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Complementary Goods: Definition & Examples

Complementary Goods Definition

A Complementary good is a product or service that adds value to another. In other words, they are two goods that the consumer uses together. For example, cereal and milk, or a DVD and a DVD player.

On occasion, the complementary good is absolutely necessary, as is the case with petrol and a car. However, a complementary good can add value to the initial product. For instance, pancakes and maple syrup.

• A complementary good is a good that adds value to another, or, a good that cannot be used without each other.
• Complementary goods that cannot be used without each other are known to have a strong relationship. In other words, when the price goes up on one, the demand goes down for the other good.
• Examples include: Tennis Balls and Tennis Racket; PlayStations and Games; Movies and Popcorn; and Mobile Phones and Sim Cards.

Complementary Goods have a negative relationship with each other – which means that when product X increases in price, demand for product Y falls. This is because fewer people buy product X due to the higher price. As a result, fewer people are also buying product Y, which only adds value to product X. In economic jargon, this is known as ’negative cross-elasticity of demand’ .

Let us consider an iPhone. If its price increases by 10 percent, this may lead to lower levels of demand. At the same time, if fewer people are buying iPhones, then there are also fewer people buying iPhone cases. It is because of this relationship that we can consider these as complementary goods.

Weak Complementary Goods

Not all complementary goods are the same. There are ‘weak’ and ‘strong’ complementary goods. Weak complementary goods respond to increases in prices in a very limited way. In other words, they are not responsive to increases in prices of complementary goods. However, there is some connection between the two.

If we take pancakes and maple syrup as an example – they are two complementary goods. Consumers use maple syrup with pancakes, but they also use other toppings. For instance, consumers may use bananas or sugar instead. Therefore, whilst maple syrup is used to complement pancakes, there are many other alternatives that make the relationship between the two weak.

If the price of maple syrup increases by 10 percent, but the demand for pancakes falls by 1 percent, the relationship is therefore weak. This is because the price increase of the complementary product has little effect on the demand on the other.

Strong Complementary Goods

Strong Complementary Goods have a close relationship with each other. That is to say that one good is reliant on the other to add value. For example, we have a DVD and a DVD player. These are known as strong complementary goods because they are pretty useless without one another.

The relationship between strong complementary goods is very elastic. In other words, when the price of DVD players rise, the demand for DVDs is likely to fall. So we can say there is a ‘ negative cross-elasticity’ between them. In fact, if you look at any product that could not be sold by itself – it is likely a strong complementary good. So if you could only use Product X if you first had Product Y, then they are strong complementary goods.

Complementary Goods Graph

As we can see from the graph below; when the price of an iPhone decreases, the demand for iPhone cases increases. This is because the demand for iPhones increases as more consumers are buying it at the lower prices. In turn, those same consumers are demanding iPhone cases – which translates into high sales.

Complementary Goods Examples

Complementary goods are goods which rely on each other to add value. There are a large number of complementary goods which are necessary in order for the other to work. For example, petrol is needed for cars to work. However, there are also weak complementary goods that are not necessarily needed in order to function. An iPhone does not need a phone case in order to work, but is still classed as a complementary good. Other examples include:

• Tennis Balls and Tennis Racket
• Mobile Phones and Sim Cards
• Petrol and Cars
• Burger and Burger Buns
• PlayStation and Games
• Movies and Popcorn
• Shoes and Insoles
• Pencils and Notebooks

A Complementary good can be a product or service that is sold separately that adds value to another. In other words, they are two or more goods that are used together.

Substitute goods are two goods that can be used i n place of one another , for example, Dominos and Pizza Hut. By contrast, complementary goods are those that are used with each other . For example, pancakes and maple syrup. The key difference is that substitute goods replace one another, whilst complementary goods add value to the other.

