Question

The cross-price elasticity of the demand for cell phones and DVDs is 1.2. Explain. The cross-price elasticity of the demand for the iPod and DVDs is -1.4. Explain.

Short answer

Answer: Positive cross-price elasticity values indicate that the goods are substitutes, meaning their demand moves in the same direction when the price of one changes. In this case, cell phones and DVDs are substitutes with a positive value of 1.2. Negative cross-price elasticity values indicate that the goods are complements, meaning their demand moves in opposite directions when the price of one changes. For iPods and DVDs, a negative value of -1.4 indicates that they are complements.

Step-by-step solution

Understanding Cross-Price Elasticity of Demand

Cross-price elasticity of demand is the measure of the percentage change in the quantity demanded of one good (A) in response to a percentage change in the price of another good (B). It is calculated using the formula: Cross-price elasticity of demand = (% change in quantity demanded of A) / (% change in price of B)

Interpreting Positive and Negative Values

A positive cross-price elasticity value indicates that the two goods are substitutes – When the price of one good increases, the demand for the other good increases too. In contrast, a negative value suggests that the two goods are complements – When the price of one good increases, the demand for the other good decreases.

Explaining the Cross-Price Elasticity of Cell Phones and DVDs

Given the cross-price elasticity of demand for cell phones and DVDs as 1.2, we can interpret that as the price of DVDs increases by 1%, the quantity demanded for cell phones will increase by 1.2%. This positive value suggests that cell phones and DVDs are substitutes for each other, meaning that consumers tend to buy more cell phones when the price of DVDs increases.

Explaining the Cross-Price Elasticity of iPods and DVDs

The cross-price elasticity of demand for iPods and DVDs is given as -1.4. This means that when the price of DVDs increases by 1%, the quantity demanded for iPods will decrease by 1.4%. The negative value indicates that iPods and DVDs are complements – they are usually purchased or consumed together, so when the price of DVDs increases, the demand for iPods decreases. In conclusion, the cross-price elasticity values given reveal the relationships between the products. Cell phones and DVDs act as substitutes, with their demand moving in the same direction when one's price changes. Conversely, iPods and DVDs act as complements, with their demand moving in opposite directions when one's price changes.

Key concepts

Substitute Goods

Substitute goods are products that can replace each other in the eyes of consumers. When the price of one product rises, consumers may switch to a substitute product to save money or achieve similar satisfaction. For example, if you usually buy brand A of shampoo and it becomes more expensive, you might decide to purchase brand B instead.

The key here is that the two goods fulfill a similar need or purpose, so buying one reduces the need for the other. This relationship is clearly illustrated through the concept of cross-price elasticity of demand. When the cross-price elasticity of demand between two products is positive, it signals that they are substitutes. As the original exercise suggests, the cross-price elasticity between cell phones and DVDs was calculated as 1.2, showing these goods are substitutes. When the price of DVDs increases by 1%, the demand for cell phones increases by 1.2%, indicating that consumers switch to buying more cell phones as DVDs become pricier.

Some key points about substitute goods include:

• They serve similar needs or functions for consumers.
• A rise in the price of one good typically leads to an increase in demand for its substitute.
• The value of positive cross-price elasticity signifies a substitutive relationship.

Complement Goods

Complement goods are those products that are often consumed together. The purchase or usage of one product increases the demand for its complement. A classic example of complementary goods includes peanut butter and jelly. If you buy peanut butter, you are likely to buy jelly as well since they are often paired.

The relationship between complementary goods is reflected through a negative cross-price elasticity of demand. This means that if the price of one good rises, the demand for the other decreases because they are typically used in conjunction. For the exercise, the cross-price elasticity of demand between iPods and DVDs was calculated as -1.4. This shows that as the price of DVDs increases by 1%, the quantity demanded for iPods decreases by 1.4%. This illustrates a complementary relationship since higher prices for DVDs lead to fewer purchases of iPods as they are used together by consumers.

Important insights concerning complement goods include:

• They are usually consumed or purchased together.
• An increase in the price of one good generally causes a drop in demand for its complement.
• A negative cross-price elasticity value evidences a complementary relationship.

Elasticity Interpretation

Elasticity interpretation is crucial for understanding how changes in price affect quantity demanded across related goods. Cross-price elasticity of demand helps us see whether products are substitutes or complements based on their elasticity values.

When interpreting cross-price elasticity:

• A positive value indicates substitutability. This means consumers view the goods as alternatives and will switch if prices change.
• A negative value indicates complementarity. This suggests that an increase in the price of one leads to a decreased demand for the other, as they are typically used together.

In practical applications, businesses and economists use these elasticity interpretations to make informed pricing, marketing, and production decisions.

For instance, knowing that cell phones and DVDs are substitutes allows companies to adjust strategies to target consumers shifting due to price changes. On the other hand, understanding that iPods and DVDs are complements helps businesses realize that promotions and price reductions should consider both products together to maximize sales.

Thus, cross-price elasticity of demand not only aids in classifying product relationships but also plays a pivotal role in shaping business strategies and economic outcomes.