Complementary good

From Wikipedia, the free encyclopedia

A complementary good or complement good in economics is a good which is consumed with another good; its cross elasticity of demand is negative. This means that, if goods A and B were complements, more of good A being bought would result in more of good B also being bought. An increase in the price of one of the goods will result in a leftward shift of both demand curves; less of each good would be demanded. A decrease in the price of one of the goods will result in a rightward shift of both demand curves; more of each good would be demanded. An example of this would be the demand for hotdogs and hotdog buns. If the price of hotdogs increases, then less hotdog buns would be demanded at any given price given that the total price of the two goods is higher than before. If the price of hotdogs decreases, then more hotdog buns would be demanded at any given price given that the total price of the two goods is lower than before.

A perfect complement is a good that has to be consumed with another good. Many goods in the real world exhibit characteristics close to perfect complementariness. An example would be a left shoe and a right. Because of this, shoes are naturally sold in pairs, and the ratio between sales of left and right shoes will never shift noticeably from 1:1 - even if, for example, someone is missing a leg and buys just one shoe.

The degree of complementariness, however, does not have to be mutual; it can be measured by cross price elasticity of demand. In the case of video games, a specific video game (the complement good) has to be consumed with a video game console (the base good). It does not work the other way: a video game console does not have to be consumed with that game.

A classic example of mutual perfect complements is the case of pencils and erasers. Imagine an Accountant who will need to prepare financial statements or tax liability, but in doing so he or she must use pencils to make all calculations and an eraser to remove all calculations and present a clear and clean final product (number). The Accountant knows that for every 3 pencils, 1 eraser will be needed. Any more pencils will serve no purpose, because he or she will not be able to erase the calculations. Any more erasers will not be useful either, because there will not be enough pencils for him or her to make a large enough mess with in order to require more erasers. The accountant is then left to determine how many of each he or she would like to purchase.

In economics, primarily microeconomics, a utility curve would need to be drawn to represent the accountant's preferences. In the case of perfect complements, such a function would look like; Utility = Min (Pencils, Erasers). This is slightly misleading, because it implies that the accountant is equally well off if he or she has either a bundle of [3 pencils and 1 eraser] or [1 pencil and 1 eraser]. However, we know this is not the case because the accountant knows he or she needs 3 pencils for every 1 eraser. We will need to construct a model or function which suggests the following:

1. Given a bundle of (3 pencils & 1 eraser), a bundle where only one of these goods is greater (Example: 500 pencils & 1 eraser) is just as good as the (3,1) bundle. 2. Given a bundle of (3 pencils & 1 eraser), a bundle where one or both of these goods is less (Example: 2 pencils & 1 eraser) is not as good or, less preferred than the (3,1) bundle.

To do this, we must understand that the accountant has noticed something very important; for every 3 pencils, 1 eraser is required; and for every 1 eraser, 3 pencils are required to give the same level of satisfaction or in this case, performance. We can then identify each component of the accountant's preference for these goods in terms of the other. For instance, we know that since he or she requires 3 pencils for every 1 eraser, he or she must value them equally. We can then express his preferences for both of these goods in terms of one:

1. Since every 3 pencils require 1 eraser; 3 units of utility require 3 pencils and 1 eraser. What value must we give to each eraser to make this equation hold? 2. We know that 3 pencils, in terms of pencils, are equal to 3 pencils; that is simple; 3p=3p. Therefore, 1p=1p. 3. But what about 1 eraser? In terms of pencils, one eraser is necessary to get three units of utility. Therefore, the value of erasers can be expressed in the value of pencils, 1e=3p. 4. We must now finalize our utility function. Since we know that 1 pencil is valued to be as good as 1 pencil, and that 1 eraser is valued the be as good as 3 pencils, our utility function looks like: Utility=Min(1p,3e). This is because, if we represent utility in terms of preference to pencils, each pencil is to be multiplied by (1), because it's only as good as itself. However, each eraser is to be multiplied by (3), because it is as good as 3 pencils. 5. Since this is a mutual example, we can express the entire utility function in terms of erasers. One eraser is only as good as itself, so we can expect to multiply it by (1). However, each pencil is only as good as (1/3) of an eraser, so we can expect to multiply it by (1/3). In fact, when we work out the problem, we see that in this case, Utility=Min([1/3]p,1e).

In marketing, complementary goods give additional market power to the company. It allows vendor lock-in as it increases the switching cost. A few types of pricing strategy exist for complementary good and its base good:

Pricing the base good at a relatively low price to the complementary good - this approach allows easy entry by consumers (e.g. consumer printer vs ink jet cartridge)
Pricing the base good at a relatively high price to the complementary good - this approach creates a barrier to entry and exit (e.g. golf club membership vs green fees)