Some examples of complementary goods include: 1. Tennis Balls and Tennis Racket 2. Mobile Phones and Sim Cards 3. Petrol and Cars 4. Burger and Burger Buns 5. PlayStation and Games 6. Movies and Popcorn 7. Shoes and Insoles 8. Pencils and Notebooks

Paul Boyce is an economics editor with over 10 years experience in the industry. Currently working as a consultant within the financial services sector, Paul is the CEO and chief editor of BoyceWire. He has written publications for FEE, the Mises Institute, and many others.

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Aren't PB&J, chips and salsa, or cookies and milk perfect duos? Of course, they are! Goods that are usually consumed together are called complementary goods in economics. Keep reading to learn the definition of complementary goods and how their demand is intertwined. From the classic complementary goods diagram to the effect of price changes, we'll explore everything you need to know about this type of goods. Plus, we'll give you some examples of complementary goods that make you want to grab a snack! Don't confuse them with substitute goods ! We'll show you the difference between substitute goods and complementary goods too! 

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Aren't PB&J, chips and salsa, or cookies and milk perfect duos? Of course, they are! Goods that are usually consumed together are called complementary goods in economics. Keep reading to learn the definition of complementary goods and how their demand is intertwined. From the classic complementary goods diagram to the effect of price changes, we'll explore everything you need to know about this type of goods. Plus, we'll give you some examples of complementary goods that make you want to grab a snack! Don't confuse them with substitute goods ! We'll show you the difference between substitute goods and complementary goods too!

Complementary Goods Definition

Complementary goods are products that are typically used together. They are goods that people tend to buy at the same time because they go well together or enhance each other's use. A good example of complementary goods would be tennis rackets and tennis balls. W hen the price of one good goes up, the demand for the other also goes down, and when the price of one good goes down, the demand for the other goes up.

Complementary goods are two or more goods typically consumed or used together, such that a change in the price or availability of one good affects the demand for the other good.

A good example of complementary goods would be video games and gaming consoles. People who buy gaming consoles are more likely to buy video games to play on them, and vice versa. When a new gaming console is released, the demand for compatible video games usually increases as well. Similarly, when a new popular video game is released, the demand for the gaming console it is compatible with may also increase.

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.

Complementary Goods Diagram

The complementary goods diagram shows the relationship between the price of one good and the quantity demanded of its complement. T he 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 diagram.

As Figure 1 below 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.

Effect of Price Change on Complementary Goods

The effect of price change on complementary is that the increase in the price of one good causes a decrease in demand for its complement. It is measured using cross price elasticity of demand .

Cross price elasticity of demand measures the percentage change in the quantity demanded of one good in response to a one percent change in the price of its complementary good.

It is calculated using the following formula:

\(Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ B}\)

• I f the cross price elasticity is negative , it indicates that the two products are complements , and an increase in the price of one will lead to a decrease in the demand for the other.
• If the cross price elasticity is positive , it indicates that the two products are substitutes , and an increase in the price of one will lead to an increase in the demand for the other.

Let's say that the price of tennis rackets increases by 10%, and as a result, the demand for tennis balls decreases by 5%.

\(Cross\ Price\ Elasticity\ of\ Demand=\frac{-5\%}{10\%}=-0.5\)

The cross price elasticity of tennis balls with respect to tennis rackets would be -0.5, indicating that tennis balls are a complementary good for tennis rackets. When the price of tennis rackets increases, consumers are less likely to purchase balls, decreasing the demand for tennis balls.

Complementary Goods Examples

Examples of complementary goods include:

• Hot dogs and hot dog buns
• Chips and salsa
• Smartphones and protective cases
• Printer and ink cartridges
• Cereal and milk
• Laptops and laptop cases

To better understand the concept, analyze the example below.

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?

\(Cross\ Price\ Elasticity\ of\ Demand=\frac{-10\%}{20\%}\)

\(Cross\ Price\ Elasticity\ of\ Demand=-0.5\)

A negative cross-price elasticity of demand indicates that fries and ketchup are complementary goods.

Complementary Goods vs Substitute Goods

The main difference between complementary and substitute goods is that complements are consumed together whie substitute goods are consumed in place of each other. Let's break the differences down for better understanding.

