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In economics, a complementary good or complement is a good with a negative cross elasticity of demand, in contrast to a substitute good. This means a good's demand is increased when the price of another good is decreased. Conversely, the demand for a good is decreased when the price of another good is increased. If goods A and B are complements, an increase in the price of A will result in a leftward movement along the demand curve of A and cause the demand curve for B to shift in; less of each good will be demanded. A decrease in price of A will result in a rightward movement along the demand curve of A and cause the demand curve B to shift outward; more of each good will be demanded. Basically this means that since the demand of one good is linked to the demand of another good, if a higher quantity is demanded of one good, a higher quantity will also be demanded of the other, and if a lower quantity is demanded of one good, a lower quantity will be demanded of the other. The prices of complementary goods are related in the same way: if the price of one good rises, so will the price of the other, and vice versa. With substitute goods, however, the price and quantity demanded of one good is related inversely to the price and quantity demanded of a substitute good, meaning that if the price or quantity demanded of one good rises, the price or quantity demanded of its substitute will fall.
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When two goods are complements, they experience joint demand. For example, the demand for razor blades may depend upon the number of razors in use; this is why razors have sometimes been sold as loss leaders, to increase demand for the associated blades.
Recent work in food consumption has elucidated the psychological processes by which the consumption of one good (e.g., cola) stimulates demand for its complements (e.g., a cheeseburger, pizza, etc.). Consumption of a food or beverage activates a goal to consume its complements: foods that consumers believe would produce super-additive utility (i.e., would taste better together). Eating peanut-butter covered crackers, for instance, increases the consumption of grape-jelly covered crackers more than eating plain crackers. Drinking cola increases consumers' willingness to pay for a voucher for a cheeseburger. This effect appears to be contingent on consumers' perceptions of what foods are complements rather than their sensory properties.
Examples
An example of this would be the demand for hot dogs and hot dog buns. The supply and demand of hot dogs is represented by the figure at the right with the initial demand D1. Suppose that the initial price of hot dogs is represented by P1 with a quantity demanded of Q1. If the price of hot dog buns were to decrease by some amount, this would result in a higher quantity of hot dogs demanded. This higher quantity demanded would cause the demand curve to shift outward to a new position D2. Assuming a constant supply curve S of hot dogs, the new quantity demanded will be at D2 with a new price P2.
Other examples include:
Perfect complement
A perfect complement is a good that has to be consumed with another good. The indifference curve of a perfect complement will exhibit a right angle, as illustrated by the figure at the right. Such preferences are often represented by a Leontief utility function.
Few goods in the real world will 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 - even if, for example, someone is missing a leg and buys just one shoe.
The degree of complementarity, however, does not have to be mutual; it can be measured by 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
A classic example of mutually perfect complements is the case of pencils and erasers. Imagine an accountant who will need to prepare financial statements, but in doing so he or she must use pencils to make all calculations and an eraser to correct errors. The accountant knows that for every 3 pencils, 1 eraser will be needed. Any more pencils will serve no purpose, because he or she will not be able to erase the calculations. Any more erasers will not be useful either, because there will not be enough pencils for him or her to make a large enough mess with in order to require more erasers.
In this case the utility would be given by an increasing function of:
min (number of pencils, 3 × number of erasers)In marketing, complementary goods give additional market power to the company. It allows vendor lock-in as it increases the switching cost. A few types of pricing strategy exist for complementary good and its base good: