Cross Price Elasticity: Definition, Formula for Calculation, and Example

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. It's also referred to as 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.

Cross Elasticity of Demand Formula

 $\begin{aligned} &E_{xy} = \frac {\text{Percentage Change in Quantity of X} }{ \text{Percentage Change in Price of Y} } \\ &\phantom{ E_{xy} } = \frac { \frac { \displaystyle \Delta Q_x }{ \displaystyle Q_x } }{ \frac { \displaystyle \Delta P_y }{ \displaystyle P_y } } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ Q_x } \times \frac {P_y }{ \Delta P_y } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ \Delta P_y } \times \frac {P_y }{ Q_x } \\ &\textbf{where:} \\ &Q_x = \text{Quantity of good X} \\ &P_y = \text{Price of good Y} \\ &\Delta = \text{Change} \\ \end{aligned}$​Exy​=Percentage Change in Price of YPercentage Change in Quantity of X​Exy​=Py​ΔPy​​Qx​ΔQx​​​Exy​=Qx​ΔQx​​×ΔPy​Py​​Exy​=ΔPy​ΔQx​​×Qx​Py​​where:Qx​=Quantity of good XPy​=Price of good YΔ=Change​

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. 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. You can do this by dividing the final and initial prices by the total sum of the last and initial prices.
5. Calculate the cross price elasticity of demand by dividing the percentage change in quantity by the percentage change in price.
   

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. Cross elasticity is one of the main types of demand elasticity.

You can use the 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.

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.

The quantity demanded 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 denominator (the price of coffee) show positive increases.

Items with a coefficient 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 higher impact on another company’s green tea demand.

Complementary Goods

The cross elasticity of demand for complementary goods is negative. An item closely associated with that item and necessary for its consumption decreases as the price for one 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.

The Usefulness of Cross Elasticity of Demand

Companies use the cross elasticity of demand to establish prices to sell their goods. Products with no substitutes can be sold at higher prices because there's no cross elasticity of demand to consider. But 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 it wants to make more in profits 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.

The Bottom Line

Prices and demand often go hand-in-hand in economics. Economic theory generally 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 taking the percentage change in the quantity demanded of one good by the percentage change in price for another good.