Income Elasticity and Cross-Price Elasticity

Two more kinds of elasticity measure how demand reacts to changes in buyers' income and to changes in the prices of other goods.

Price elasticity of demand tells you how quantity demanded reacts when a good’s own price changes. But price is not the only thing that moves demand. Two other measures use the same basic idea for different causes. Income elasticity of demand measures how much quantity demanded changes when buyers’ incomes change. Cross-price elasticity of demand measures how much quantity demanded of one good changes when the price of a different good changes. Both are calculated the same way as price elasticity: a percentage change in quantity demanded divided by a percentage change in something else.

Income elasticity: what happens when people earn more

Income elasticity is the percentage change in quantity demanded divided by the percentage change in income. Its sign tells you what kind of good you are looking at. For a normal good, income elasticity is positive: as incomes rise, people buy more. Most goods are normal goods - restaurant meals, clothing, travel, and books. When income elasticity is greater than one, meaning demand rises faster than income, the good is often called a luxury, since spending on it grows as a share of the budget as people become better off.

For an inferior good, income elasticity is negative: as incomes rise, people buy less of it, usually because they switch to something they prefer. Which goods are inferior depends on the place and the time. Very cheap staple foods, second-hand goods, and long-distance bus travel are common examples, as people may switch to more varied diets, new products, or air and train travel as they earn more. “Inferior” is a technical term here, not a judgment about quality.

Calculating income elasticity

Suppose a family's income rises by 10 percent, and they increase their spending on restaurant meals from 4 meals a month to 5 meals a month - a 25 percent increase. Income elasticity for restaurant meals is 25 percent divided by 10 percent, which is 2.5. That positive number above one tells us restaurant meals behave like a luxury for this family. If, over the same period, they cut their purchases of the cheapest brand of instant noodles by 20 percent, income elasticity for those noodles is negative 20 divided by 10, or negative 2, marking them as an inferior good for this family.

Cross-price elasticity: how goods are connected

Cross-price elasticity is the percentage change in quantity demanded of one good divided by the percentage change in the price of another good. Again, the sign carries the meaning. If it is positive, the goods are substitutes: when the price of tea rises, people buy more coffee. If it is negative, the goods are complements, meaning they are used together: when the price of printers rises, people buy fewer ink cartridges too. If it is close to zero, the goods are basically unrelated, such as shoelaces and rice.

Why businesses and governments care

These measures help predict the future. During an economic boom, when incomes rise, sellers of luxury goods can expect sales to grow quickly, while sellers of inferior goods may see sales fall. During a recession, the reverse can happen. Cross-price elasticity helps firms understand their competition: a high positive value between two brands means buyers see them as close substitutes, so a price cut by one could pull many customers away from the other. Competition authorities use similar reasoning when deciding whether two companies really compete in the same market.

Mixing up the sign with the size

A common mistake is to focus only on how big an elasticity number is and ignore whether it is positive or negative. For income and cross-price elasticity, the sign is often the most important part: it tells you whether a good is normal or inferior, and whether two goods are substitutes or complements. A cross-price elasticity of negative 2 and one of positive 2 describe completely different relationships.

Key takeaways

Income elasticity measures how demand responds to changes in buyers' income.
Normal goods have positive income elasticity; inferior goods have negative income elasticity.
Cross-price elasticity measures how demand for one good responds to another good's price.
Positive cross-price elasticity signals substitutes; negative signals complements.
Both measures help firms and policymakers predict how demand will shift.