# Cross Price Elasticity of Demand: Definition and Formula

Learn what cross price elasticity of demand means. Find out why business owners and economists like to know cross price elasticity, and discover how to calculate it. See some everyday examples.
Definition and Use
Have you ever thought about buying a gaming system and thought, ‘Wow I can’t afford the games.’ Maybe you had your eye on a certain vehicle, but learned they were expensive to work on. Have you ever gone shopping and found some suit pants or maybe it was a dress, and realized the suit coat or shoes that go along with it were too expensive to justify the purchase? All of these are everyday examples of how the price of one good influences your decision to purchase another good. The formula and term for that reasoning and logic is known as the cross price elasticity of demand.
You may remember from previous lessons and study that price elasticity of demand is a measure of how responsive the quantity demanded for a product is after a change in price. Sometimes, economists also like to know the cross price elasticity of demand which is how responsive or elastic the quantity demanded for a good is in response to a change in the price of another good. It is measured as the percentage change in demand for the first good that occurs in response to a percentage change in price of the second good. Summarized, it tells us how the price of one good can influence the sales of another good.
Cross price elasticity helps economists figure out things like how likely you are to buy the new gaming system if the price of games goes down. By calculating cross-price elasticity, we can measure the responsiveness and determine if the goods are substitutes, complements, or not related to each other. This information can help business owners and industries figure out how to price certain goods or help them project the sales impact a business may feel from price changes of other products.
From other lessons, you may remember that if two goods are substitutes (for example, chicken and red meat), we should expect to see consumers purchase more of one good when the price of its substitute increases. This results in a high positive cross price elasticity. The demand for both goods moves in opposite directions of each other.
On the other hand, if the two goods are complements (for example, peanut butter and jelly), we should see a price rise in one good cause the demand for both goods to fall. This results in a negative number or negative cross price elasticity. Likewise, if the price fell for one complement, quantity demanded for both goods should increase. The demand for both goods should move in the same direction.
Formula and Rule of Thumb
The following is the simple formula for calculating cross price elasticity of demand.
CROSS PRICE ELASTICITY OF DEMAND = % change in quantity demanded for Product A / % change in price of product B
Let’s put the formula in action. Assume the following:
Product A (butter) has a 10% positive change in quantity demanded when product B (margarine) has a positive 5% change or increase in price.
If we enter those numbers in to our formula, we see that 10% / 5% is equal to 2.
So what does that tell us? Let’s use the following rules of thumb to help us determine the relationship between the two goods.
If cross price elasticity > 0, then the two goods are substitutes
If cross price elasticity = 0, then the two goods are independent
If cross price elasticity < 0, then the two goods are complements
From this example we can see that the answer 2 tells us that butter and margarine are substitute goods for each other. When the price of margarine went up, more people switched to butter. You can increase the sales of one good, by increasing the price of the other.
Examples
Let’s look at a few more examples to really help us understand the concept and math behind cross price elasticity of demand.

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