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## Complementary good

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.

## Examples

Supply and demand of hotdogs An example of this would be the demand for hotdogs and hotdog buns. The supply and demand of hotdogs is represented by the figure at the right with the initial demand D1. Suppose that the initial price of hotdogs is represented by P1 with a quantity demanded of Q1. If the price of hotdog buns were to decrease by some amount, this would result in a higher quantity of hotdogs demanded. This higher quantity demanded would cause the demand curve to shift outward to a new position D2. Assuming a constant supply S of hotdogs, the new quantity demanded will be at D2 with a new price P2.

Other examples include:

• Peanut butter and jelly
• Printers and ink cartridges
• DVD players and DVDs
• Computer hardware and computer software
• Left footed and right footed shoes

## 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

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