Complementary good
In economics, a complementary good is a good whose appeal increases with the popularity of its complement.Template:Explain Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases.<ref>Template:Cite book</ref> If <math>A</math> is a complement to <math>B</math>, an increase in the price of <math>A</math> will result in a negative movement along the demand curve of <math>A</math> and cause the demand curve for <math>B</math> to shift inward; less of each good will be demanded. Conversely, a decrease in the price of <math>A</math> will result in a positive movement along the demand curve of <math>A</math> and cause the demand curve of <math>B</math> 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.<ref>Template:Cite book</ref>
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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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.<ref name="Newman">Template:Cite journal</ref> If <math>x</math> and <math>y</math> are rough complements in an everyday sense, then consumers are willing to pay more for each marginal unit of good <math>x</math> as they accumulate more <math>y</math>. The opposite is true for substitutes: the consumer is willing to pay less for each marginal unit of good "<math>z</math>" as it accumulates more of good "<math>y</math>".
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.<ref>Template:Cite journal</ref>
ExamplesEdit
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 <math>D_1</math>. Suppose that the initial price of cars is represented by <math>P_1</math> with a quantity demanded of <math>Q_1</math>. 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 <math>D_2</math>. Assuming a constant supply curve <math>S</math> of cars, the new increased quantity demanded will be at <math>Q_2</math> with a new increased price <math>P_2</math>. Other examples include automobiles and fuel, mobile phones and cellular service, printer and cartridge, among others.
Perfect complementEdit
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.<ref name=mankiw>Template:Cite book</ref> Such preferences can be represented by a Leontief utility function.
Few goods behave as perfect complements.<ref name=mankiw /> 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.
ExampleEdit
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 complementsEdit
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 <math>x</math> is a gross complement of <math>y</math> if <math>\frac{\partial f_x (p, \omega)}{\partial p_y}</math> is negative, where <math>f_i (p, \omega)</math> for <math>i = 1, 2 , \ldots , n</math> denotes the ordinary individual demand for a certain good." In fact, in Mosak's case, <math>x</math> is not a gross complement of <math>y</math> but <math>y</math> is a gross complement of <math>x</math>. The elasticity does not need to be symmetrical. Thus, <math>y</math> is a gross complement of <math>x</math> while <math>x</math> can simultaneously be a gross substitutes for <math>y</math>.<ref>Template:Cite journal</ref>
ProofEdit
The standard Hicks decomposition of the effect on the ordinary demand for a good <math>x</math> of a simple price change in a good <math>y</math>, utility level <math>\tau^*</math> and chosen bundle <math>z^* = (x^*, y^*, \dots)</math> is
<math>\frac{\partial f_x(p, \omega)}{\partial p_y} = \frac{\partial h_x (p, \tau^*)}{\partial p_y} - y^* \frac{\partial f_x(p, \omega)}{\partial \omega}</math>
If <math>x</math> is a gross substitute for <math>y</math>, 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 <math>x^*</math>, the first term of right-hand side stays the same while some extreme cases exist where <math>x^*</math> is large enough to make the whole right-hand-side negative. In this case, <math>y</math> is a gross complement of <math>x</math>. Overall, <math>x</math> and <math>y</math> are not symmetrical.