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 shoes and right shoes is expected to be negative, as they are complementary goods. A change in the price of one shoe will lead to an opposite change in the demand for the other shoe.

Step-by-step solution

Understand the concept of cross-price elasticity

Cross-price elasticity (CPE) is an economic concept used to describe the responsiveness of the quantity demanded of one good when the price of another good changes. It is defined as the percentage change in the quantity demanded of good X when the price of good Y changes by one percent. Mathematically, it is represented as follows: \[CPE_{X,Y} = \frac{ \% \Delta Q_{X}}{\% \Delta P_{Y}}\] Where: \(CPE_{X,Y}\) is the cross-price elasticity between good X and good Y \(\%\Delta Q_{X}\) is the percentage change in the quantity demanded of good X \(\%\Delta P_{Y}\) is the percentage change in the price of good Y

Define the goods involved in the problem

In this problem, we are considering left shoes (good X) and right shoes (good Y) as separate entities.

Determine the relationship between left shoes and right shoes

Left shoes and right shoes are complementary goods. Complementary goods are products or services that are used together, such that when the price of one good increases, the demand for its complement will typically decrease.

Calculate the cross-price elasticity between left shoes and right shoes

Since left shoes and right shoes are complementary goods, we expect a negative value for their cross-price elasticity. When the price of left shoes increases, the demand for right shoes is expected to decrease and vice versa. We can't provide an exact numerical value for the cross-price elasticity without actual data on prices and demand, but we can predict that it will be negative.

Conclusion

The cross-price elasticity between left shoes and right shoes is expected to be negative, as they are complementary goods. A change in the price of one shoe will lead to an opposite change in the demand for the other shoe.