Question

Suppose you could buy shoes one at a time, rather than in pairs. What do you predict the cross-price elasticity for left shoes and right shoes would be?

Short answer

The cross-price elasticity between left and right shoes would likely be negative, indicating they are complements. Since customers intend to buy both left and right shoes together to form a pair, when the price of one shoe increases, the demand for the other shoe decreases. However, without specific data on percentage changes in price and quantity, it is not possible to determine the exact numerical value of this cross-price elasticity.

Step-by-step solution

Identify the products and their relationship

In this exercise, we are dealing with two types of products: left shoes and right shoes. Consumers typically intend to buy both products together to form a pair of shoes. Therefore, the relationship between these two products is complementary.

Define cross-price elasticity

The cross-price elasticity of demand is a measure of how the quantity demanded for one product changes in response to a change in the price of another product. It is calculated using the following formula: Cross-price elasticity = \(\frac{\text{Percentage change in quantity demanded for Product A}}{\text{Percentage change in price of Product B}}\)

Analyze the relationship between left and right shoes

As mentioned previously, left and right shoes are complementary goods. When a person buys a left shoe, they will also need a matching right shoe to form a pair, and vice versa. Thus, when the price of one type of shoe changes, we can expect that the demand for the other type will also change in the same direction. For example, if the price of a right shoe increases, the demand for left shoes will presumably decrease, as customers will likely buy fewer right shoes, and therefore fewer left shoes to match.

Calculate the cross-price elasticity

Due to the complementary relationship between left and right shoes, we expect that the cross-price elasticity should be negative, indicating that when the price of one type increases, the quantity demanded for the other type decreases. However, since we do not have specific numbers for the percentage change in quantity and price, we cannot calculate an exact value for the cross-price elasticity. But we can make qualitative statements: we can predict that the cross-price elasticity between left and right shoes would be negative and quite substantial in magnitude, because they are strong complements and if one type of shoe becomes more expensive, people will reduce their consumption of both types to keep the pairs matching. In conclusion, the cross-price elasticity for left shoes and right shoes would likely be negative due to their complementary relationship. However, without specific data on the percentage changes in price and quantity, it is not possible to determine the exact numerical value.