Cross Price Elasticity Calculator

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 the price elasticity of supply calculator and the income elasticity of demand calculator.

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 would 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 that in the price elasticity of demand calculator – make sure to check it out, too!

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.

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 of substitute goods. This means that as the price of product A increases, the demand for product B also increases. 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 of complementary goods. When the price of product A increases, the demand for product B decreases. A good example would be the situation of coffee machines and capsules 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 or unrelated. The change in the price of product A does not influence the demand for product B.

Another aspect of interpreting the result is determining the degree of response. If the absolute value of the cross-price elasticity is greater than 1, the cross-elasticity of demand is elastic. In this case, the change in the price of product A leads to a more than proportionate change in quantity demanded for product B. In other words, a change in the cost of good A has a relatively significant effect on the change in quantity demanded for good B.

Conversely, if the absolute value of the cross-price elasticity is between 1 and 0, the cross-elasticity of demand is inelastic. In this case, a change in the price of product A results in a less than proportionate change in quantity demanded for product B. In other words, a change in the price of product A has a relatively small impact on the change in quantity demanded for product B.

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.