Substitutes vs Complements: How to Tell Them Apart

Substitutes are goods you buy instead of one another, so a price rise in one pushes buyers toward the other; complements are goods you buy and use together, so a price rise in one drags down demand for both. Coffee and tea are substitutes: if coffee gets expensive, more people switch to tea. Coffee and coffee filters are complements: if coffee gets expensive, people brew less and buy fewer filters too. That single behavioral difference, whether two goods compete for your dollar or travel together in your basket, is the whole distinction, and economists make it precise with one number: cross-price elasticity of demand. This guide shows you how to classify any pair of goods by the sign of that number, works through examples in both directions, and lists real product pairs so the idea sticks.

The one-sentence definitions

A substitute good is a product that can replace another to satisfy a similar want. Butter and margarine, an Uber ride and a bus fare, Coke and Pepsi, a physical book and its e-book edition: in each pair, more of one means you need less of the other. When the price of one substitute rises, some buyers abandon it for the alternative, so demand for the alternative goes up. See the full entry on substitute goods for the exam definition.

A complementary good is a product that is consumed alongside another, so the two are used in combination. Cars and gasoline, phones and phone cases, hot dogs and buns, printers and ink: you rarely want one without the other. When the price of one complement rises, people buy less of it and therefore less of its partner, so demand for the partner goes down. The glossary entry on complementary goods has more.

Notice that both definitions are about what happens to the demand for good B when the price of good A changes. That is exactly what the law of demand does not capture, because the law of demand is about a good's own price. Substitutes and complements are about the price of a *different* good, which is why they shift the whole demand curve rather than move you along it.

The sign rule: cross-price elasticity

The cleanest way to classify a pair is with cross-price elasticity of demand (XED), which measures how responsive the quantity demanded of one good is to a change in the price of another:

XED = (% change in quantity demanded of Good B) / (% change in price of Good A)

The magnitude tells you how strong the relationship is, but the sign is what classifies the pair, and the logic is worth committing to memory:

• Positive XED means substitutes. Price of A goes up, quantity of B goes up. Both move the same direction, so the ratio is positive. The stronger the substitute relationship, the larger the positive number.
• Negative XED means complements. Price of A goes up, quantity of B goes down. The two move in opposite directions, so the ratio is negative. The stronger the complement relationship, the more negative the number.
• XED near zero means unrelated goods. Price of A changes and quantity of B barely moves. Textbooks call these independent or unrelated goods: think toothpaste and lawnmowers.

So the sign is not arbitrary. It falls straight out of the direction each good's quantity moves. If both go the same way, positive; if they go opposite ways, negative. For a deeper walkthrough of the formula, including a full interpretation grid and business uses, see our companion guide on cross-price elasticity explained.

Worked example 1: substitutes (positive XED)

A coffee shop raises the price of a latte from $4.00 to $4.40, a 10% increase. Over the next month, sales of its tea drinks rise from 500 to 560 cups, a 12% increase, as some customers switch away from the pricier coffee.

XED = (+12%) / (+10%) = +1.2

The number is positive, which confirms coffee and tea are substitutes. It is also greater than 1, meaning the response is strong: a 10% coffee price hike drove an even larger percentage jump in tea sales. That makes sense for two drinks many customers view as close alternatives. Anytime the numerator and denominator carry the same sign, price up and quantity up, you land on a positive XED and a substitute pair.

Worked example 2: complements (negative XED)

Now the same shop sees the price of espresso machines it sells jump from $200 to $240, a 20% increase. Sales of its subscription coffee-bean bags, which customers buy to use in those machines, fall from 300 to 264 bags, a 12% decrease.

XED = (−12%) / (+20%) = −0.6

The number is negative, confirming machines and beans are complements: pricier machines mean fewer machines sold, and fewer machines mean fewer bean subscriptions. The magnitude, 0.6, is less than 1, so the relationship is real but not overwhelming. Whenever the quantity of the second good falls as the first good's price rises, the numerator and denominator carry opposite signs and XED comes out negative.

Real product pairs to anchor the idea

Classic substitutes (positive XED): Coke and Pepsi, butter and margarine, beef and chicken, an airline flight and a train ticket, Netflix and Disney+, a taxi and a rideshare, tea and coffee, a name-brand drug and its generic. In each case a price rise in one nudges buyers toward the other.

Classic complements (negative XED): cars and gasoline, printers and ink cartridges, smartphones and cases, game consoles and games, hot dogs and buns, tennis rackets and tennis balls, cameras and memory cards, pancakes and syrup. In each case the two are consumed as a bundle, so their fortunes rise and fall together.

A useful subtlety: whether two goods are substitutes or complements can depend on context and on how broadly you define them. Coffee and milk are complements for a latte drinker but nearly unrelated for someone who drinks black coffee. Two goods can even flip categories over time as tastes and technology change. The sign of XED is measured for a specific market at a specific time, not fixed forever.

Why the distinction matters

Substitutes and complements are among the key determinants of demand, the factors that shift an entire demand curve left or right (as opposed to a good's own price, which moves you along the curve). When the price of a substitute rises, a good's demand curve shifts right. When the price of a complement rises, a good's demand curve shifts left. Getting the direction right is a staple of AP and IB free-response questions, and it is the reason these two categories show up constantly in elasticity problems.

The distinction also drives real business strategy. Firms watch their substitutes like hawks, because a rival's price cut can steal their customers, and they price complements they sell together with an eye on the whole bundle (the classic razor-and-blades model: sell the razor cheap, make the money on the blades). Understanding which goods compete with yours and which travel with yours is the difference between a pricing decision that grows revenue and one that quietly hands sales to a competitor.

Putting it together

To classify any two goods, ask one question: when the price of the first rises, does demand for the second go up or down? Up means they compete for the buyer's dollar, so they are substitutes and their cross-price elasticity is positive. Down means they are used together, so they are complements and their cross-price elasticity is negative. No change means they are unrelated. That is the entire framework. Practice the arithmetic on the cross-price elasticity calculator, work through the full formula in the cross-price elasticity guide, and reinforce the vocabulary, substitute goods and complementary goods, in the glossary. Once the sign rule is automatic, these questions become some of the fastest points on the exam.