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 or complements. The formula is:

$\frac{∆Q_1}{∆P_2}$

Where $Q_1$ is the quantity demanded of good 1 and $P_2$ is the price of good 2. A positive value indicates substitutes, while a negative value indicates complements.

The sign of cross-price elasticity of demand indicates the relationship between two goods. A positive cross-price elasticity suggests that the goods are substitutes, meaning an increase in the price of one good leads to an increase in the quantity demanded of the other. Conversely, a negative cross-price elasticity indicates that the goods are complements, meaning 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.

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

$\frac{∆Q_1}{∆P_2}=\frac{\left(19,000\; -\; 21,000\right)}{\left(55\; -\; 45\right)}=\frac{-2,000}{10}=\; -0.1$

Then, the cross-price elasticity is:

$\frac{-0.1}{0.2}=\; -0.5$

Since the result is negative, tennis rackets and tennis balls are complements.

A cross-price elasticity of demand of zero indicates that the two goods are unrelated. This means that a change in the price of one good has no effect on the quantity demanded of the other good. For example, if the price of tennis rackets changes but the quantity demanded of bread remains the same, the cross-price elasticity between tennis rackets and bread would be zero, indicating no relationship between the two goods.

Cross-price elasticity of demand helps businesses understand the relationships between products. By knowing whether goods are substitutes or complements, businesses can make informed decisions about pricing strategies, product bundling, and marketing. For example, if a company knows that two products are complements, it might bundle them together or offer discounts on one product when the other is purchased. Conversely, if products are substitutes, a business might adjust prices to remain competitive. Understanding these relationships can help maximize revenue and market share.