---
title: "Complements — AP Micro Definition & Cross-Price Elasticity"
description: "Complements are goods consumed together, shown by a negative cross-price elasticity of demand. Learn how AP Micro tests this in Topic 2.5 with calculations."
canonical: "https://fiveable.me/ap-micro/key-terms/complements"
type: "key-term"
subject: "AP Microeconomics"
unit: "Unit 2"
---

# Complements — AP Micro Definition & Cross-Price Elasticity

## Definition

Complements are goods typically consumed together, like hot dogs and hot dog buns. In AP Micro, two goods are complements when their cross-price elasticity of demand is negative, meaning a price increase for one good decreases the quantity demanded of the other.

## What It Is

Complements are goods you use together. Think peanut butter and jelly, printers and ink, or [game](/ap-micro/unit-4/oligopoly-game-theory/study-guide/mBvl1ZO2oahFuA0W4Zfe "fv-autolink") consoles and games. Because they're consumed as a pair, a price change for one good spills over onto demand for the other. If the price of hot dogs jumps, you buy fewer hot dogs, and since you're not eating plain buns, you buy fewer buns too. The [demand curve](/ap-micro/key-terms/demand-curve "fv-autolink") for buns shifts left even though the price of buns never changed.

The AP exam wants you to identify complements with a number, not a vibe. [Cross-price elasticity of demand](/ap-micro/key-terms/cross-price-elasticity-of-demand "fv-autolink") is the percentage change in quantity demanded of one good divided by the percentage change in the price of another good. If that number is **negative**, the goods are complements. If it's positive, they're substitutes. The sign does all the work. A cross-price elasticity of -2 says that a 1% price increase for good A cuts quantity demanded of good B by 2%, so these two goods are tightly linked complements.

## Why It Matters

Complements live in Topic 2.5 (Other Elasticities) inside [Unit 2](/ap-micro/unit-2 "fv-autolink"): Supply and Demand. They're the test case for learning objective [AP Micro](/ap-micro "fv-autolink") 2.5.A, which has you define cross-price elasticity and use it to classify pairs of goods, and they show up in 2.5.C, where you calculate elasticity values from a table or graph and then interpret the sign. This is one of the cleanest 'sign tells the story' moments in the course. Negative means complements, positive means substitutes, and you'll be asked to read that sign in both directions. Sometimes you compute the number and label the relationship; sometimes you're told the relationship and predict what happens to the other good's demand curve. Complements also reinforce the determinants of demand from earlier in Unit 2, since a price change in a related good is one of the classic demand shifters.

## Connections

### [Cross-Price Elasticity of Demand (Unit 2)](/ap-micro/key-terms/cross-price-elasticity-of-demand)

This is the formula that defines complements. You divide the percentage change in [quantity demanded](/ap-micro/key-terms/quantity-demanded "fv-autolink") of one good by the percentage change in the price of the other, and a negative result is the official AP proof that two goods are complements.

### [Substitutes (Unit 2)](/ap-micro/key-terms/substitutes)

[Substitutes](/ap-micro/key-terms/substitutes "fv-autolink") are the mirror image. They're goods consumed instead of each other, so their cross-price elasticity is positive. Every cross-price question on the exam is really asking you to pick between these two labels based on a sign.

### Demand Shifters in Topic 2.1 (Unit 2)

Complements connect elasticity back to basic demand curves. When the price of a complement rises, the demand curve for the related good shifts left. [Cross-price elasticity](/ap-micro/key-terms/cross-price-elasticity "fv-autolink") just puts a precise number on a shift you already learned to draw.

### [Income Elasticity of Demand (Unit 2)](/ap-micro/key-terms/income-elasticity-of-demand)

Same Topic 2.5 logic, different variable. Income elasticity uses its sign to sort goods into normal versus inferior, just like cross-price elasticity uses its sign to sort pairs into complements versus substitutes. Master one and you've mastered both.

## On the AP Exam

Multiple-choice questions hit complements from two angles. One type gives you a cross-price elasticity value, like -2, and asks what happens to demand for one good when the other's price rises (answer: quantity demanded falls, and a value of -2 means it falls by twice the percentage of the price change). The other type describes a relationship and asks you to identify the sign of the elasticity. Practice questions on this topic constantly drill the negative-means-complements, positive-means-substitutes distinction, so lock that in. On FRQs, complements often appear inside larger consumer-choice or supply-and-demand setups. The 2019 FRQ Q2, for example, built around a marginal benefit table for bottles of water and another good, the kind of stimulus where understanding how related goods interact matters. Be ready to calculate cross-price elasticity from a table, state the sign, name the relationship, and explain the demand shift it implies.

## Complements vs Substitutes

Both terms describe related goods, but the relationship runs in opposite directions. Substitutes replace each other (Coke and Pepsi), so when one gets pricier, demand for the other rises, giving a positive cross-price elasticity. Complements pair up (coffee and creamer), so when one gets pricier, demand for the other falls, giving a negative cross-price elasticity. The fastest exam check is the sign. Negative cross-price elasticity always means complements. If you blank on which is which, remember that complements 'go down together,' just like the negative sign suggests.

## Key Takeaways

- Complements are goods consumed together, and their defining feature on the AP exam is a negative cross-price elasticity of demand.
- Cross-price elasticity equals the percentage change in quantity demanded of one good divided by the percentage change in the price of another good.
- When the price of a complement rises, the demand curve for the related good shifts left, even though that good's own price never changed.
- The sign of cross-price elasticity is the answer. Negative means complements, positive means substitutes, and a value near zero means the goods are unrelated.
- A cross-price elasticity of -2 means a 1% increase in one good's price causes a 2% decrease in the quantity demanded of the other good, signaling strong complements.

## FAQs

### What are complements in AP Microeconomics?

Complements are goods typically consumed together, like printers and ink cartridges. In AP Micro, you identify them with cross-price elasticity of demand. A negative value confirms the goods are complements.

### If cross-price elasticity is negative, are the goods complements or substitutes?

Complements. A negative cross-price elasticity means a price increase for one good lowers quantity demanded of the other, which only happens when goods are used together. Positive values mean substitutes.

### Does a price change in a complement shift the demand curve or cause movement along it?

It shifts the demand curve. If hot dog prices rise, the entire demand curve for buns shifts left, because the price of buns themselves didn't change. Movement along a curve only happens when a good's own price changes.

### What's the difference between complements and substitutes on the AP Micro exam?

Complements are consumed together and have a negative cross-price elasticity, so a price increase for one decreases demand for the other. Substitutes replace each other and have a positive cross-price elasticity, so a price increase for one increases demand for the other.

### What does a cross-price elasticity of -2 mean?

It means the goods are complements, and a 1% increase in one good's price causes a 2% decrease in the quantity demanded of the other. The negative sign identifies the relationship, and the size shows how strongly the goods are linked.

## Related Study Guides

- [2.5 Other Elasticities](/ap-micro/unit-2/other-elasticities/study-guide/6ozj5y47OvVKtCAIdv97)

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