Complementary Goods - Key takeaways

• Complementary goods are products that are typically used together and influence each other's demand.
• The demand curve for complementary goods is downward sloping, indicating that an increase in the price of one good decreases the quantity demanded of the other good.
• The cross price elasticity of demand is used to measure the effect of price changes on complementary goods.
• A negative cross price elasticity means that the goods are complements, while a positive cross price elasticity means that they are substitutes.
• Examples of complementary goods include hot dogs and hot dog buns, smartphones and protective cases, printer and ink cartridges, cereal and milk, and laptops and laptop cases.
• The main difference between complementary and substitute goods is that complementary goods are consumed together while substitute goods are consumed in place of each other.

Frequently Asked Questions about Complementary Goods

--> what are complementary goods.

Complementary goods are products that are typically used together and influence each other's demand. An increase in the price of one good decreases the quantity demanded of the other good.

--> How do complementary goods affect demand?

Complementary goods have a direct impact on the demand for each other. When the price of one complementary good increases, the demand for the other complementary good decreases, and vice versa. This is because the two goods are typically consumed or used together, and a change in the price or availability of one good affects the demand for the other good

--> Do complementary goods have derived demand?

Complementary goods do not have derived demand. Consider the case of coffee and coffee filters. These two goods are typically used together - coffee is brewed using a coffee maker and a coffee filter. If there is an increase in the demand for coffee, it will lead to an increase in the demand for coffee filters since more coffee will be brewed. However, coffee filters are not an input in the production of coffee; they are simply used in the consumption of coffee.

--> Are oil and natural gas complementary goods?

Oil and natural gas are often considered substitute goods rather than complementary goods because they can be used for similar purposes, such as heating. When the price of oil increases, consumers may switch to natural gas as a cheaper alternative and vice versa. Therefore, the cross-price elasticity of demand between oil and natural gas is likely to be positive, indicating that they are substitute goods.

--> What is the cross elasticity of demand for complementary goods?

The cross elasticity of demand for complementary goods is negative. This means that when the price of one good increases, the demand for the other good decreases. Conversely, when the price of one good decreases, the demand for the other good increases.

--> What is the difference between complementary goods and substitute goods?

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.

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Complementarity of Goods and Cooperation Among Firms in a Dynamic Duopoly

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• Mario Alberto Garcia Meza 13 &
• Cesar Gurrola Rios 13  

Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

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We construct a simple model to show how complementarities between goods yield a possibility for cooperation between rival firms. To show this, we use a simple dynamic model of Cournot oligopoly under sticky prices. While cooperation in an oligopoly model with sticky prices is not feasible, there exists a feasible cooperation when good are perfect complements and not substitutes.

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Meza, M.A.G., Rios, C.G. (2020). Complementarity of Goods and Cooperation Among Firms in a Dynamic Duopoly. In: Petrosyan, L.A., Mazalov, V.V., Zenkevich, N.A. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-51941-4_11

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• Supply and Demand
• Supply Curve
• Supply Function
• Law of Supply
• Demand Curve
• Demand Function
• Law of Demand
• Market Demand
• Quantity Supplied vs Supply
• Quantity Demanded vs Demand
• Market Equilibrium
• Market Clearing Price
• Changes in Market Equilibrium
• Determinants of Supply
• Determinants of Demand
• Types of Elasticity of Demand
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• Price Elasticity of Supply
• Price Elasticity of Demand
• Elastic vs Inelastic Demand
• Cross Elasticity of Demand
• Income Elasticity of Demand
• Normal Good vs Inferior Good
• Substitute vs Complements
• Price Floor
• Price Ceiling

Substitute goods (or simply substitutes) are products which all satisfy a common want and complementary goods (simply complements) are products which are consumed together. Demand for a product’s substitutes increases and demand for its complements decreases if the product’s price increases.

One of the determinants of demand i.e. factors that can bring about a shift in the demand curve of a product is the price of the related goods. There are two types of related goods in general: good(s) which can be consumed instead of the product and good(s) which is consumed together with the product. The former is called a substitute good and the latter is a complementary good.

