Complementary Goods vs Quantity Demanded
Complementary Goods and Quantity Demanded are two Supply & Demand concepts in AP Economics that students often mix up. Complementary goods are goods that are typically used or consumed together. Quantity demanded is the amount of a good or service consumers are willing and able to purchase at a given price. 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 quantity demanded is determined by the market price, holding all else constant. As price rises, quantity demanded falls. Producers use the concept to determine output levels and pricing strategies. It is graphically represented by the demand curve.
Complementary Goods vs Quantity Demanded: One Price Cut, Two Markets
| Complementary Goods | Quantity Demanded | |
|---|---|---|
| What the term describes | A relationship linking two markets | One number in one market at one price |
| Response to a price fall next door | Demand for this good shifts right | Unchanged unless this good's own price fell |
| Curve that moves | The complement's entire demand curve | None, you read a different point on the same curve |
| What is held constant | This good's own price, while the partner price moves | Every determinant, while this good's price moves |
| How it is measured | Cross-price elasticity, negative for complements | A single coordinate read off the demand curve |
| Wording that scores on an FRQ | Demand for the complement increases | Quantity demanded increases |
The cross-price test only works if you hold the bun price still
Confirming that buns are a complement means computing cross-price elasticity, and the computation carries a condition students skip. The hot dog price fell from 6 to 4, roughly 33 percent. Bun quantity demanded rose from 24 to 30, exactly 25 percent, but only because the two figures were compared at the same bun price of 3. Divide 25 by negative 33 and cross-price elasticity is about negative 0.75, negative as complements require. Compare the two bun quantities at different bun prices and the number means nothing, because part of the change would be a movement along the bun curve rather than the shift you set out to measure. That is why the definition specifies the other good's own price is held constant. In the real sequence the bun price will not stay at 3, since a rightward shift in bun demand raises the bun equilibrium price and pulls quantity supplied up with it. The final traded quantity of buns therefore mixes a shift and a movement, and only the shift is the complement effect. More elasticity practice sits at /micro/elasticity.
Bun sales really do rise, and the phrase quantity demanded still loses the mark
The trap here is that the intuition is right while the vocabulary is wrong. More buns get bought once hot dogs are cheaper, so writing that the quantity demanded of buns increases feels like an accurate description of the world. Rubrics reject it anyway, because the phrase names the wrong operation. An increase in quantity demanded is reserved for the case where a good's own price changed and nothing else did, and the bun price did not fall on its own. The sentence that scores is that demand for buns increases, shifting the bun demand curve right, which raises the bun price and the equilibrium quantity of buns together. Notice the scoring answer still contains a quantity increase; it simply arrives as the consequence of a shift rather than as the name of the effect. A fast way to audit your own sentence: if the stem did not change the price of the good you are describing, the words quantity demanded should not be the subject of your verb.
Frequently asked questions
Does a fall in the price of one good raise the quantity demanded of its complement?
A fall in the price of one good raises demand for its complement, and the quantity of the complement traded rises as a result of that shift. The distinction matters on the exam, because quantity demanded is reserved for a response to the good's own price, and the complement's own price did not change. Describe the effect as a rightward shift in the complement's demand curve, which raises the complement's equilibrium price and quantity together.
How do you prove two goods are complements?
Two goods are complements when the cross-price elasticity of demand between them is negative, meaning a higher price for one reduces quantity demanded of the other with that other good's own price held constant. In the worked example a 33 percent fall in the hot dog price raised bun quantity demanded by 25 percent at an unchanged bun price of 3, giving a cross-price elasticity near negative 0.75.
Is quantity demanded a curve or a point?
Quantity demanded is a single point, never a curve. Naming a quantity demanded requires naming a price, since the number is one coordinate read off a demand curve that already exists. Demand is the whole curve, the full set of price and quantity pairs. That difference is why a complement's price change moves the entire curve while the good's own price change only moves you along it.
Live Supply and Demand graph. Drag the curves, or open the full version.
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