# What is the cross price elasticity?

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.

- Page: https://www.acalculator.org/finance/cross-price-elasticity-calculator
- JSON spec: https://www.acalculator.org/finance/cross-price-elasticity-calculator.json
- Version: 71626c65ea01

## Default answer

Example with the default inputs (Starting price of good B $4.00, New price of good B $5.00, Starting quantity of good A 200, New quantity of good A 240): The cross price elasticity is 0.8182: the goods are substitutes.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| p1 | Starting price of good B | The price of the other good before the change. |
| p2 | New price of good B | The price of the other good after the change. |
| q1 | Starting quantity of good A | How many units of good A buyers want before the change. |
| q2 | New quantity of good A | How many units of good A buyers want after the change. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| elasticity | Cross price elasticity | % change in the quantity of good A ÷ % change in the price of good B (midpoint method), with its sign. |
| relation | The goods are | Substitutes when the elasticity is positive, complements when it is negative. |
| quantityChange | % change in quantity of good A | (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) × 100. |
| priceChange | % change in price of good B | (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2) × 100. |

## 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.

## Worked examples

1. p1 = $4.00, p2 = $5.00, q1 = 200, q2 = 240 gives elasticity = 0.8182, relation = substitutes, quantityChange = 18.18%, priceChange = 22.22%. Source: 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).
2. p1 = $2.50, p2 = $3.00, q1 = 100, q2 = 80 gives elasticity = −1.2222, relation = complements, quantityChange = −22.22%, priceChange = 18.18%. Source: 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).
3. p1 = $4.00, p2 = $5.00, q1 = 50, q2 = 50 gives elasticity = 0, relation = neither: the quantity did not change. Source: 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).

## FAQ

### What is cross price elasticity of demand?

It measures how the quantity of one good responds to a change in the price of another: the percent change in the quantity of good A divided by the percent change in the price of good B.

### How do I calculate cross price elasticity?

If coffee rises from $4 to $5 and tea sales rise from 200 to 240, the % change in tea is 40 ÷ 220 = 18.18% and the % change in coffee’s price is 1 ÷ 4.5 = 22.22%. The cross price elasticity is 18.18 ÷ 22.22 = 0.8182.

### What does a positive cross price elasticity mean?

The goods are substitutes: when one gets more expensive, buyers want more of the other.

### What does a negative cross price elasticity mean?

The goods are complements: they are used together, so when one gets more expensive, buyers want less of the other.

### Why does this page use the midpoint method?

Each percent change is measured against the average of the two values, so a move from A to B gives the same result as a move from B to A. OpenStax defines the method in section 5.1, and this page applies it to the formula in section 5.4.

### Why is the sign kept here?

The sign is the point of this measure, since it separates substitutes from complements. So unlike price elasticity of demand, it is not shown as an absolute value.

## 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