# Complementary good

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Complementary goods exhibit a negative cross elasticity of demand: as the price of good Y rises, the demand for good X falls.

In economics, a complementary good is a good with a negative cross elasticity of demand, in contrast to a substitute good.[1] 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.[2] 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.

## Examples

Supply and demand of hotdogs

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 S of hot dogs, the new quantity demanded will be at D2 with a new price.P2

Other examples include:

• Printers and ink cartridges
• DVD players and DVDs
• Computer hardware and computer software
• Boots and laces
• Flashlight and battery

## Perfect complement

Indifference curve for perfect complements

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.[3] Few goods in the real world will behave as perfect complements.[4] 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:

• Pricing the base good at a relatively low price to the complementary good - this approach allows easy entry by consumers (e.g. consumer printer vs. ink jet 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. golf club membership vs. green fees)

## References

1. ^ Sullivan, Arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p. 88. ISBN 0-13-063085-3.
2. ^ Carbaugh, Robert (2006). Contemporary Economics: An Applications Approach. Cengage Learning. p. 35. ISBN 978-0-324-31461-8.
3. ^ Mankiw, Gregory (2008). Principle of Economics. --~~~~Cengage Learning. pp. 463–464. ISBN 978-0-324-58997-9.
4. ^ Mankiw, 2008.