# Cross Price Elasticity: Definition, Formula, and Example

> **Definition**
>
> The cross elasticity of demand is an economic concept that measures the responsiveness of the quantity demanded of one good when the price of another good changes.

## What Is Cross Elasticity of Demand?

Cross elasticity of demand is a measurement of how much the demand for one good changes when the price of another good changes as well. Also referred to as cross price elasticity of demand, it's 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. An example is how an increase in the price of hot dogs might result in a change in demand for hot dog buns.  

### Key Takeaways

*   The cross elasticity of demand for substitute goods is always positive because demand for it rises when the price of the initial good goes up_._
*   The cross elasticity of demand for complementary goods is negative.
*   There's generally no cross elasticity of demand when dealing with unrelated goods.
*   Companies often use the cross elasticity of demand to determine and set the prices of their goods and services.  
    

![Cross Elasticity of Demand](https://www.investopedia.com/thmb/ifzYXWlhYkrfyWRLZO3i6O79Mgk=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/cross-elasticity-demand-Final-a26aada5972d4cda8fdd2c02a1f2724e.jpg)

*Businesses use cross elasticity of demand to predict how changes in prices of related goods can affect their sales. — Investopedia / Theresa Chiechi*

## Understanding Cross Elasticity of Demand

The cross elasticity of demand refers to how sensitive the demand for a product is to changes in the price of another product. It measures how demand for one good changes when the price of another typically related good does so. Cross elasticity is one of the main [types of demand elasticity](https://www.investopedia.com/ask/answers/040815/what-are-some-examples-demand-elasticity-other-price-elasticity-demand.asp).

You can use a formula to make comparisons of products that are considered perfect substitutes for each other or those that are complementary to each other. The cross elasticity of demand for substitute goods remains positive: prices increase when demand for one good rises. Demand for complementary goods drops when the price rises for another good. This is referred to as negative cross elasticity of demand.

> **Important**
>
> Unrelated products don't affect each other. An increase in the price of eggs doesn't directly relate to an increase in demand for olives.

### Substitute Goods

The cross elasticity of demand for a [substitute good](https://www.investopedia.com/terms/s/substitute.asp) is always positive because demand for it rises when the price of the initial good goes up.

The [quantity demanded](https://www.investopedia.com/terms/q/quantitydemanded.asp) for tea, a substitute beverage, increases as consumers switch to a less expensive yet substitutable alternative if coffee prices increase. This is reflected in the cross elasticity of the demand formula because both the numerator (percentage change in the demand for tea) and the denominator (the price of coffee) show positive increases.

Items with a [coefficient](https://www.investopedia.com/ask/answers/032515/what-does-it-mean-if-correlation-coefficient-positive-negative-or-zero.asp) of 0 are unrelated items. They're independent of each other. Items may be weak substitutes because the two products have a positive but low cross elasticity of demand. This is often the case for product substitutes such as tea versus coffee.

Items that are strong substitutes have a higher cross elasticity of demand, such as different brands of tea. A price increase in one company’s green tea has a more significant impact on another company’s green tea demand.

> **Fast Fact**
>
> Different brands of toothpaste are also an example of substitute goods. The demand for a competitor's brand of toothpaste increases if the price of one brand of toothpaste increases.

### Complementary Goods

The cross elasticity of demand for complementary goods is negative. The demand for an item that's closely associated with another item and necessary for its consumption decreases as the price of the other item increases because the demand for the main good has also dropped.

The quantity demanded for coffee stir sticks drops as consumers drink less coffee and purchase fewer sticks because the price of coffee has increased. 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.

## Cross Elasticity of Demand Formula

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

## How to Calculate Cross Elasticity of Demand

The next step is how to use the formula to make your calculations. Here's a step-by-step run-through of how to do so:

1.  Figure out the total quantity demanded of X and the initial price of Y.
2.  Determine the final quantity demanded of X and the ending price of Y.
3.  Calculate the percentage change in the quantity demanded of X to find the numerator. You can do this by subtracting the last and first quantities and dividing that by the total sum of the initial and final quantities.
4.  Now you must calculate the denominator: the percentage change in price. Divide the final and initial prices by the total sum of the last and initial prices.
5.  Calculate the cross price elasticity of [demand](https://www.investopedia.com/terms/d/demand.asp) by dividing the percentage change in quantity by the percentage change in price.  
    

## How Cross Elasticity of Demand Is Used

Companies use the cross elasticity of demand to establish [prices at which to sell their goods](https://www.investopedia.com/ask/answers/06/commodityprices.asp). Products with no substitutes can be sold at higher prices because there's no cross elasticity of demand to consider. Incremental price changes to goods with substitutes are analyzed to determine the appropriate level of demand desired and the associated price of the good.

Complementary goods are also strategically priced based on the cross elasticity of demand. Printers may be sold at a loss with the understanding that the demand for future complementary goods, such as printer ink, should increase.

## Examples of Cross Elasticity of Demand

Let's take a look at two substitute goods: chicken burritos from two restaurants. Suppose both restaurants sell their burritos for $6 each, but Restaurant A decides that it wants to make more in [profits](https://www.investopedia.com/terms/p/profitmargin.asp), so it raises the price to $8. Most people don't want to spend the extra money, and the two goods are equal substitutes, so there's a very good chance that demand for Restaurant B's chicken burritos will increase.  

Now let's take a look at complementary goods and how they're affected by the cross price elasticity of demand. Consider burgers and fries. They aren't necessarily related, but they tend to go hand-in-hand. People who eat burgers also tend to eat fries. Demand for fries may increase if the price drops for burgers.

## How Will I Use This in Real Life?

Consumers are constantly making choices based on the changing prices of different goods and comparing them to alternatives. You're likely to eat at other restaurants more often if your favorite restaurant raises prices, but you're more likely to order a drink if your favorite restaurant lowers the price of appetizers. Your choices demonstrate cross-price elasticity even if you're not conscious of the fact.  

## Explain Like I'm Five

Cross-price elasticity measures how a change in the price of one good affects the consumption of another good. Some goods are often consumed together, like burgers and fries or movies and popcorn. Consumers are likely to see fewer movies and, consequently, eat less popcorn if the price of movies goes up. This is an example of positive elasticity.

Some goods are considered substitutes. You might find yourself eating hamburgers more often if the price of pizza goes up. The cross elasticity is negative in this case.

## What Does a Positive Cross Elasticity of Demand Indicate?

A positive cross elasticity of demand means that the demand for Good A will increase as the price of Good B goes up. Goods A and B are good substitutes. People are happy to switch to A if B gets more expensive.

An example would be the price of milk. Consumers may switch to 2% milk if whole milk goes up in price. Whole milk becomes more in demand if 2% milk rises in price instead.

## What Does a Negative Cross Elasticity of Demand Indicate?

A negative cross elasticity of demand indicates that the demand for Good A will decrease as the price of Good B goes up. This suggests that A and B are complementary goods, such as a printer and printer toner. Demand for the printer will drop if its price goes up. Less toner will be sold as a result of fewer printers being sold.

## How Does Cross Elasticity of Demand Differ From Demand Elasticity?

Cross elasticity looks at the proportional changes in demand among two goods. [Demand elasticity](https://www.investopedia.com/terms/p/priceelasticity.asp) or price elasticity of demand looks at the change in demand of a single item as its price changes.

## How Does Cross Elasticity of Demand Differ From the Cross Elasticity of Supply?

The cross elasticity of [supply](https://www.investopedia.com/terms/s/supply.asp) measures the proportional change in the quantity supplied or produced in relation to changes in the price of a good. This is in contrast to changes in demand for two goods in response to prices.

## The Bottom Line

Prices and demand often go hand-in-hand in economics. Economic theory dictates that demand for another good generally goes up when the price of one good goes up, too. This is called the cross price elasticity of demand. You can easily calculate this figure by looking at the percentage change in the quantity demanded of one good by the percentage change in price for another good.

_**Correction—Sept. 13, 2025:** This article has been corrected to state that cross elasticity of demand is a measurement of the change in demand and the change in price between two products._  

> **Article Sources**
>
> 1.  Economicshelp.org. "[Substitute Goods](https://www.economicshelp.org/blog/glossary/substitute-goods/)."
>     
> 2.  Strictly Economics. "[Complementary Goods: Their Impact on Demand](https://strictlyeconomics.com/complementary-goods-their-impact-on-demand/)."