Complementary Goods vs Law of Demand
Complementary Goods and Law of Demand are two Supply & Demand concepts in AP Economics that students often mix up. Complementary goods are goods that are typically used or consumed together. The law of demand states that quantity demanded falls when price rises, holding all else constant. Here is how they compare side by side.
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.
The law of demand describes the inverse relationship between price and quantity demanded. When the price of a good rises, consumers are willing and able to buy less of it. Conversely, when the price falls, consumers are willing and able to buy more. This holds true as long as other factors like income and preferences remain constant.
Complementary Goods vs Law of Demand: Whose Price Is Changing
| Complementary Goods | Law of Demand | |
|---|---|---|
| Price doing the work | Another good's price | This good's own price |
| What it tells you | Which way the whole curve moves | Why the curve slopes downward |
| Result on the diagram | A shift of demand | A movement along demand |
| Relationship described | One good's price against another good's demand | One good's price against its own quantity demanded |
| Status of the claim | An empirical fact about one specific pair | A general rule assumed for every demand curve you draw |
| Role in ceteris paribus | One of the conditions being held constant | The rule that applies once they are held constant |
| Wording that earns the point | Demand for the partner good rose or fell | Quantity demanded rose or fell |
A complement's price is one of the conditions the law of demand holds still
The law of demand is a conditional statement: quantity demanded falls as the good's own price rises, provided nothing else changes. The price of a complement is squarely inside that nothing else. So when a complement's price moves, you are not testing the law, you are altering one of the conditions it assumes and redrawing the curve in a new place. Take cartridges with a demand schedule of Qd equal to 90 minus 3P, which puts quantity demanded at 60 when the price is 10. Printers get cheaper, more households own one, and buyers now want 15 more cartridges at every single price, so the schedule becomes 105 minus 3P and quantity demanded at a price of 10 is 75. Notice what did not change: the coefficient on price is still negative 3, so the new curve slopes down exactly as the law of demand requires. The law survived the shift untouched, because it was never a claim about where the curve sits, only about which way it tilts.
Selling more cartridges at a higher cartridge price does not break the law
Run the same schedules forward and a result appears that looks impossible. On the original curve, a price of 10 sold 60 cartridges. On the post shift curve, a price of 12 sells 105 minus 36, which is 69. Price up, quantity up, and the law of demand fully intact, because the two observations sit on different curves. Comparing points across a shift is not a test of anything; only two points on one curve are. This is also the moment to count the events correctly, since one printer price cut produces exactly one movement and one shift, in two different markets. In the printer market, the price drop from 80 to 60 traces along an unchanged printer demand curve, and printers sold climb from 40 to 55. In the cartridge market, that new fleet of printers shifts cartridge demand right. Students routinely shift both curves, which double counts the event, or shift neither and describe the whole thing as quantity demanded rising. Draw both markets side by side at /sandbox/supply-demand, and check the wording rules at /glossary/law-of-demand.
Frequently asked questions
Does the law of demand apply to complementary goods?
Yes, and separately for each good. The law is about a good's own price, so it governs the slope of the cartridge demand curve and the slope of the printer demand curve independently. The complementary relationship between them is a different statement, about how a change in one good's price relocates the other good's curve rather than about how either curve tilts.
Does a fall in a complement's price shift the demand curve or move along it?
Shifts it, to the right. Only the good's own price moves you along its curve. A cheaper complement makes the pair more attractive, so buyers want more of this good at every price, which is a shift. In the market for the complement itself, the very same price cut is a movement along that good's own curve, so one event yields a shift in one market and a movement in the other.
Can price and quantity both rise without violating the law of demand?
Yes, whenever the demand curve moved between the two observations. Cartridges at a price of 10 sold 60 units on the old schedule, while a price of 12 sells 69 on the new schedule after a cheaper printer shifted demand right. Each curve still slopes down. The law compares two prices on one curve, never two points drawn from different curves.
Live Supply and Demand graph. Drag the curves, or open the full version.
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