Substitutes vs Complements

Complementary goods are products that are consumed together to enhance the value or utility of each other. For example, a printer and printer ink are complementary goods as they are used together to produce printed documents.

Now, let's explain. If the price of a can of Pepsi increases, people are expected to buy more Coke, since Coke and Pepsi are substitutes for each other. This captures the idea of substitutes.

What about complements? Consumers often eat cookies with milk. Therefore, if the price of cookies increases such that people cannot consume as many cookies as they used to, milk consumption will also decline.

What about a good whose consumption does not change when the price of other good changes? If price changes in two goods do not affect the consumption of either of the goods, economists say that the goods are independent goods.

The concept of substitutes vs complements suggests that studying the impact of changes in one market on other related markets is necessary. Keep in mind that economists typically determine whether two goods are substitutes or complements by evaluating what a change in the price of one good does to the demand for the other good.

Difference between a Substitute and a Complement

The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together. Let's break the differences down for better understanding.

• The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together.

Substitutes and Complements Graph

A substitute and complements graph is used to show the relationship between two goods that are either substitutes or complements. We use the demand graphs of the goods to demonstrate the concept. However, the price of Good A is plotted on the vertical axis, whereas the quantity demanded of Good B is plotted on the horizontal axis of the same graph. Let's have a look at Figures 1 and 2 below to help us illustrate how substitutes and complements work.

Fig. 1 - Graph for complementary goods

As Figure 1 above demonstrates, when we plot the price and quantity demanded of complementary goods against each other, we get a downward-sloping curve, which shows that the quantity demanded of a complementary good increases as the price of the initial good decreases. This means that consumers consume more of a complementary good when the price of one good decreases.

Now, let's have a look at the case of a substitute good in Figure 2.

Fig. 2 - Graph for substitute goods

Since the quantity demanded of a substitute good increases when the price of an initial good increases, Figure 2 above shows an upward-sl curve. This shows that when the price of a good increases, consumers consume less of it and consume more of its substitute.

Substitutes and Complements Cross Price Elasticity

Cross-price elasticity of demand, in the context of substitutes and complements, refers to how a price change for one good causes a change in the quantity demanded of the other good. You should note that if the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of demand of the two goods is negative, then the goods are complements. Therefore, economists use the cross-price elasticity of demand of two goods to determine whether they are complements or substitutes.

• If the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of the two goods is negative, then the goods are complements.

Economists calculate cross-price elasticity by dividing the percentage change in quantity demanded of one good by the percentage change in the price of another good. We present this mathematically as:

\(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)

Where ΔQ_D represents change in quantity demanded and ΔP represents change in price.

Substitutes and Complements Examples

A couple of examples will help you grasp the concept of substitutes and complements better. Let's try some examples where we calculate the cross-price elasticity of two goods to determine whether they are substitutes or complements.

Example 1

Example 2