Cross-price elasticity of demand is a way to see how the amount of one product that people want changes when the price of another product changes. This idea is very important for figuring out how people shop and how companies interact with each other.

Here’s the formula for cross-price elasticity (CPE):

$$CPE = \frac{\%\text{ Change in Quantity Demanded of Good A}}{\%\text{ Change in Price of Good B}}$$

Types of Goods

1. Substitutes: These are goods that can be used instead of each other.

   • If the price of butter goes up by 10%, and as a result, more people want margarine (let's say by 15%), then we can find the cross-price elasticity.
   • It would look like this: $$CPE = \frac{15\%}{10\%} = 1.5$$
   • This positive number shows that butter and margarine are substitutes for each other.

2. Complements: These are goods that are often used together.

   • If the price of printers goes up by 20%, and this causes the demand for ink cartridges to go down by 10%, we calculate the cross-price elasticity like this: $$CPE = \frac{-10\%}{20\%} = -0.5$$
   • This negative number tells us that printers and ink cartridges are complementary goods – when one is more expensive, the other one sells less.

Real-World Examples

• A study found that if the price of coffee goes up by 1%, the demand for tea goes up by 0.5%. This shows that coffee and tea can be substitutes.

• Another report showed that if gas prices increase by 10%, the demand for cars can drop by 3%. This shows the connection between fuels and vehicles, which are complementary goods.

Understanding cross-price elasticity helps companies and decision-makers figure out better pricing, production, and marketing strategies.