Substitute Goods

Coke and Pepsi, iPhone and Galaxy S series, Nike and Adidas are a few examples of substitute goods. If price of Coke increases, demand for Pepsi should increase because many Coke consumers will switch over to Pepsi. Similarly, prices of iPhone and Galaxy S affect their mutual demand. Given that there are many fanboys who will reprioritize their spending to afford an iPhone even after the price increase, many rational consumers will weight their preference for one product over the other and the premium they are willing to pay.

Complementary Goods

iPhones and iPhone skins, air travel and hotels, etc. are examples of complementary goods i.e. goods that are used/consumed together. If iPhone becomes expensive and its quantity demanded decreases, you would expend the demand for iPhone covers to drop too and vice versa. It follows that demand for a product is to some extent dependent on the price of its complementary goods.

Other examples of complementary goods include cars and gasoline, Big Mac and McFries, coffee and cheesecake, etc.

Substitutes, Complements and Cross Elasticity of Demand

The extent to which two products are substitutes or complements can be measured by calculating their mutual cross elasticity of demand. The cross elasticity of demand measures the percentage change in quantity demanded of the product that occurs in response a percentage change in price of a substitute good. If the cross elasticity of demand is positive, the products are substitute goods. On the other hand, if cross elasticity is negative, the products are complements.

The following chart shows what happens to demand for two substitute goods, iPhone and Galaxy S, when the price of Galaxy S changes.

When the price of Galaxy S changes from $950 to $1,050, its quantity demanded falls from 330 million per annum to a little more than 290 million. In response, the demand curve for iPhone shifts outward, i.e. its demand increases.

by Obaidullah Jan, ACA, CFA and last modified on Feb 5, 2019

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Complementary Goods, Oligopoly and Bundling: a reassessment of Cournot’s merger effects

In recent years the Antitrust authorities in the U.S. and EU have been addressing the issues involving non-horizontal mergers, which include vertical and conglomerate mergers, including complementary products mergers. The EU commissioned two reports on the economic knowledge about these mergers, totaling over 500 pages. This work has not recognized what we analyze here. Complementary products mergers are guided by the intuition behind Cournot’s complementary monopoly merger analysis. Pre merger there is “double marginalization”; merger leads to lower prices. We show how tenuous this intuition is if applied to oligopolists. We start with Merger Guidelines and three statements from antitrust authorities. We formalize these as theoretical propositions about such mergers. The propositions are: 1) Cournot effects will lower prices; 2) Complementary products mergers will never lead to higher prices (barring specific perverse effects); 3) if these mergers lead to mixed bundling they will be to the consumers’ advantage by offering more choice. These are all positive economics statements about what will happen. We prove these are all theoretically false via counter example. If there is vertical/quality product differentiation, price setting oligopoly and compatible components, the Cournot result disappears in price setting oligopoly modeling even using the Cournot demand structure. Such mergers will not lower prices. We show an alternative demand structure for which such mergers raise prices for all buyers through bundling. And we show a third demand structure in which mixed bundling is the culprit in extracting high prices – the mixed bundling doesn’t so much offer a discount from individual component pricing as it instead endogenously raises the individual component prices, before offering a “discount” for the purchase of a bundle. We do not do a full policy analysis, and our proofs by counter example use stylized demand structures. We emphasize, however, that before attempting a normative policy analysis, the positive economics must be understood. The views expressed herein are the authors’ own and are not purported to reflect those of the employers.

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Robert Masson , Serdar Dalkir

DESCRIPTION In recent years the Antitrust authorities in the U.S. and EU have been addressing the issues involving non-horizontal mergers, which include vertical and conglomerate mergers, including complementary products mergers. The EU commissioned two reports on the economic knowledge about these mergers, totaling over 500 pages. This work has not recognized what we analyze here. Complementary products mergers are guided by the intuition behind Cournot’s complementary monopoly merger analysis. Pre merger there is “double marginalization”; merger leads to lower prices. We show how tenuous this intuition is if applied to oligopolists. We start with Merger Guidelines and three statements from antitrust authorities. We formalize these as theoretical propositions about such mergers. The propositions are: 1) Cournot effects will lower prices; 2) Complementary products mergers will never lead to higher prices (barring specific perverse effects); 3) if these mergers lead to mixed bundling...

