Cross-Elasticity of Demand

Finally, let’s address the third kind of elasticity, which is referred to as cross-elasticity of demand. Cross-elasticity refers to cross-comparing two different products (it’s the only elasticity formula where we compare two different products).

The formula is as follows:

Cross-Elasticity of Demand = % Change in Quantity Demanded for Product B / % Change in Price for Product A

The goal here is to determine whether we have substitute goods or complementary goods. Let’s consider two examples to understand this concept better.

First, let’s examine an example of two substitute goods. Imagine two different cell phones from two distinct companies. When people buy a cell phone, they generally buy one or the other. They might purchase a cell phone from company A, or they might buy a cell phone from company B. Initially, we observe that product A increases its price by 20%. As the demand curve indicates, when the price increases, the quantity demanded decreases. Now, fewer people want product A because the price increased. We find that Product B’s quantity demanded actually increased by 10%. This suggests that since fewer people wanted product A and those people instead chose product B.

According to the formula, the 20% increase in price for product A resulted in a 10% increase in quantity demanded for Product B, giving us a 0.5 cross-elasticity of demand. Similar to the income elasticity of demand, a positive value indicates that we have two substitute goods, and a negative value means that we have two complementary goods.

Next, let’s consider an example of two complementary goods, hamburgers and hamburger buns. Complementary goods are two items that people often buy together. Assume that the price of hamburgers increases by 16%. Naturally, the quantity demanded for hamburgers will decrease, but we’re interested in the impact this has on product B, the hamburger buns.

The price increase of hamburgers will cause the quantity demanded for hamburger buns to decrease. Fewer people buying hamburgers means fewer hamburger buns are being purchased. In the formula, we notice a 16% price increase for the hamburgers and a 10% decrease in the quantity demanded for the hamburger buns. The cross elasticity of demand is therefore -0.625 (-10%/16%). As it’s negative, we conclude that these are two complementary goods.

Study Tip: A Positive Cross-Elasticity of Demand = Substitute Goods; A Negative Cross-Elasticity of Demand = Complementary Goods