## What Is Cross Elasticity of Demand?

The cross elasticity of demand is an economic concept that measures the responsiveness in the quantity demanded of one good when the price for another good changes. Also called cross-price elasticity of demand, this measurement is calculated by taking the percentage change in the quantity demanded of one good and dividing it by the percentage change in the price of the other good.

### Key Takeaways

- The cross elasticity of demand is an economic concept that measures the responsiveness in the quantity demanded of one good when the price for another good changes.
- The cross elasticity of demand for substitute goods is always positive because the demand for one good increases when the price for the substitute good increases.
- Alternatively, the cross elasticity of demand for complementary goods is negative.

In economics, the elasticity of demand refers to how sensitive the demand for a product is to changes in price of another product.

#### Cross Elasticity of Demand

## Cross Elasticity Demand Formula

$\begin{aligned} &E_{xy} = \frac {\text{Percentage Change in Quantity of X} }{ \text{Percentage Change in Price of Y} } \\ &\phantom{ E_{xy} } = \frac { \frac { \displaystyle \Delta Q_x }{ \displaystyle Q_x } }{ \frac { \displaystyle \Delta P_y }{ \displaystyle P_y } } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ Q_x } \times \frac {P_y }{ \Delta P_y } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ \Delta P_y } \times \frac {P_y }{ Q_x } \\ &\textbf{where:} \\ &Q_x = \text{Quantity of good X} \\ &P_y = \text{Price of good Y} \\ &\Delta = \text{Change} \\ \end{aligned}$

## Explaining Cross Elasticity of Demand

### Substitute Goods

The cross elasticity of demand for substitute goods is always positive because the demand for one good increases when the price for the substitute good increases. For example, if the price of coffee increases, the quantity demanded for tea (a substitute beverage) increases as consumers switch to a less expensive yet substitutable alternative. This is reflected in the cross elasticity of demand formula, as both the numerator (percentage change in the demand of tea) and denominator (the price of coffee) show positive increases.

Items with a coefficient of 0 are unrelated items and are goods independent of each other. Items may be weak substitutes, in which the two products have a positive but low cross elasticity of demand. This is often the case for different product substitutes, such as tea versus coffee. Items that are strong substitutes have a higher cross-elasticity of demand. Consider different brands of tea; a price increase in one company’s green tea has a higher impact on another company’s green tea demand.

### Complementary Goods

Alternatively, the cross elasticity of demand for complementary goods is negative. As the price for one item increases, an item closely associated with that item and necessary for its consumption decreases because the demand for the main good has also dropped.

For example, if the price of coffee increases, the quantity demanded for coffee stir sticks drops as consumers are drinking less coffee and need to purchase fewer sticks. In the formula, the numerator (quantity demanded of stir sticks) is negative and the denominator (the price of coffee) is positive. This results in a negative cross elasticity.

Toothpaste is an example of a substitute good; if the price of one brand of toothpaste increases, the demand for a competitor's brand of toothpaste increases in turn.

## Usefulness of Cross Elasticity of Demand

Companies utilize cross-elasticity of demand to establish prices to sell their goods. Products with no substitutes have the ability to be sold at higher prices because there is no cross-elasticity of demand to consider. However, incremental price changes to goods with substitutes are analyzed to determine the appropriate level of demand desired and the associated price of the good.

Additionally, complementary goods are strategically priced based on cross-elasticity of demand. For example, printers may be sold at a loss with the understanding that the demand for future complementary goods, such as printer ink, should increase.