What this calculator does
Cross-price elasticity of demand measures how the quantity demanded of one good responds when the price of a different good changes, rather than when its own price changes. It answers a specific question: if good B gets more expensive, does demand for good A rise, fall, or stay put?
This is a genuinely different calculation from the elasticity of a good's own price and demand. A positive cross-price elasticity points to substitute goods, such as two brands of the same product, where a price rise in one pushes buyers toward the other. A negative value points to complementary goods, such as a product and an accessory that is normally bought alongside it, where a price rise in one drags down demand for the other too.
The formula
Work out the percentage change in the quantity demanded of good A, and separately the percentage change in the price of good B. Cross-price elasticity is the first divided by the second. The sign of the result, not just its size, is the important part: positive means substitutes, negative means complements, and a value near zero means the two goods are largely unrelated.
| Term | Meaning |
|---|---|
| Good A | The good whose change in quantity demanded is being measured. |
| Good B | The good whose price changed, triggering the response in good A. |
| Cross-price elasticity | (% change in quantity demanded of A) ÷ (% change in price of B). Positive values indicate substitutes, negative values indicate complements. |
The inputs explained
| Field | What to enter |
|---|---|
| Good A: original quantity demanded | The quantity of good A demanded before the price change in good B. |
| Good A: new quantity demanded | The quantity of good A demanded after the price change in good B. |
| Good B: original price ($) | The original price of good B, before the change. |
| Good B: new price ($) | The new price of good B, after the change. |
When to use it
Checking whether two products are substitutes
If raising the price of one brand of a product visibly lifts sales of a competing brand, a positive cross-price elasticity confirms and quantifies that substitute relationship rather than relying on a hunch.
Checking whether two products are complements
If a price rise on one product (such as a games console) is followed by falling demand for a related product normally bought alongside it (such as its games), a negative cross-price elasticity confirms that complementary relationship.
Setting pricing strategy across a product range
A retailer or manufacturer stocking related products can use cross-price elasticity to anticipate how a price change on one item is likely to shift demand for others in the range, before making the change.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How cross-price elasticity changes with the size of the price change in good B
A fixed rise in good A's quantity demanded, from 100 to 120 units, against a range of price rises in good B from a $10 starting price.
| New price of good B | Cross-price elasticity of demand |
|---|---|
| $11.00 | 2.000 |
| $12.00 | 1.000 |
| $13.00 | 0.667 |
| $15.00 | 0.400 |
| $18.00 | 0.250 |
| $20.00 | 0.200 |
How cross-price elasticity changes when good B gets cheaper instead of more expensive
A fixed $10 starting price for good B, falling to a range of lower prices, against a fixed fall in demand for good A from 100 to 80 units.
| New price of good B | Cross-price elasticity of demand |
|---|---|
| $9.00 | 2.000 |
| $8.00 | 1.000 |
| $7.00 | 0.667 |
| $6.00 | 0.500 |
| $5.00 | 0.400 |
| $4.00 | 0.333 |
Questions
How is this different from the price elasticity of demand calculator?
The price elasticity of demand calculator measures how a good's own price affects its own quantity demanded. This calculator measures a cross effect: how a price change in one good affects demand for a separate, different good.
What does a positive result mean?
A positive cross-price elasticity means the two goods are substitutes: when good B becomes more expensive, buyers shift toward good A instead, increasing demand for it.
What does a negative result mean?
A negative cross-price elasticity means the two goods are complements: they tend to be used together, so a price rise in good B (making it less attractive to buy) drags down demand for good A as well.
What if the result is very close to zero?
A cross-price elasticity near zero suggests the two goods have little or no relationship in the eyes of buyers; a price change in one is not meaningfully shifting demand for the other.
For how a good's own price affects its own demand, see the price elasticity of demand calculator, or the supply-side equivalent at the price elasticity of supply calculator.