In Chapter 3 you learned that the demand for a good is often affected by the prices of other, related goods—goods that are substitutes or complements. There you saw that a change in the price of a related good shifts the demand curve of the original good, reflecting a change in the quantity demanded at any given price. The strength of such a “cross” effect on demand can be measured by the cross-price elasticity of demand, defined as the ratio of the percent change in the quantity demanded of one good to the percent change in the price of the other.

When two goods are substitutes, like hot dogs and hamburgers, the cross-price elasticity of demand is positive: a rise in the price of hot dogs increases the demand for hamburgers—that is, it causes a rightward shift of the demand curve for hamburgers. If the goods are close substitutes, the cross-price elasticity will be positive and large; if they are not close substitutes, the cross-price elasticity will be positive and small. So when the cross-price elasticity of demand is positive, its size is a measure of how closely substitutable the two goods are, with a higher number meaning the goods are closer substitutes.

When two goods are complements, like hot dogs and hot dog buns, the cross-price elasticity is negative: a rise in the price of hot dogs decreases the demand for hot dog buns—that is, it causes a leftward shift of the demand curve for hot dog buns. As with substitutes, the size of the cross-price elasticity of demand between two complements tells us how strongly complementary they are: if the cross-price elasticity is only slightly below zero, they are weak complements; if it is very negative, they are strong complements.

Note that in the case of the cross-price elasticity of demand, the sign (plus or minus) is very important: it tells us whether the two goods are complements or substitutes. So we cannot drop the minus sign as we did for the price elasticity of demand.

Our discussion of the cross-price elasticity of demand is a useful place to return to a point we made earlier: elasticity is a unit-free measure—that is, it doesn’t depend on the units in which goods are measured.

To see the potential problem, suppose someone told you that “if the price of hot dog buns rises by $0.30, Americans will buy 10 million fewer hot dogs this year.” If you’ve ever bought hot dog buns, you’ll immediately wonder: is that a $0.30 increase in the price per bun, or is it a $0.30 increase in the price per package? Buns are usually sold in packages of eight. It makes a big difference what units we are talking about! However, if someone says that the cross-price elasticity of demand between buns and hot dogs is −0.3, it doesn’t matter whether buns are sold individually or by the package. So elasticity is defined as a ratio of percent changes, as a way of making sure that confusion over units doesn’t arise.