# Cross Price Elasticity Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jul 04, 2022

This cross-price elasticity calculator helps you determine the correlation between the price of one product and the quantity sold of a different product. Thanks to this tool, you can immediately tell whether two products are substitute goods, complementary goods, or maybe entirely uncorrelated products.

In this article, we will provide you with a cross-price elasticity formula and show you an example of step-by-step calculations.

Once you have learned how to calculate the cross-price elasticity of demand, we recommend looking at the optimal price calculator.

Also, you may try other elasticity-related tools, such as:

## What is the cross-price elasticity of demand?

As mentioned before, the cross-price elasticity measures how the demand for a product (let's call it product B) changes if we change the price of product A. At first glance, the concept sounds a bit complicated, but we'll clarify it with a simple example.

Imagine that you are the owner of a company that produces both coffee capsule machines and coffee capsules. Until now, you sold the coffee machine for $120. You decide to drastically decrease the price to$80.

Now, let's analyze what will happen with the demand for coffee capsules. As you could expect, the price drop will cause an increase in the quantity of sold machines. More customers will need your coffee capsules, so the demand for them will increase, too!

This concept is similar to the price elasticity of demand – make sure to check it out, too!

## Cross price elasticity formula

Now that we know what this metric shows, it's time to learn how to calculate it. All you have to do is apply the following cross-price elasticity formula:

elasticity = (price₁A + price₂A) / (quantity₁B + quantity₂B) × ΔquantityB / ΔpriceA

where:

• price₁A – Initial price of product A;
• price₂A – Final price of product A;
• ΔpriceA – Change in price of product A;
• quantity₁B – Initial demand for product B;
• quantity₂B – Final demand for product B; and
• ΔquantityB – Change in demand for product B.

## Understanding the results

You can get one of three results: a cross-price elasticity coefficient that is positive, negative, or equal to zero.

A positive elasticity is characteristic for substitute goods. It means that as the price of product A increases, the demand for product B increases, too. For example, this can be true for butter and margarine; once the price of butter goes up, more people opt for margarine, increasing the demand. This phenomenon is especially visible in situations in which only two competitors try to monopolize the market.

A negative elasticity is characteristic for complementary goods. When the price of product A increases, the demand for product B decreases. A good example would be the coffee machine and capsules situation described earlier. If you increased the price of the coffee machine, fewer people would be inclined to buy the capsules, hence decreasing the demand.

If the elasticity is equal or very close to zero, it means that the two products are uncorrelated. The change in the price of product A does not influence the demand for product B.

## How to calculate cross-price elasticity?

If you're still unsure if you understand how the cross-price elasticity works, take a look at the example below.

1. Choose your product A and its initial price. Let's say the product is Coca-Cola, sold at $0.69 per can. 2. Choose product B and the initial quantity sold. We can take Pepsi as product B - they sell 680 million cans per day in America only. 3. In this step, choose the final price of product B. Let's say that Coca-Cola decided to decrease the price to$0.59.

4. Observe how the demand for Pepsi cans changed. Let's assume it decreased to 600 million cans.

5. Now, all you have to do is apply the cross-price elasticity formula:

elasticity = (price₁A + price₂A) / (quantity₁B + quantity₂B) × ΔquantityB / ΔpriceA

elasticity = ($0.69 +$0.59) / (680 mln + 600 mln) × 80 mln / $0.10 elasticity =$1.28 / 1280 mln × 80 mln / $0.10 elasticity = ($1.28 / $0.10) × 80 mln / 1280 mln elasticity = 12.8 × 0.0625 elasticity = 0.8 6. The elasticity is equal to 0.8. It is a positive value, meaning that Coca-Cola and Pepsi are substitute goods. Bogna Szyk At time point 1 Price of product A$
Demand for product B
At time point 2
Price of product A
\$
Demand for product B
Cross price elasticity
Elasticity
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