A complementary good is one that must be used in conjunction with another to satisfy consumer demand .
That is, two (or more) complementary goods are able to cover a need together. But separately they do not generate the same utility (even this can be null).
It should be mentioned that the proportion in which the complementary goods should be used is not necessarily one to one (1: 1), but may vary according to each case.
Example of complementary good
A common example of complementary goods is the printing machine and the ink it requires to work.
Another example is coffee and sugar. The vast majority of people do not enjoy coffee alone (with nothing), but want to sweeten it.
Characteristics of complementary goods
Complementary goods have a related demand . Then, when a consumer wishes to purchase one of the products, he must also consider buying his complement.
Given the above, if the price of a good increases, the demand for its complementary good will fall. That is, if the price of coffee goes up, people will buy less sugar.
In economic terms, the above means that complementary products have a negative cross-demand elasticity .
The elasticity of cross demand is expressed mathematically as follows:
exy: Cross elasticity of goods X and Y.
Qx: Amount demanded of good X
Py: Price of good Y
When the goods complement each other, exy <0. The opposite happens in the case of substitute goods (which can replace others).
Degree of complementarity of goods
Two or more goods can be complementary in varying degrees. When they are perfect complements, they must be consumed in fixed proportions and one does not deliver utility without the other. This is the case, for example, of footwear, where the left shoe is useless without the right.
However, there are also softer degrees of complementarity. For example, bread and butter. Usually they are not consumed in fixed proportions and the bread itself can deliver utility to the consumer.
Graphically, goods that are perfect complements (X1 and X2) are represented as follows:
As we can see in the graph above, the user only obtains satisfaction when he consumes both goods in fixed proportions. So, if you are given only one additional unit of the product without its complement, the added utility is zero.
In addition, another point to highlight in the image is that as the user consumes more units of both complementary goods, greater utility is obtained (up the 45º line).