Review of Law & Economics

Serdar Dalkir , Robert Masson

Antitrust policy in the US and EU toward non-horizontal mergers between oligopolists is based on a strong presumption of Cournot effects and/ or improvements in consumer welfare through post-merger bundling. We show that complementary goods mergers between firms that possess market power in their respective components markets do not always assure either. The analysis underscores the importance of fully specifying the nature of premerger rivalry among all market participants and the assumed distribution of consumer preferences when making predictions about the likely effects of such transactions. https://masson.economics.cornell.edu/docs/rle-2013-0014_2.pdf

Journal of Retailing and Consumer Services

Subir Bandyopadhyay

In an attempt to provide a framework that can help firms find optimum bundling product categories and pricing strategies that maximize their profits, this study develops a profit-maximization model. The results indicate that optimum bundles and price strategies exist; specifically, if a firm uses a bundling strategy to sell its products, it should combine highly complementary products and charge a relatively lower price. The value of a bundling strategy always increases with the size of market and price sensitivity. Managers can use the provided model framework and related advice and examples to plan their bundling strategies.

The Journal of Industrial Economics

Nicholas Economides

This article analyzes the competition and integration among complementary products that can be combined to create composite goods or systems. The model generalizes the Cournot duopoly complements model to the case in which there are multiple brands of compatible components. It analyzes equilibrium prices for a variety of organizational and market structures that differ in their degree of competition and integration. The model applies to a variety of product networks including ATMs, real estate MLS, airlines CRS, as well as to non-network markets of compatible components such as computer CPUs and peripherals, hardware and software, and long distance and local telephone services.

Elisa Barocio

The existing literature shows that a decrease in the degree of substitutability increases a monopoly's incentive to bundle. This paper in addition takes into account competition in the second product market and then reexamines how intra-brand and inter-brand product differentiations affect the incentive to bundle. In order to formally examine the above conjectures, this research builds up a two-firm, two-product model in which product 1 (monopoly product) is produced only by the bundling firm and product 2 (competing product) is produced by both firms. The analysis shows that under both Bertrand and Cournot competitions the incentive to bundle does not necessarily increase with the degree of intra-brand differentiation, while it strictly decreases with the degree of inter-brand differentiation. Moreover, under Bertrand competition bundling always decreases consumer surplus, but may increase the competitor's profit and social surplus. Under Cournot competition bundling always reduces the opponent's profit and social welfare, but may increase consumer surplus.

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Research in Economics

Poudou Jean-Christophe

We study the incentives to collude when firms use mixed bundling or independent pricing strategies for the sale of two components of a composite good. The main finding is that collusion is less sustainable under mixed bundling, because this increases the profitability of deviations from the collusive path. The result is robust to extensions with an endogenous choice of the mode of competition (with bundling or independent pricing) and to competition in quantities. These results offer a novel argument against a per se rule concerning bundling in antitrust policy. JEL classification: D4, L1

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Pricing of Complementary Goods and Network Effects

We discuss the case of a monopolist of a base good in the presence of a complementary good provided either by it or by another firm. We assess and calibrate the extent of the influence of the profits from the base good that is created by the existence of complementary good, i.e., the extent of the network effect. We establish an equivalence between a model of a base and a complementary good and a reduced-form model of the base good in which network effects are assumed in the consumers’ utility functions as a surrogate for the presence of direct or indirect network effects, such as complementary goods produced by other firms. We also assess and calibrate the influence on profits of the intensity of network effects and quality improvements in both goods. We evaluate the incentive that a monopolist of the base good has to improve its quality rather than that of the complementary good under different market structures. Finally, based on our results, we discuss a possible explanation of the fact that Microsoft Office has a significantly higher price that Microsoft Windows although both products have comparable market shares.

