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Substitutes and Complements Explanation
Substitute goods are products that consumers use for the same purpose as other similar products. In other words, if two products are substitutes, they can be used interchangeably to satisfy the same need.
A substitute good is a good that serves the same purpose as another good for consumers.
For example, butter and margarine are substitutes for each other as they both serve the same purpose of being a spread for bread or toast.
Complementary goods are products that are consumed together to enhance the value or utility of each other. For example, a printer and printer ink are complementary goods as they are used together to produce printed documents.
A complementary good is a good that adds value to another good when they are consumed together.
Now, let's explain. If the price of a can of Pepsi increases, people are expected to buy more Coke, since Coke and Pepsi are substitutes for each other. This captures the idea of substitutes.
What about complements? Consumers often eat cookies with milk. Therefore, if the price of cookies increases such that people cannot consume as many cookies as they used to, milk consumption will also decline.
What about a good whose consumption does not change when the price of other good changes? If price changes in two goods do not affect the consumption of either of the goods, economists say that the goods are independent goods.
Independent goods are two goods whose price changes do not influence the consumption of each other.
The concept of substitutes vs complements suggests that studying the impact of changes in one market on other related markets is necessary. Keep in mind that economists typically determine whether two goods are substitutes or complements by evaluating what a change in the price of one good does to the demand for the other good.
Read our article on Supply and Demand to learn more.
Difference between a Substitute and a Complement
The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together. Let's break the differences down for better understanding.
- The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together.
| Substitutes | Complements |
| Consumed in place of each other | Consumed with each other |
| A price reduction in one good increases the demand for the other good. | A price increase in one good decreases demand for the other good. |
| Upward slope when the price of one good is plotted against the quantity demanded of the other good. | Downward slope when the price of one good is plotted against the quantity demanded of the other good. |
Read our article on A Change in Demand to learn more.
Substitutes and Complements Graph
A substitute and complements graph is used to show the relationship between two goods that are either substitutes or complements. We use the demand graphs of the goods to demonstrate the concept. However, the price of Good A is plotted on the vertical axis, whereas the quantity demanded of Good B is plotted on the horizontal axis of the same graph. Let's have a look at Figures 1 and 2 below to help us illustrate how substitutes and complements work.
Fig. 1 - Graph for complementary goods
As Figure 1 above demonstrates, when we plot the price and quantity demanded of complementary goods against each other, we get a downward-sloping curve, which shows that the quantity demanded of a complementary good increases as the price of the initial good decreases. This means that consumers consume more of a complementary good when the price of one good decreases.
Now, let's have a look at the case of a substitute good in Figure 2.
Fig. 2 - Graph for substitute goods
Since the quantity demanded of a substitute good increases when the price of an initial good increases, Figure 2 above shows an upward-sl curve. This shows that when the price of a good increases, consumers consume less of it and consume more of its substitute.
Note that in all the above cases, we assume that the price of the other good (Good B) remains constant while the price of the main good (Good A) changes.
Substitutes and Complements Cross Price Elasticity
Cross-price elasticity of demand, in the context of substitutes and complements, refers to how a price change for one good causes a change in the quantity demanded of the other good. You should note that if the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of demand of the two goods is negative, then the goods are complements. Therefore, economists use the cross-price elasticity of demand of two goods to determine whether they are complements or substitutes.
Cross-price elasticity of demand refers to how a price change in one good causes a change in the quantity demanded of another good.
- If the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of the two goods is negative, then the goods are complements.
Economists calculate cross-price elasticity by dividing the percentage change in quantity demanded of one good by the percentage change in the price of another good. We present this mathematically as:
\(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)
Where ΔQD represents change in quantity demanded and ΔP represents change in price.
Substitutes and Complements Examples
A couple of examples will help you grasp the concept of substitutes and complements better. Let's try some examples where we calculate the cross-price elasticity of two goods to determine whether they are substitutes or complements.
Example 1
A 20% increase in the price of fries causes a 10% decrease in the quantity demanded of ketchup. What is the cross-price elasticity of demand for fries and ketchup, and are they substitutes or complements?
Solution:
Using:
\(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)
We have:
\(Cross\ Price\ Elasticity\ of\ Demand=\frac{-10%}{20%}\)
\(Cross\ Price\ Elasticity\ of\ Demand=-0.5\)
A negative cross-price elasticity of demand indicates that fries and ketchup are complementary goods.
Example 2
A 30% increase in the price of honey causes a 20% increase in the quantity demanded of sugar. What is the cross price elasticity of demand for honey and sugar, and determine whether they are substitutes or complements?
Solution:
Using:
\(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)
We have:
\(Cross\ Price\ Elasticity\ of\ Demand=\frac{20%}{30%}\)
\(Cross\ Price\ Elasticity\ of\ Demand=0.67\)
A positive cross-price elasticity of demand indicates that honey and sugar are substitute goods.
Read our article on Cross-Price Elasticity of Demand Formula to learn more.
Substitutes Vs Complements - Key takeaways
- A substitute good is a good that serves the same purpose as another good for consumers.
- A complementary good is a good that adds value to another good when they are consumed together.
- The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together.
- The formula for cross-price elasticity of demand is \(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)
- If the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of demand of the two goods is negative, then the goods are complements.
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Frequently Asked Questions about Substitutes vs Complements
What is the difference between complements and substitutes?
The main difference between a substitute and a complement is that substitute goods are consumed in place of each other, whereas complements are consumed together.
What are the substitutes and complements and give examples?
A substitute good is a good that serves the same purpose as another good for consumers.
A complementary good is a good that adds value to another good when they are consumed together.
Pepsi and Coke are a typical example of substitute goods, whereas fries and ketchup may be considered complements of each other.
How do substitutes and complements affect demand?
When the price of a substitute increases, the demand for the other good increases. When the price of a complement increases, the demand for the other good decreases.
How do you know if its complement or substitute?
If the cross-price elasticity of demand of the two goods is positive, then the goods are substitutes. On the other hand, if the cross-price elasticity of the two goods is negative, then the goods are complements.
What happens when the price of a complement increases?
When the price of a complement increases, the demand for the other good decreases.
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