Principles of Microeconomics / Unit 4 MIC 0321 worked example, 60 to 90 seconds
Classifying Goods by the Sign
The idea
Two elasticities are read by sign, not by size. For income elasticity, divide the percentage change in quantity by the percentage change in income; positive is a normal good, negative an inferior good. For cross-price elasticity, divide the percentage change in one good's quantity by the percentage change in the other good's price; positive means substitutes, negative complements, zero unrelated. Compute the ratio, read the sign, name the class, and only then look at the size, which says how strong the relation is.
In practice
Worked example: when incomes rise ten percent, bus rides at the current fare fall three percent, so the income elasticity is minus zero point three and bus rides are inferior. When bagel prices rise ten percent, cream cheese demand falls four percent at its own price, so the cross-price elasticity is minus zero point four and the two are complements. When the price of one streaming service rises ten percent, a rival's subscriptions rise six percent, so the cross elasticity is plus zero point six and they are substitutes.
Where people slip
The error is to drop the sign out of habit from price elasticity, which turns an inferior good into a normal one. The second error is to divide by the wrong price: the cross elasticity uses the other good's price change in the denominator, never the good's own.
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