Understanding Cross Elasticity of Demand

The question asks about the meaning of the cross elasticity of demand. This is a concept in economics that measures how the quantity demanded of one good changes when the price of a different, related good changes. It helps us understand the relationship between different products in the market.

Defining Cross Elasticity of Demand

The cross elasticity of demand (often denoted as \(E_{xy}\) or \(CED\)) quantifies the responsiveness of the quantity demanded of good X to a change in the price of good Y.

The formula for cross elasticity of demand is:

\( E_{xy} = \frac{\text{% Change in Quantity Demanded of Good X}}{\text{% Change in Price of Good Y}} \)

Or, using calculus for instantaneous change:

\( E_{xy} = \frac{\partial Q_x}{\partial P_y} \times \frac{P_y}{Q_x} \)

Where:

• \(Q_x\) is the quantity demanded of good X
• \(P_y\) is the price of good Y

The sign of the cross elasticity of demand tells us the relationship between the two goods:

• If \(E_{xy} > 0\), goods X and Y are substitutes (e.g., tea and coffee). An increase in the price of Y leads to an increase in the quantity demanded of X.
• If \(E_{xy} < 0\), goods X and Y are complements (e.g., cars and petrol). An increase in the price of Y leads to a decrease in the quantity demanded of X.
• If \(E_{xy} = 0\), goods X and Y are unrelated. A change in the price of Y has no effect on the quantity demanded of X.

Analyzing the Options

Let's look at each option in the context of what elasticity measures:

1. consumer's income: The responsiveness of the quantity demanded of a good to a change in consumer's income is measured by the income elasticity of demand, not the cross elasticity of demand.

2. producer's income: Producer's income is not a standard variable used to measure the responsiveness of demand for a good.

3. its own price: The responsiveness of the quantity demanded of a good to a change in its own price is measured by the price elasticity of demand (or own-price elasticity of demand), not the cross elasticity of demand.

4. price of other goods: As defined above, the responsiveness of the quantity demanded of a good to a change in the price of other goods is precisely what the cross elasticity of demand measures.

Based on the definition and the analysis of options, the cross elasticity of demand specifically relates to how demand for a good changes when the price of a *different* good changes.

Conclusion

The cross elasticity of demand is a measure of the responsiveness of the quantity demanded of a good to a change in the price of other goods. This distinguishes it from price elasticity of demand (responsiveness to own price) and income elasticity of demand (responsiveness to income).

Revision Table: Key Elasticities of Demand

Additional Information on Cross Elasticity and Related Goods

Understanding the sign and magnitude of the cross elasticity of demand is crucial for businesses and policymakers.

• For Substitutes: If two goods, like Coca-Cola and Pepsi, are substitutes, an increase in the price of Coca-Cola will lead people to buy more Pepsi. The cross elasticity of demand between Coca-Cola and Pepsi would be positive (\(E_{xy} > 0\)). The higher the positive value, the stronger the substitute relationship.
• For Complements: If two goods, like printers and ink cartridges, are complements, an increase in the price of printers will likely lead to a decrease in the demand for ink cartridges (since fewer printers are sold). The cross elasticity of demand between printers and ink cartridges would be negative (\(E_{xy} < 0\)). The more negative the value, the stronger the complementary relationship.
• For Unrelated Goods: If two goods, like cars and bananas, are unrelated, a change in the price of cars will have no significant effect on the demand for bananas. The cross elasticity of demand would be close to zero (\(E_{xy} \approx 0\)).

Firms use cross elasticity of demand analysis to understand competitive markets, pricing strategies, and the impact of competitor actions. For example, a firm selling a good with a high positive cross elasticity with a competitor's product knows that a price cut by the competitor will significantly reduce demand for its own product.