Understanding the Relationship Between Goods X and Y

The question describes a specific relationship between two goods, good 'X' and good 'Y'. It states that when the price of good 'X' increases, the demand for good 'Y' also increases.

Analyzing the Price and Demand Relationship

Let's break down the given information:

• Observation 1: The price of good 'X' goes up ($\Delta P_X > 0$).
• Observation 2: The demand for good 'Y' goes up ($\Delta D_Y > 0$).

We are looking for the type of relationship between good 'X' and good 'Y' based on this observed pattern.

Identifying the Type of Goods Relationship

In economics, the relationship between two goods based on how a change in the price of one affects the demand for the other is categorized primarily into substitute goods and complementary goods.

Substitute Goods

Substitute goods are goods that can be used in place of one another. Consumers typically choose one over the other based on factors like price. If the price of one substitute good increases, consumers are likely to switch to the other, cheaper substitute good, thus increasing the demand for the other good.

Example: Tea and Coffee. If the price of tea increases, people might buy less tea and more coffee, leading to an increase in the demand for coffee.

In the given scenario, an increase in the price of 'X' leads to an increase in the demand for 'Y'. This perfectly matches the definition and behavior of substitute goods. Consumers likely see 'X' and 'Y' as alternatives. When 'X' becomes more expensive, they shift their purchases towards 'Y'.

Complementary Goods

Complementary goods are goods that are typically used together. If the price of one complementary good increases, the demand for that good decreases, which in turn leads to a decrease in the demand for the good that is used with it.

Example: Cars and Petrol. If the price of cars increases, fewer cars might be bought, leading to less demand for petrol.

In this case, an increase in the price of 'X' would lead to a decrease in the demand for 'Y' if they were complementary goods, which is the opposite of what is stated in the question.

Normal Goods and Inferior Goods

Normal goods and inferior goods are classifications based on how their demand changes in response to changes in consumer income, not changes in the price of other goods. This concept is related to income elasticity of demand, not cross-price elasticity of demand.

Summary Table of Goods Relationships

Based on the scenario where an increase in the price of good 'X' causes an increase in the demand for good 'Y', good 'X' and good 'Y' are related as substitute goods.

Revision Table: Types of Goods and Their Relationships

Additional Information: Cross-Price Elasticity of Demand

The relationship discussed in the question is formally measured by the concept of Cross-Price Elasticity of Demand ($E_{XY}$).

The formula for cross-price elasticity of demand between good X and good Y is:

$\qquad E_{XY} = \frac{\text{% Change in Quantity Demanded of Good Y}}{\text{% Change in Price of Good X}}$

• If $E_{XY} > 0$, the goods are substitutes. This means the percentage change in demand for Y is positive when the percentage change in price of X is positive (or both negative), confirming the relationship described.
• If $E_{XY} < 0$, the goods are complements. The percentage change in demand for Y is negative when the percentage change in price of X is positive (or vice versa).
• If $E_{XY} \approx 0$, the goods are unrelated.

The observation in the question clearly indicates a positive cross-price elasticity, which is the defining characteristic of substitute goods.