# Cross-Price Elasticity

How sensitive the demand of a product is over a shift of a corresponding product price

Over 2 million + professionals use CFI to learn accounting, financial analysis, modeling and more. Unlock the essentials of corporate finance with our free resources and get an exclusive sneak peek at the first chapter of each course.

## What is Cross-Price Elasticity?

Cross-price elasticity measures how sensitive the demand of a product is over a shift of a corresponding product price. Often, in the market, some goods can relate to one another. This may mean a product’s price increase or decrease can positively or negatively affect the other product’s demand.

### Summary

• Cross-price elasticity measures how sensitive the demand of a product is over a shift of a corresponding product’s price.
• A price increase of a complementary product will lead to lower demand or negative cross-price elasticity, and a price increase in a substitute product will lead to increased demand or a positive cross-price elasticity.
• Unrelated products have zero cross-price elasticity.

### Understanding Cross-Price Elasticity

While explaining cross-price elasticity, there are three categories of product relationships to examine.

1. First, there are products that are closely related to one another – sometimes known as substitute products. These products compete for the same customers in the market.
2. Second, there are products that are consumed together. The demand for one product directly affects the consumption of related products. These products are known as complementary products.
3. The final group belongs to products that are entirely unrelated to one another. These products do not affect the consumption of one another.
4. By having a clear understanding of the concepts behind product relationships, business owners can strategically compete in their industry or stock their inventories accordingly. For example, lowering the price of printers could lead to increased purchases of toners and ink. The more printers consumers buy, the more revenues are generated by selling complementary products.

### Cross-Price Elasticity Formula

Where:

• Qx = Average quantity between the previous quantity and the changed quantity, calculated as (new quantityX + previous quantityX) / 2
• Py = Average price between the previous price and changed price, calculated as (new pricey + previous pricey) / 2
• Δ = The change of price or quantity of product X or Y

Note: In cross-price elasticity, unlike in income elasticity, the ΔQx and ΔPy are calculated by finding the averages between the change in either price or quantity demanded.

### Cross-Price Elasticity of Substitute Products

For substitute products, an increase in the price of a substitute product increases the demand for the competing product. This is often because consumers always try to maximize utility. The less they spend on something, the higher the perceived satisfaction.

Similarly, when the competing product price is reduced, the mirroring effect is depicted by an increase in demand for the substitute product. In either of these scenarios, the change will either drive a negative or a positive cross-price elasticity. For cross-price elasticity, where there is an increase in the price of the competing products, there will be a positive coefficient.

Practical Example

Two competing airlines – A and B – are a perfect example of substitute products. If Airline A decides to increase their flights’ round-trip ticket price by even a small margin, consumers will likely notice the difference. As a result, more people will opt for Airline B because it is cheaper.

### Categories of Substitute Products

Substitute products can be categorized as either close or weak.

#### Close Substitutes

A close substitute is realized when a minimal increase in price leads to a large demand increase of the substitute product. The graph below shows this interpretation.

#### Weak Substitutes

For a weak substitute, a large increase in the price of product X will lead to only a small increase in demand for product Y. See the graph below for the interpretation.

### Cross-Price Elasticity of Complementary Products

Complementary products have the opposite effect. If the price of one product increases, the demand for the complementary product decreases. To consumers, the increased joint cost will force them to buy less.

Practical Example

An example of a complementary product is an eBook reader. If the price of an eBook reader drops, the consumption of eBooks and audiobooks will increase because more consumers can afford the reader.

### Categories of Complementary Products

Complementary products can either be close or weak complements.

#### Close Complements

In the case of a strong complement product, a minimal price decrease leads to a large increase in demand for the complement product. The graph below shows this impact.

#### Weak Complements

For weak complementary products, a large price decrease leads to a small increase in demand for the complementing products. The graph below shows this shift.

### Cross-Price Elasticity of Unrelated Products

Unrelated products do not affect one another. This means the cross-effect elasticity is zero, and the graph would be represented by a vertical line.