# Cross-Price Elasticity of Demand

## The cross-price elasticity of demand measures the change in demand for one good in response to a change in price of another good.

#### Key Points

• Complementary goods have a negative cross-price elasticity: as the price of one good increases, the demand for the second good decreases.

• Substitute goods have a positive cross-price elasticity: as the price of one good increases, the demand for the other good increases.

• Independent goods have a cross-price elasticity of zero: as the price of one good increases, the demand for the second good is unchanged.

#### Terms

• A good with a negative cross elasticity of demand, meaning the good's demand is increased when the price of another good is decreased.

• A good with a positive cross elasticity of demand, meaning the good's demand is increased when the price of another is increased.

#### Figures

1. ##### Complements

Two goods that complement each other have a negative cross elasticity of demand: as the price of good Y rises, the demand for good X falls.

2. ##### Substitutes

Two goods that are substitutes have a positive cross elasticity of demand: as the price of good Y rises, the demand for good X rises.

3. ##### Independent

Two goods that are independent have a zero cross elasticity of demand: as the price of good Y rises, the demand for good X stays constant.

The cross-price elasticity of demand shows the relationship between two goods or services. More specifically, it captures the responsiveness of the quantity demanded of one good to a change in price of another good. Cross-Price Elasticity of Demand (EA,B) is calculated with the following formula:

$E_{A,B} = \frac { \% Change\; in\; Quantity\; Demanded\; for\; Good\; A }{ \%\; Change\; in\; Price\; of\; Good\; B }$

The cross-price elasticity may be a positive or negative value, depending on whether the goods are complements or substitutes. If two products are complements, an increase in demand for one is accompanied by an increase in the quantity demanded of the other. For example, an increase in demand for cars will lead to an increase in demand for fuel. If the price of the complement falls, the quantity demanded of the other good will increase. The value of the cross-price elasticity for complementary goods will thus be negative (Figure 1).

A positive cross-price elasticity value indicates that the two goods are substitutes. For substitute goods, as the price of one good rises, the demand for the substitute good increases. For example, if the price of coffee increases, consumers may purchase less coffee and more tea. Conversely, the demand for a substitute good falls when the price of another good is decreased. In the case of perfect substitutes, the cross elasticity of demand will be equal to positive infinity (Figure 2).

Two goods may also be independent of each other. In this instance, if the price of one good changes, demand for the other good will stay constant. For independent goods, the cross-price elasticity of demand is zero (Figure 3): the change in the price of one good with not be reflected in the quantity demanded of the other.

#### Key Term Glossary

Complement
A good with a negative cross elasticity of demand, meaning the good's demand is increased when the price of another good is decreased.
##### Appears in these related concepts:
consumer
An individual who trades money for goods.
##### Appears in these related concepts:
demand
The desire to purchase goods and services.
##### Appears in these related concepts:
elasticities
Elasticity is the ratio of the percentage change in one variable to the percentage change in another variable. It is a tool for measuring the responsiveness of a function to changes in parameters in a unitless way.
##### Appears in these related concepts:
elasticity
The sensitivity of changes in a quantity with respect to changes in another quantity.
##### Appears in these related concepts:
goods
That which is produced, then traded, bought, or sold, and finally consumed.
##### Appears in these related concepts:
perfect substitute
Goods that have a constant marginal rate of substitution are perfect substitutes.
##### Appears in this related concept:
price
The cost required to gain possession of something.
##### Appears in these related concepts:
Price
The quantity of payment or compensation given by one party to another in return for goods or services.
##### Appears in these related concepts:
price elasticity
A measure of how a product's demand and supply will change if you adjust its price.
##### Appears in these related concepts:
Substitute
A good with a positive cross elasticity of demand, meaning the good's demand is increased when the price of another is increased.
##### Appears in these related concepts:
Substitute Good
A good that fulfills a consumer need in a way that is similar to another good.
##### Appears in this related concept:
value
The amount (of money or goods or services) that is considered to be a fair equivalent for something else.