good A buyers want after the change.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "elasticity": {
      "label": "Cross price elasticity",
      "description": "% change in the quantity of good A ÷ % change in the price of good B (midpoint method), with its sign.",
      "format": "number"
    },
    "relation": {
      "label": "The goods are",
      "description": "Substitutes when the elasticity is positive, complements when it is negative.",
      "format": "text"
    },
    "quantityChange": {
      "label": "% change in quantity of good A",
      "description": "(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) × 100.",
      "format": "percent"
    },
    "priceChange": {
      "label": "% change in price of good B",
      "description": "(P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2) × 100.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "p1": 4,
      "p2": 5,
      "q1": 200,
      "q2": 240
    },
    "outputs": {
      "elasticity": 0.8181818181818182,
      "relation": "substitutes",
      "quantityChange": 18.181818181818183,
      "priceChange": 22.22222222222222
    },
    "text": "The cross price elasticity is 0.8182: the goods are substitutes."
  },
  "examples": [
    {
      "given": {
        "p1": 4,
        "p2": 5,
        "q1": 200,
        "q2": 240
      },
      "expect": {
        "elasticity": 0.8181818181818182,
        "relation": "substitutes",
        "quantityChange": 18.181818181818183,
        "priceChange": 22.22222222222222
      },
      "source": "hand calculation in content.mdx; OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (cross-price elasticity of demand = % change in Qd of good A ÷ % change in price of good B; substitutes positive, complements 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": {
        "p1": 2.5,
        "p2": 3,
        "q1": 100,
        "q2": 80
      },
      "expect": {
        "elasticity": -1.2222222222222223,
        "relation": "complements",
        "quantityChange": -22.22222222222222,
        "priceChange": 18.181818181818183
      },
      "source": "hand calculation in content.mdx; OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (cross-price elasticity of demand = % change in Qd of good A ÷ % change in price of good B; substitutes positive, complements 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": {
        "p1": 4,
        "p2": 5,
        "q1": 50,
        "q2": 50
      },
      "expect": {
        "elasticity": 0,
        "relation": "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 (cross-price elasticity of demand = % change in Qd of good A ÷ % change in price of good B; substitutes positive, complements 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",
    "income-elasticity",
    "price-elasticity-of-supply"
  ],
  "changelog": []
}