How to Use the Cross-Price Elasticity Formula (With Example)

By Indeed Editorial Team

Published June 10, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Cross-price elasticity refers to how the change in the price of one product affects the demand for another. A formula is used to calculate this relationship. Using this formula can help guide you in making decisions about changing prices. In this article, we define cross-price elasticity, list different types, discuss when companies may use it, and show how to use the cross-price elasticity formula.

What is the cross-price elasticity formula?

The cross-price elasticity formula is what you can use to calculate cross-price elasticity, which measures, in percentage form, how likely it is for the demand for one product to be impacted by the change in price of another. Businesses can use this calculation to determine if it's beneficial to increase or decrease the prices of an item or change product offerings. This calculation is called cross-price elasticity of demand, represented as XED. The formula is:

Cross-price elasticity (XED) = (% Change in demand of product A) / (% Change of price of product B)

To use this formula, it's first necessary to know the percentage of change in demand for product A and the percentage of change in the price of product B. You can calculate this using the following formulas:

% Change in demand of a product = (New product quantity - Old product quantity) / (Old product quantity)

% Change in the price of a product = (New selling price - Old selling price) / (Old selling price)

Types of cross-price elasticity

There are three different types of cross-price elasticity. When you use the formula to calculate it, the results allow you to determine the type of cross-price elasticity. Types include:

Substitutes

Under cross-price elasticity, substitutes refer to products and services that are similar but may satisfy customer needs differently. For example, a rise in the price of product B might increase demand for the similar product A, motivating customers to replace product B with product A. When a substitution occurs in cross-price elasticity, it creates a result with a value above zero.

Related: What Is Macroeconomics?

Complements

Complements are the opposite of substitutes in cross-price elasticity. Complements refer to demonstrating that the two products have the most value for the customer when consumed together. For example, if there's an increase in the price of product B that results in less demand for product A, then this may indicate that customers are choosing to purchase this pair of products less frequently because they're too expensive together. When the cross-price formula is used to calculate results for a pair of products that are complements of each other, then the result is a value less than zero.

Unrelated offerings

When two products are unrelated, there's no relationship between changes in selling prices and the quantity demanded. This means that changing the selling price for one product doesn't change the demand for another product. When products are resulting in being unrelated offerings, the value is zero when using the formula.

Uses of cross-price elasticity

There are several reasons businesses and organizations may want to calculate cross-price elasticity. Companies can use this information to learn more about the market and respond effectively to consumer behaviour. In addition to learning more about the consumer base the business serves, organizations can use cross-price elasticity to:

Perform a competitive analysis

A competitive analysis helps companies to understand their competitors so that they can work to develop strategies and products that help to differentiate themselves and gain market share. Companies can use cross-price elasticity to help identify these competitors that offer similar products and services. They can then determine how the marketing strategies of their competitors are affecting their revenue.

Related: How to Write an Analysis (With Importance and Tips)

Identify and manage risk

Businesses can use cross-price elasticity calculations to identify potential risks to their revenue and financial growth. For example, these calculations can help businesses determine what may happen when the prices of complementary or competing products increase or decrease. This can help the team create effective strategies to manage risk.

Related: A Guide to Risk Management Process (With Practical Examples)

Develop marketing strategies

When a business is developing new marketing strategies, knowing the cross-price elasticity can be helpful. This is because it can help the business understand how the pricing of complementary and competitive markets impacts the demand. Businesses can then use this information to develop marketing strategies to improve demand or increase revenue.

Related: What Are Market Entry Strategies? (With Types and Tips)

How to calculate cross-price elasticity

You can use the following steps to calculate cross-price elasticity:

1. Calculate the percentage of change in the quantity of demand

First calculate the percentage of change in the quantity of demand. After calculating this, you can use it as the percentage of change of demand for product B in the cross-price formula. The formula for the percentage of change in the quantity of demand is:

% Change in demand of a product = (New product quantity - Old product quantity) / Old product quantity

For example, if the new product quantity is 3,000 and the old product quantity is 9,000, you can use the formula to find a product's percentage of change in demand:

% Change in demand = (3,000 - 9,000) / 9,000
% Change in demand = -6,000 / 9,000
% Change in demand = -0.667 or -66.7%

This indicates that the rate of consumption of the new product decreases by 66.7%.

2. Find the percentage of change in selling price

After determining the percentage of change in the price of product B for the cross-price formula, you can determine the percentage of change in the selling price for product B. The formula for this is:

% Change in the price of a product = (New selling price - Old selling price) / Old selling price

For example, if you assume that the new selling price of the product is $55 and the old selling price is $45, you can use the formula to calculate the percentage of change in the product's price:

% Change in price = (55 - 45) / 55
% Change in price = 10 / 55
% Change in price = 0.18 or 18%

This result represents that the selling price increases by 18% for the new product.

3. Use the formula to determine cross-price elasticity

After calculating the values for the percentage of change in demand for product A and the percentage of change in price for product B, you can insert these values into the formula to calculate cross-price elasticity. The formula for this is:

Cross-price elasticity (XED) = % Change in demand of product A / % Change of price of product B

Using the values for percentage of change in demand and selling price, you can calculate the cross-price elasticity:

Cross-price elasticity (XED) = -66.7% / 18%
Cross-price elasticity (XED) = -3.71

4. Examine the results to determine the type of cross-price elasticity

After determining the value of cross-price elasticity, determine the type of cross-price elasticity to gain a better understanding of your customers and the market. To do this, determine if the value is negative, positive, or zero. A negative value is a complement, a positive is similar, and a result of zero is unrelated.

The cross-price elasticity of -3.71 is a negative value, so the increase in the price of product B results in lower demand. This means that the products are complements, or designed to be purchased together. The higher price of product B makes the pair too expensive for customers to purchase, lowering demand. By lowering the price of product B, you can likely increase the demand for both products A and B together, resulting in overall higher revenue.

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