Term
Another important elasticity is the cross-price elasticity of demand, which reveals the responsiveness of the demand for a good to changes in the price of a related good. This elasticity helps managers ascertain how much its demand will rise or fall due to a change in the price of another firm's product. The cross-price elasticity of demand between goods X and Y, denoted is mathematically defined as
For instance, if the cross-price elasticity of demand between Corel WordPerfect and Microsoft Word word processing software is 3, a 10 percent hike in the price of Word will increase the demand for WordPerfect by 30 percent, since 30%/10% = 3. This increase in demand for WordPerfect occurs because consumers substitute away from Word and toward WordPerfect, due to the price increase.
A Calculus Alternative
When the demand function is the cross-price elasticity of demand between goods X and Y may be found using calculus:
More generally, whenever goods X and Y are substitutes, an increase in the price of Y leads to an increase in the demand for X. Thus, whenever goods X and Y are substitutes. When goods X and Y are complements, an increase in the price of Y leads to a decrease in the demand for X. Thus, whenever goods X and Y are complements.
Table 3-4 provides some representative cross-price elasticities. For example, clothing and food have a cross-price elasticity of −0.18. This means that if the price of food increases by 10 percent, the demand for clothing will decrease by 1.8 percent; food and clothing are complements. More important, these data provide a quantitative measure of the impact of a change in the price of food on the consumption of clothing.
d
Based on the data summarized in Table 3-4, are food and recreation complements or substitutes? If the price of recreation increased by 15 percent, what would happen to the demand for food? These questions are embedded in the following problem.
Page 90
Demonstration Problem 3–1
You
For instance, if the cross-price elasticity of demand between Corel WordPerfect and Microsoft Word word processing software is 3, a 10 percent hike in the price of Word will increase the demand for WordPerfect by 30 percent, since 30%/10% = 3. This increase in demand for WordPerfect occurs because consumers substitute away from Word and toward WordPerfect, due to the price increase.
A Calculus Alternative
When the demand function is the cross-price elasticity of demand between goods X and Y may be found using calculus:
More generally, whenever goods X and Y are substitutes, an increase in the price of Y leads to an increase in the demand for X. Thus, whenever goods X and Y are substitutes. When goods X and Y are complements, an increase in the price of Y leads to a decrease in the demand for X. Thus, whenever goods X and Y are complements.
Table 3-4 provides some representative cross-price elasticities. For example, clothing and food have a cross-price elasticity of −0.18. This means that if the price of food increases by 10 percent, the demand for clothing will decrease by 1.8 percent; food and clothing are complements. More important, these data provide a quantitative measure of the impact of a change in the price of food on the consumption of clothing.
d
Based on the data summarized in Table 3-4, are food and recreation complements or substitutes? If the price of recreation increased by 15 percent, what would happen to the demand for food? These questions are embedded in the following problem.
Page 90
Demonstration Problem 3–1
You