![Cross elasticity of demand complements](https://upload.wikimedia.org/wikipedia/commons/0/0d/Cross_elasticity_of_demand_complements.svg)
In
economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
, a complementary good is a
good
In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil and is of interest in the study of ethics, morality, ph ...
whose appeal increases with the popularity of its complement. Technically, it displays a negative
cross elasticity of demand and that
demand
In economics, demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given time. The relationship between price and quantity demand is also called the demand curve. Demand for a specific item ...
for it increases when the
price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the ...
of another good decreases. 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
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...
for
to
shift 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
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.
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. 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.
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.
Examples
![Supply-and-demand](https://upload.wikimedia.org/wikipedia/commons/7/7a/Supply-and-demand.svg)
An example of this would be the demand for
cars and
petrol
Gasoline (; ) or petrol (; ) (see ) is a transparent, petroleum-derived flammable liquid that is used primarily as a fuel in most spark-ignited internal combustion engines (also known as petrol engines). It consists mostly of organic c ...
. 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.
Perfect complement
![Indifference-curves-perfect-complements](https://upload.wikimedia.org/wikipedia/commons/c/cd/Indifference-curves-perfect-complements.svg)
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.
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
Marketing is the process of exploring, creating, and delivering value to meet the needs of a target market in terms of goods and services; potentially including selection of a target audience; selection of certain attributes or themes to emph ...
, complementary goods give additional
market power
In economics, market power refers to the ability of a firm to influence the price at which it sells a product or service by manipulating either the supply or demand of the product or service to increase economic profit. In other words, market powe ...
to the producer. It allows
vendor lock-in
In economics, vendor lock-in, also known as proprietary lock-in or customer lock-in, makes a customer dependent on a vendor for products, unable to use another vendor without substantial switching costs.
The use of open standards and alternat ...
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 of
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
.
Proof
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.
Effect of price change of complementary goods
*
Substitute good
References
{{Goodtypes
Goods (economics)
Utility function types