Complementary good explained

In economics, a complementary good is a good whose appeal increases with the popularity of its complement. Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases.^[1] If

A is a complement to B , an increase in the price of A will result in a negative movement along the demand curve of A and cause the demand curve for B to shift inward; less of each good will be demanded. Conversely, a decrease in the price of A will result in a positive movement along the demand curve of A and cause the demand curve of B to shift outward; more of each good will be demanded. This is in contrast to a substitute good, whose demand decreases when its substitute's price decreases.^[2]

When two goods are complements, they experience joint demand - the demand of one good is linked to the demand for another good. Therefore, if a higher quantity is demanded of one good, a higher quantity will also be demanded of the other, and vice versa. For example, the demand for razor blades may depend on the number of razors in use; this is why razors have sometimes been sold as loss leaders, to increase demand for the associated blades.^[3] Another example is that sometimes a toothbrush is packaged free with toothpaste. The toothbrush is a complement to the toothpaste; the cost of producing a toothbrush may be higher than toothpaste, but its sales depends on the demand of toothpaste.

All non-complementary goods can be considered substitutes.^[4] If

x and y are rough complements in an everyday sense, then consumers are willing to pay more for each marginal unit of good x as they accumulate more y . The opposite is true for substitutes: the consumer is willing to pay less for each marginal unit of good "z " as it accumulates more of good "y ".

Complementarity may be driven by psychological processes in which the consumption of one good (e.g., cola) stimulates demand for its complements (e.g., a cheeseburger). Consumption of a food or beverage activates a goal to consume its complements: foods that consumers believe would taste better together. Drinking cola increases consumers' willingness to pay for a cheeseburger. This effect appears to be contingent on consumer perceptions of these relationships rather than their sensory properties.^[5]

Examples

An example of this would be the demand for cars and petrol. The supply and demand for cars is represented by the figure, with the initial demand

D _{1} . Suppose that the initial price of cars is represented by P _{1} with a quantity demanded of Q _{1} . If the price of petrol were to decrease by some amount, this would result in a higher quantity of cars demanded. This higher quantity demanded would cause the demand curve to shift rightward to a new position D _{2} . Assuming a constant supply curve S of cars, the new increased quantity demanded will be at Q _{2} with a new increased price P _{2} . Other examples include automobiles and fuel, mobile phones and cellular service, printer and cartridge, among others.

Perfect complement

A perfect complement is a good that must be consumed with another good. The indifference curve of a perfect complement exhibits a right angle, as illustrated by the figure.^[6] Such preferences can be represented by a Leontief utility function.

Few goods behave as perfect complements. One example is a left shoe and a right; shoes are naturally sold in pairs, and the ratio between sales of left and right shoes will never shift noticeably from 1:1.

The degree of complementarity, however, does not have to be mutual; it can be measured by the 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.

Example

In marketing, complementary goods give additional market power to the producer. It allows vendor lock-in by increasing switching costs. A few types of pricing strategy exist for a complementary good and its base good:

• Pricing the base good at a relatively low price - this approach allows easy entry by consumers (e.g. low-price consumer printer vs. high-price 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., a costly car vs inexpensive gas)

Gross complements

Sometimes the complement-relationship between two goods is not intuitive and must be verified by inspecting the cross-elasticity of demand using market data.

Mosak's definition states "a good

x is a gross complement of y if (\partial f _{x} (p, \omega))/(\partial p _{y}) is negative, where f _{i} (p, \omega) for i = 1 , 2 , \ldots , n denotes the ordinary individual demand for a certain good." In fact, in Mosak's case, x is not a gross complement of y but y is a gross complement of x . The elasticity does not need to be symmetrical. Thus, y is a gross complement of x while x can simultaneously be a gross substitutes for y .^[7]

Proof

The standard Hicks decomposition of the effect on the ordinary demand for a good

x of a simple price change in a good y , utility level \tau ^{*} and chosen bundle z ^{*} = (x ^{*,} y ^{*,} ... ) is(\partial f _{x(p,} \omega))/(\partial p _{y}) = (\partial h _{x} (p, \tau ^{*)})/(\partial p _{y}) - y ^{*} (\partial f _{x(p,} \omega))/(\partial \omega)

If

x is a gross substitute for y , the left-hand side of the equation and the first term of right-hand side are positive. By the symmetry of Mosak's perspective, evaluating the equation with respect to x ^{*} , the first term of right-hand side stays the same while some extreme cases exist where x ^{*} is large enough to make the whole right-hand-side negative. In this case, y is a gross complement of x . Overall, x and y are not symmetrical.

Effect of price change of complementary goods

• Substitute good

Notes and References

1. Book: Carbaugh, Robert. Contemporary Economics: An Applications Approach. Cengage Learning. 2006. 978-0-324-31461-8. 35. registration.
2. Book: Economics: Principles in Action . limited . O'Sullivan . Arthur . Sheffrin . Steven M. . Pearson Prentice Hall . 2003 . 0-13-063085-3 . Upper Saddle River, New Jersey . 88 . Arthur O'Sullivan (economist) . Steven M. Sheffrin.
3. Web site: Customer in Marketing by David Mercer . Future Observatory . https://web.archive.org/web/20130404042855/http://futureobservatory.dyndns.org/9432.htm . 2013-04-04 . dead.
4. Newman . Peter . 2016-11-30 . 1987 . Substitutes and Complements . The New Palgrave: A Dictionary of Economics . 1–7 . 10.1057/978-1-349-95121-5_1821-1 . 978-1-349-95121-5 . 2022-05-26.
5. Huh . Young Eun . Vosgerau . Joachim . Morewedge . Carey K. . 4800997 . 2016-03-14 . Selective Sensitization: Consuming a Food Activates a Goal to Consume its Complements . Journal of Marketing Research . 53 . 6 . 1034–1049 . 10.1509/jmr.12.0240 . 0022-2437.
6. Book: Mankiw, Gregory. Principle of Economics. Cengage Learning. 2008. 978-0-324-58997-9. 463–464.
7. Mosak . Jacob L. . 1944 . General equilibrium theory in international trade . Cowles Commission for Research in Economics, Monograph No. 7 . Principia Press . 33.