Cross-Price Elasticity of Demand: Videos & Practice Problems

Cross price elasticity of demand measures how the quantity demanded of one good responds to the price change of another good, indicating whether they are substitutes, complements, or unrelated. The formula involves the quantity demanded of one good in the numerator and the price of another good in the denominator. A negative result indicates complements, while a positive result suggests substitutes. For example, if the price of tennis rackets rises and the quantity demanded for tennis balls falls, the cross price elasticity is negative, confirming they are complements.

Cross-Price Elasticity of Demand

The cross price elasticity of demand is a crucial concept in understanding the relationship between two goods, specifically whether they are substitutes, complements, or unrelated. This elasticity measures how the quantity demanded of one good responds to changes in the price of another good. The formula for calculating cross price elasticity of demand is given by:

\[E_{xy} = \frac{\%\Delta Q_x}{\%\Delta P_y}\]

In this formula, \(E_{xy}\) represents the cross price elasticity, \(\%\Delta Q_x\) is the percentage change in the quantity demanded of good X, and \(\%\Delta P_y\) is the percentage change in the price of good Y. The quantity demanded of one good is always in the numerator, while the price of the other good is in the denominator.

To calculate cross price elasticity, the midpoint method is often employed, which involves several steps. First, determine the changes in quantity and price. For example, if the price of tennis rackets increases from \$45 to \$55, and the quantity demanded of tennis balls decreases from 21,000 to 19,000, the changes can be calculated as follows:

1. Calculate the change in quantity demanded: \(21,000 - 19,000 = 2,000\).

2. Calculate the change in price: \(55 - 45 = 10\).

3. Find the average quantity demanded: \((21,000 + 19,000) / 2 = 20,000\).

4. Find the average price: \((55 + 45) / 2 = 50\).

Next, calculate the percentage changes:

Percentage change in quantity demanded: \[\frac{2,000}{20,000} = 0.1\]

Percentage change in price: \[\frac{10}{50} = 0.2\]

Now, substitute these values into the cross price elasticity formula:

\[E_{xy} = \frac{0.1}{0.2} = 0.5\]

Since the price of tennis rackets increased (positive change) and the quantity demanded of tennis balls decreased (negative change), the overall cross price elasticity is negative, resulting in:

\[E_{xy} = -0.5\]

This negative value indicates that the two goods are complements. In general, if the cross price elasticity is positive, the goods are substitutes; if negative, they are complements; and if zero, they are unrelated. Thus, in this example, the increase in the price of tennis rackets led to a decrease in the quantity demanded of tennis balls, confirming their complementary relationship.

Understanding cross price elasticity is essential for businesses and economists as it helps in predicting consumer behavior and making informed pricing and production decisions. Practice problems can further enhance comprehension of this concept and its applications in real-world scenarios.

An increase in the demand for chicken, from 8,000 to 12,000, was caused by an increase in the price of beef from \$4.50 to \$5.50. Therefore, the cross-price elasticity for these two products is:

• A. 0.5
• B. -2.0
• C. 2.0
• D. -0.5

Answer: (C)

Here’s what students ask on this topic:

What is cross-price elasticity of demand and how is it calculated?

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.

How do you interpret the sign of cross-price elasticity of demand?

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.

Can you provide an example of calculating cross-price elasticity of demand?

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.

What are some real-world examples of substitutes and 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.

Why is cross-price elasticity of demand important in economics?

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.