Complementary good

: as the price of goods Y rises, the demand for good X falls. In economics, a complementary good is a good whose appeal increases with the popularity of another good, which is known as its complement. Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases. 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. 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.…

: as the price of goods Y rises, the demand for good X falls.]] In economics, a complementary good is a good whose appeal increases with the popularity of another good, which is known as its complement. Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases. 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. 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 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. ==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== for perfect complements]] 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. ==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 \frac{\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 . ===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^*, \dots) is \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} 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.

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