Complementary Goods
What is Complementary Goods?
Complementary goods are goods that are typically used or consumed together.
When the price of one good increases, the demand for its complement decreases, as consumers buy less of both goods. Examples include cars and gasoline, or printers and ink cartridges.
Complementary Goods: a worked example
A store sells printers and ink cartridges. When the printer price rises from $80 to $100, monthly cartridge sales fall from 400 units to 340. The percentage change in cartridge quantity is (340 minus 400) / 400 = negative 15 percent. The percentage change in printer price is (100 minus 80) / 80 = positive 25 percent. Cross-price elasticity of demand equals negative 15 / 25 = negative 0.6. The negative sign is the whole test: the two goods are complements, because a higher price for one shrinks demand for the other. On paper, the printer market shows a movement along its own demand curve while the cartridge market shows its entire demand curve sliding left, cutting equilibrium cartridge price and quantity together. The magnitude of 0.6 says the link is real but loose, since a value near negative 2 would mark a far tighter pairing.
The mistake students make with complementary goods
The recurring slip is shifting demand in the market whose own price changed. If gasoline gets more expensive, gasoline shows a movement along its own demand curve, and it is the car market whose demand curve shifts left. Students shift both curves, then cannot say what caused the second shift. A second slip is dropping the sign. Complements carry a negative cross-price elasticity because the price of one and the quantity of the other move in opposite directions, while substitutes carry a positive one, so a lost minus sign converts a complement into a substitute.
Complementary Goods questions
How can I tell if two goods are complements?
Complements reveal themselves through a negative cross-price elasticity of demand. Raise the price of one and demand for the other falls, so the percentage change in quantity and the percentage change in price carry opposite signs. If ski pass prices rise 10 percent while ski rentals fall 12 percent, the elasticity is negative 1.2 and the goods are complements. Substitutes produce a positive value, and goods with no relationship produce something close to zero.
What happens to demand for a complement when the price of the other good rises?
Demand for the complement falls, shifting its entire demand curve left. Costlier game consoles push some buyers out of the console market altogether, and those buyers stop shopping for games at every price, not only at the current one. The leftward shift lowers both equilibrium price and equilibrium quantity in the game market. The console market itself shows no shift at all, only a movement up along its own demand curve.
Are complements and substitutes opposites?
Complements and substitutes sit at opposite ends of one measure, cross-price elasticity of demand. Complements score negative because the goods get consumed together, so pricing one out of reach drags the other down with it. Substitutes score positive because buyers priced out of one simply switch to the other. A pair can also be neither, returning a value near zero, which is why exam questions ask for the sign of the elasticity rather than a yes or no.
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Related terms
Common comparisons
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