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.

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

Now that you have the formula for cross price elasticity of demand, it's important to know how to use it 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. For the numerator in the formula above, calculate the percentage change in the quantity demanded of X. 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'll need to calculate the denominator, which is 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

In economics, the cross elasticity of demand refers to how sensitive the demand for a product is to changes in the price of another product. This means it determines the relationship between the quantity demanded of one good when the price for another good or product changes. Put simply, it measures how demand for one good changes when the price of another (usually related one) 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 one another or those that are complementary to one another. For substitute goods, the cross elasticity of demand remains positive, which means prices increase when demand for one good rises. Demand for complementary goods drops when the price rises for another good. This is called 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. For example, if coffee prices increase, then 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 the demand formula, as 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 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.

Usefulness of Cross Elasticity of Demand

Companies utilize the 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 the 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.

Examples of Cross Elasticity of Demand

Here are a couple of examples of how cross-price elasticity of demand works. First, let's take a look at two substitute goods. Let's consider chicken burritos from two different 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. Since most people don't want to spend the extra money and the two goods are equal substitutes, 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 are affected by the cross-price elasticity of demand. Consider burgers and fries, which aren't necessarily related but tend to go hand-in-hand. When people eat burgers, they also tend to eat fries. If the price drops for burgers, demand for fries may increase.

The Bottom Line

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