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Complementary goods: Creating, capturing and competing for value

Marketing Science

Publishing details

Marketing Science 2013 October Vol 32:4 p 554-569

Authors / Editors

Yalcin T;Ofek E;Koenigsberg O;Biyalogorsky E

Biographies

Oded Koenigsberg

Publication Year

This paper studies the strategic interaction between firms producing strictly complementary products. With strict complements, a consumer derives positive utility only when both products are used together. We show that value-capture and value-creation problems arise when such products are developed and sold by separate firms (“nonintegrated” producers). Although the firms tend to price higher for given quality levels, their provision of quality is so low that, in equilibrium, prices are set well below what an integrated monopolist would choose. When one firm can mandate a royalty fee from the complementor producer (as often occurs in arrangements between hardware and software makers), we find that the value-capture problem is mitigated to some extent and consumer surplus rises. However, because royalty fees greatly reduce the incentives of the firm paying them to invest in quality, the arrangement exacerbates the value-creation problem and leads to even lower total quality. Surprisingly, this result can reverse with competition. Specifically, when the firm charging the royalty fee faces a vertically differentiated competitor, the value-creation problem is greatly reduced—opening the door for the possibility of a Pareto-improving outcome in which all firms and consumers benefit. It is worth noting that this outcome cannot be achieved by giving firms the option of introducing a line of product variants; competition serves as a necessary “commitment” ingredient.

complementary goods; product quality; royalty fees; competition; game theory

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Complementary Goods

Complementary goods also impact demand. Complementary goods are goods that go together or are related: beer and pretzels, cameras and film, polyester bell bottoms and platform shoes, Rogaine and hair gel.

When the price of one good changes, its complementary good is affected. If film prices increase, people will buy fewer cameras. If polyester bells drop in price, demand for the four-inch platforms that best highlight the timeless lines of the disco-era bad-boys will rise.  And so on.

The demand curve for a good will shift to the left if the price of its complementary good increases. And vice versa.

Why It Matters Today

One awesome example of complementary goods: baseball tickets and hot dogs.  Because what goes better with America's pastime than a delicious piece of mystery meat on a bun, with ketchup and mustard?

Sometimes a Song Says it Better: We Go Together, by Grease

Complementary goods go together.

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W hy's T his F unny?

• Circular Flow
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• Aggregate Demand
• Supply-Side
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• Game Theory
• Monopolistic Comp.
• Economies of Scale
• Market Failure
• Complementary Goods

Complementary Goods & Substitute Goods Explained (with Examples)

By Steve Bain ©

Complementary goods are products that are consumed or used together. When the demand for one good increases, it leads to an increase in the demand for its complementary counterpart. The classic example of complementary goods is peanut butter and jelly. When people buy peanut butter, they often purchase jelly as well, as the two products are commonly used together in sandwiches.

Substitute goods, on the other hand, are products that can be used interchangeably to satisfy a similar need. When the price of one substitute good increases, consumers tend to switch to a more affordable option. An example of substitute goods is butter and margarine. Both products serve the same purpose of spreading on bread or cooking, so when the price of butter rises, consumers may opt for margarine as a cheaper alternative.

Examples of Complementary Goods

Complementary goods refer to products that are consumed or used together, enhancing the marginal utility that each good provides. The demand for one good is directly related to the demand for the other. When the price or availability of one complementary good changes, it can significantly impact the demand for the other. Here are four examples:

• Peanut butter and jelly – Often bought and consumed together, a change in the price of one affects the demand for the other.
• Printers and printer ink cartridges – As printer prices decline, the demand for printers increases, leading to a higher demand for ink cartridges.
• Gaming consoles and video games – A new gaming console's release increases the demand for compatible video games to enjoy the full gaming experience.
• Hot dogs and hot dog buns – The number of hot dog buns sold is closely related to the number of hot dogs, as people usually buy them together.

