# Cross Price Elasticity of Demand

## Cross Price Elasticity of Demand Definition

Cross Price Elasticity of Demand (XED) measures the responsiveness of demand for one good to the change in the price of another good. It is the ratio of the percentage change in quantity demanded of Good X to the percentage change in the price of Good Y.

For businesses, XED is an important strategic tool. This elasticity measure can help determine whether or not it is a good move to increase or decrease selling prices, or to substitute one product for another to generate greater revenues.

There are three types of cross-price elasticity of demand: substitute goods, complementary goods, and unrelated products.

## Types of Cross Elasticity of Demand

### Cross Price Elasticity of Demand for Substitutes

When the cross-price elasticity of demand for product A relative to a change in the price of product B is positive, it means that the quantity demanded of product A has increased in response to a rise in the price of product B. Many consumers have switched from consuming product B to consuming product A. This implies that most consumers perceive products A and B as substitutes that satisfy similar preferences.

Substitutes will always have a positive Cross Price Elasticity or greater than zero.

### Cross Price Elasticity of Demand for Complements

When the cross elasticity of demand for product A relative to a change in the price of product B is negative, it means that the quantity demanded of A has decreased relative to a rise in the price of product B. Even though the price of product A is unchanged, many consumers still decreased their consumption of it because the price increase for product B made consuming these products together more expensive. This implies that most consumers perceive products A and B as complements that are more enjoyable consumed together than consumed separately.

Complements will always have a negative Cross Price Elasticity or less than zero.

### Cross Elasticity of Demand for Unrelated

These are goods that show no relationship in consumer consumption patterns. Price changes in one product don’t affect the quantity consumed of the other product.

Unrelated goods will always have a Cross Price Elasticity of 0

## Uses of Cross Price Elasticity of Demand

Knowing a product’s cross price elasticity of demand for other related products allows a firm to better understand the market that it is serving. This firm can better identify how many competitors share the same product space in the eyes of consumers, as well as how sensitive sales revenues are to changes in the marketing strategy of complementary products outside of its own market. This kind of valuable information can reduce the firm’s exposure to financial risk. Firms use this information to develop targeted strategies that optimally respond to the price changes of both competing and complementary products.

## How to Calculate Cross Price Elasticity

Cross Price Elasticity of Demand (XED) = Percentage Change in Quantity Demanded of Good x / Percentage Change in Price of Good y

= (New Quantity Demanded of Good x – Old Quantity Demanded of Good x)/(Old Quantity Demanded of Good x) / (New Price of Good y – Old Price of Good y)/(Old Price of Good y)

This can be calculated following these simple steps:

- Calculate any percent change by taking the difference between the new value and the old value, and dividing this difference by the old value.
- For % change in Quantity (Qx) of Product X: (Qnew – Qold)/Qold
- For % change in Price (Py) of Product Y: (Pnew – Pold)/Pold
- The ratio of % change in Qx to % change in Py yields the cross price elasticity.

## Cross Price Elasticity Formula

The Cross Price Elasticity of Demand Formula is

= %∆ in Quantity Demanded of Good x / %∆ in Price of Good y

If **XED > o**, then the two goods are **substitutes**. For example: Coke and Pepsi

If **XED < o**, then they are **complements**. For example: Bread and Butter

If **XED = 0**, then they are **unrelated**. For example: Bread and Soda