Cross-Price Elasticity of Demand: Definition and Formula

Cross-price elasticity, also called cross-price elasticity of demand or XED for short, is a microeconomic tool that businesses use to observe the relationship in quantitative demand between goods. Specifically, cross-price elasticity of demand measures the responsiveness of the demand of one good in relation to the increased demand or price of another good. This tool can help businesses to analyze the relationship between goods as prices and demand change to calculate the effect on consumption levels.

In order to calculate cross-price elasticity of demand, you’ll need to find the demand and price changes for the goods you’re comparing. You can calculate these adjustments by finding the difference between the new and old quantity and price values with the following price and demand formulas.

The formula for percent change in demand quantity is:

(New Quantity – Initial Quantity) / Initial Quantity

The formula for percent change in price is:

(New Price – Initial Price) / Initial price

Once you have these two values, you can enter them into the cross-price elasticity of demand formula:

Cross-price Elasticity of Demand (XED) = Percentage Change in Quantity Demanded of Product A / Percentage Change in Price of Product B

Comparing the cross-price elasticity of products helps elucidate their relationship to one another. Here are three different types of goods and what their cross-price elasticity reflects.

• Complementary goods: These are closely associated products, such as chips and salsa. If the price of chips increases, its consumption might decrease. This might complement a lower demand for salsa since consumers often associate the product with chips, even if there’s been no price increase for salsa. Complementary goods always have a negative cross-price elasticity.
• Substitute goods: Substitute cross-price elasticity of demand refers to the relationship between two products that are close substitutes as they have the same function or purpose. If the price of Chips A increases, for example, then this may be reflected in the quantity demand increase for Chips B. Substitute goods always have a cross-price elasticity of zero or more.
• Unrelated goods: Unrelated or independent are terms that refer to a scenario in which two goods have a cross-price elasticity coefficient of zero. This means that analysis shows no relationship in consumption or demand trends. As such, a price change for one product is not likely to affect the demand of the other.

Consider the demand and price relationships of the following complementary, substitute, and unrelated goods when entered in the cross-price elasticity formula:

• Complementary goods: If the percentage change in the quantity of demanded salsa is -15%, and the percentage change in the price of chips is 10%, the cross-price elasticity coefficient is -1.5. The negative number indicates a complementary relationship between salsa and chips suggests that people are less likely to purchase salsa if the price of chips increases. A business that sells both salsa and chips would need to weigh the added income of more expensive chips against the loss of income from decreased salsa sales.
• Substitute goods: If the percentage change in the quantity of demanded Chips A is 20%, and the percentage change in the price of Chips B is 10%, the cross-price elasticity coefficient is two (2). The positive result for the substitute items suggests that the demand for Chips A increases as the price of Chips B increases. This is because consumers are more likely to switch to the more cost-effective option.
• Unrelated goods: If the percentage change in the quantity of demanded salsa is 10%, and the percentage change in the price of guacamole is 10%, the cross-price elasticity coefficient is zero (0). Unrelated items show no effect on the price of one product on the demand for another. In the case of salsa and guacamole, consumer demand for salsa is unaffected by the price change of guacamole. As such, price and demand of either item are irrelevant to each other, and the demand curve is represented as a flat line.

Cross-price elasticity can yield observational relationships that help businesses develop better sales strategies. A small business owner can use cross-price elasticity to analyze how much revenue a product generates in relation to another depending on the price level. Businesses and economists can also identify any products that don’t have a substitute or complementary good, which allows for greater pricing flexibility. It's also a useful tool in the broader understanding of supply and demand.

Cross-price elasticity can also help businesses identify potential threats or opportunities. If a product doesn’t have any current substitutes from another business, then it’s important to watch for any new products that may have a substituting relationship. Likewise, your business can identify other businesses’ goods with little competition or complementary products to determine whether new product launches or business expansion might be a good strategy.

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