Examples of Substitute Goods

Substitute goods are products that can be used in place of one another. If the price of one substitute good rises, the demand for that good may decrease, and consumers may opt for the alternative product instead. Here are four examples:

• Tea and coffee – If the price of coffee rises significantly, consumers may switch to tea as a more affordable alternative.
• Butter and margarine – When the price of butter goes up, some consumers may choose to buy margarine instead.
• Air travel and train travel – If airfare becomes too expensive, people may opt for trains for shorter distances, leading to an increase in the demand for train tickets.
• Brand name drugs and generic drugs – Consumers may choose to buy generic versions of medications if brand name drugs are expensive.

Perfect Complements and Perfect Substitutes

The shape of an indifference curve gives us information about whether or not two goods are substitutes or complements, and at the extremes, when we look at perfect complements and perfect substitutes, these curves are unique.

For perfect complements an indifference curve is L-shaped, and while rare we can imagine how this might be the case with shoes for left feet compared to right feet. As a refresher, each indifference curve is drawn for a given level of utility i.e. consumer satisfaction. In the graph above, with 1 left shoe and one right shoe, a higher indifference curve can only be reached with an increase in both left and right shoes, simply increasing one or the other yields no extra utility.

With perfect substitutes the indifference curve is a straight line, meaning that there is no diminishing utility from increasing more of one good and decreasing an equal amount of the other. For example, if a consumer has equal access to Shell gasoline and Exxon Mobil gasoline, he/she will be completely indifferent about using only Shell or only Exxon, or any combination of the two.

Either option yields just as much mileage for the consumer's car, and causes no greater or lesser wear and tear on the car, so these two types of gasoline are perfect substitutes.

For regular non-perfect substitutes and complements, indifference curves are bowed. The more bowed they are, the more that they are complements, and the less bowed, the more that they are substitutes.

The Importance of Understanding Substitute and Complementary Goods

For businesses, comprehending the relationship between substitute and complementary goods is pivotal in devising pricing and marketing strategies. They must consider the impact of changes in one product's demand on its complement or substitute to stay competitive in the market.

Additionally, businesses can create product bundles to promote complementary goods. Offering discounts on printer purchases while charging regular prices for ink cartridges could incentivize consumers to buy the package rather than opting for separate items.

Understanding these concepts also helps governments and policymakers analyze market behavior and formulate effective economic policies. Antitrust regulations, for instance, may come into play when investigating companies that dominate the markets of both complementary and substitute goods, potentially leading to monopolistic practices.

For consumers, knowledge of these goods can lead to more cost-effective choices. For example, if they are aware of substitute goods, they can make smart decisions when prices fluctuate, ensuring that they get the best value for their money.

The concept of cross-price elasticity

To understand the relationship between complementary and substitute goods, we need to first understand the concept of cross-price elasticity. Cross-price elasticity measures the responsiveness of the demand for one good to a change in the price of another good.

For complementary goods, the cross-price elasticity is positive because an increase in the price of one good leads to an increase in the demand for its complementary counterpart. On the other hand, for substitute goods, the cross-price elasticity is negative because an increase in the price of one substitute good leads to a decrease in the demand for the other substitute good.

Cross-price elasticity helps economists and businesses analyze the impact of price changes on consumer behavior and adjust their strategies accordingly.

Complementary and substitute goods are fundamental concepts in economics that shed light on the complex relationship between different products and consumer choices. Complementary goods work in harmony, enhancing each other's utility, while substitute goods provide alternatives that can be interchanged based on price and availability.

The cross-price elasticity of demand, which ranges from 0 to 1, is the tool used by economists to estimate the sensitivity of one good’s price & demand to another good. For perfect substitutes the elasticity is 1, for perfect complements it is 0.

By understanding market dynamics, businesses can devise effective strategies to maximize sales and profit, while consumers can make informed decisions to maximize utility in the face of changing market conditions. Substitute and complementary goods are not merely theoretical ideas; they are the building blocks that shape the modern marketplace, influencing our daily choices and driving economic progress.

