Substitutes and Complements

The Effect of a Related Good's Price

So far, the analysis of a consumer's choice has focused on the price of the good itself and the consumer's income. But a consumer's decision to buy a good is also influenced by the prices of other goods. The relationship between the quantity demanded of one good and the price of a related good is the subject of this section.

The direction of this effect — whether the quantity demanded of good X rises or falls when the price of good Y changes — depends entirely on the nature of the relationship between the two goods. Two goods can be related in one of two fundamental ways: they are either substitutes or complements.

Complementary Goods

Goods that are consumed together are called complementary goods. The defining feature of complements is that they are used jointly to satisfy a want. The textbook gives the classic examples of tea and sugar, shoes and socks, and pen and ink. You cannot drink tea without sugar (if you take sugar in your tea), and you cannot wear a shoe without a sock (in the usual case).

Because they are used together, a change in the price of one good directly affects the demand for the other. Consider tea and sugar. If the price of sugar rises, sugar becomes more expensive. This makes the act of drinking sweetened tea more costly. As a result, consumers are likely to buy less sugar, and because they are using less sugar, they will also buy less tea. The demand for tea falls.

Conversely, if the price of sugar falls, sugar becomes cheaper. Drinking sweetened tea becomes less costly, so consumers buy more sugar and, consequently, more tea. The demand for tea rises.

This is a negative relationship. If we denote the quantity demanded of good X as $q_x$ and the price of its complement good Y as $P_y$, then:

• When $P_y \uparrow$, $q_x \downarrow$.
• When $P_y \downarrow$, $q_x \uparrow$.

Substitute Goods

In contrast to complements, substitute goods are goods that can be used in place of each other. They satisfy the same kind of want. The textbook's example is tea and coffee. A consumer who wants a hot beverage can choose either tea or coffee. They are alternatives.

Because they are alternatives, a change in the price of one good gives consumers a reason to switch. Suppose the price of coffee increases. Coffee has become more expensive relative to tea. A consumer who previously bought coffee can now get a similar level of satisfaction by switching to tea, which is now relatively cheaper. Therefore, the consumption of tea is likely to go up.

On the other hand, if the price of coffee decreases, coffee becomes relatively cheaper. Consumers who were drinking tea may now switch to coffee. The consumption of tea is likely to go down.

This is a positive relationship. If we denote the quantity demanded of good X as $q_x$ and the price of its substitute good Z as $P_z$, then:

• When $P_z \uparrow$, $q_x \uparrow$.
• When $P_z \downarrow$, $q_x \downarrow$.

A Quick Comparison

The following table summarises the two relationships.