Ineconomics, a complementary good is a good whose appeal increases with the popularity of its complement.[further explanation needed] Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases.[1]If is a complement to
, an increase in the price of
will result in a negative movement along the demand curve of
and cause the demand curve for
toshift inward; less of each good will be demanded. Conversely, a decrease in the price of
will result in a positive movement along the demand curve of
and cause the demand curve of
toshift 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 and
are rough complements in an everyday sense, then consumers are willing to pay more for each marginal unit of good
as they accumulate more
. The opposite is true for substitutes: the consumer is willing to pay less for each marginal unit of good "
" as it accumulates more of good "
".
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]
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 . Suppose that the initial price of cars is represented by
with a quantity demanded of
. 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
. Assuming a constant supply curve
of cars, the new increased quantity demanded will be at
with a new increased price
. Other examples include automobiles and fuel, mobile phones and cellular service, printer and cartridge, among others.
Aperfect 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.[6] 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.
Inmarketing, 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:
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 is a gross complement of
if
is negative, where
for
denotes the ordinary individual demand for a certain good." In fact, in Mosak's case,
is not a gross complement of
but
is a gross complement of
. The elasticity does not need to be symmetrical. Thus,
is a gross complement of
while
can simultaneously be a gross substitutes for
.[7]
The standard Hicks decomposition of the effect on the ordinary demand for a good of a simple price change in a good
, utility level
and chosen bundle
is
If is a gross substitute for
, 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
, the first term of right-hand side stays the same while some extreme cases exist where
is large enough to make the whole right-hand-side negative. In this case,
is a gross complement of
. Overall,
and
are not symmetrical.