Cross-Price Elasticity of Demand: Videos & Practice Problems

Cross-price elasticity of demand measures how the quantity demanded of one good responds to a price change in another good. It helps determine if goods are substitutes, complements, or unrelated. The formula is:

$\frac{\mathrm{\Delta Q_d}/\mathrm{Q_d}}{\mathrm{\Delta P_y}/\mathrm{P_y}}$

Where $\mathrm{\Delta Q_d}$ is the change in quantity demanded of Good X, $\mathrm{Q_d}$ is the initial quantity demanded of Good X, $\mathrm{\Delta P_y}$ is the change in price of Good Y, and $\mathrm{P_y}$ is the initial price of Good Y. A positive result indicates substitutes, a negative result indicates complements, and a zero result indicates unrelated goods.

The sign of the cross-price elasticity of demand indicates the relationship between two goods. A positive cross-price elasticity suggests that the goods are substitutes, meaning that an increase in the price of one good leads to an increase in the quantity demanded of the other. A negative cross-price elasticity indicates that the goods are complements, meaning that an increase in the price of one good leads to a decrease in the quantity demanded of the other. If the cross-price elasticity is zero, the goods are unrelated, meaning that a price change in one good does not affect the quantity demanded of the other.

Sure! Let's say the price of tennis rackets increases from $45 to $55, and as a result, the quantity demanded of tennis balls decreases from 21,000 to 19,000. First, calculate the percentage change in quantity demanded and price:

$\frac{(\mathrm{21,000}-\mathrm{19,000})}{\mathrm{21,000}}=\; -0.095$

$\frac{(55-45)}{45}=\; 0.222$

Then, divide the percentage change in quantity demanded by the percentage change in price:

$\frac{-0.095}{0.222}=\; -0.43$

The cross-price elasticity of demand is -0.43, indicating that tennis rackets and tennis balls are complements.

Real-world examples of substitutes include tea and coffee, where an increase in the price of coffee may lead to an increase in the demand for tea. Another example is butter and margarine. For complements, consider smartphones and apps; an increase in the price of smartphones may decrease the demand for apps. Another example is cars and gasoline; if the price of cars increases, the demand for gasoline may decrease as fewer people buy cars.

Cross-price elasticity of demand is important because it helps businesses and policymakers understand the relationships between different goods. For businesses, knowing whether products are substitutes or complements can inform pricing strategies, marketing, and product development. For policymakers, understanding these relationships can help in assessing the impact of taxes, subsidies, and regulations on different markets. It also aids in predicting consumer behavior and market dynamics, which is crucial for making informed economic decisions.