• L. McAlister & J. Lattin - Identifying Substitute and Complementary Relationships (PDF)

Related Pages:

• Indifference Curves
• Normal Goods
• Inferior Goods
• The Price Consumption Curve
• Types of Economic Goods

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8.8 Complements and Substitutes

The way the demand curve shifts in response to the price of another good depends on the relationship between those two goods:

• Goods like peanut butter and grape jelly are complements : they are generally consumed together, for example in PB&J sandwiches.
• Goods like strawberry jam and grape jelly are substitutes : they generally serve the same purpose.
• Goods like t-shirts and jelly are independent goods: there’s no obvious relationship between them.

Let’s look at each of these in turn, by examining the effect of a price increase in one flavor of jelly on the quantity demanded of peanut butter, strawberry jam, and t-shirts.

Complements

If two goods are complements, an increase in the price of either good will result in a decrease in the quantity bought of both goods. For example, if you enjoy sandwiches made with peanut butter (good 1) and grape jelly (good 2), an increase in the price of jelly increases the price of making a PB&J sandwich; so you might have fewer such sandwiches and do something else for lunch.

• In Good 1 - Good 2 space, this means that an increase in the price of grape jelly (good 2) leads to a decrease in the quantity demanded of both goods: that is, the optimal bundle moves down and to the left . In other words, the price offer curve has a positive slope.
• If we look at the demand curve for peanut butter (good 1), we can see that the quantity of peanut butter demanded at every price of peanut butter decreases, shifting the demand curve to the left.

If peanut butter and jelly are perfect complements with the utility function $u(x_1,x_2) = \min{x_1,x_2}$, we could illustrate the effect of this price change in the following graph:

Note, however, that goods might be complements without being perfect complements . That is, we can observe complementary behavior even if you don’t only consume goods in a strict ratio. For example, you might have other uses for peanut butter than just making PB&J sandwiches!

One useful family of utility functions is a CES utility function, of the form \(u(x_1,x_2) = (ax_1^r + bx_2^r)^{1 \over r}\) In this case the $r$ parameter measures how complementary or substitutable goods are. As $r$ approaches $-\infty$, the preferences approach the “perfect complements” or Leontief functional form we’ve become familiar with. However, for any negative value of $r$ , the goods are complementary; we sometimes call these “weak complements” to distinguish them from “perfect complements,” but just “complements” works too. For example, the graph below shows the same price change for $r = -1$:

Even though these goods aren’t perfect complements, an increase in the price of good 2 still causes the consumer to buy less good 1 and less good 2, and causes the demand curve for good 1 to shift in (to the left).

Substitutes

If two goods are substitutes, an increase in the price of one good will result in a decrease in the quantity bought of that good, and an increase in the quantity of the other. For example, if you view strawberry jam (good 1) and grape jelly (good 2) as substitutes, then an increase in the price of grape jelly will cause you to use more of the relatively cheaper strawberry jam in recipes which could use either.

• In Good 1 - Good 2 space, this means that an increase in the price of grape jelly (good 2) leads to a decrease in the quantity demanded of grape jelly, but an increase in the quantity demanded of strawberry jam: that is, the optimal bundle moves down and to the right . In other words, the price offer curve has a negative slope.
• If we look at the demand curve for strawberry jam (good 1), we can see that the quantity of strawberry jam demanded at every price of strawberry jam increases, shifting the demand curve to the right.

For a CES function, a value of $r$ between 0 and 1 represents goods which are substitutes but not perfect substitutes — again, we sometimes call these “weak substitutes.” (When $r = 1$, you can check to see that they’re perfect substitutes.) For example, with $r = {1 \over 2}$, we can illustrate the effect of this price change in the following graph:

As you can see, an increase in the price of good 1 causes the consumer to buy less good 1 and more good 2 , meaning the POC has a negative slope. Likewise, an increase in the price of good 2 causes the consumer to buy more good 1 at any price , meaning an increase in the price of good 2 causes the demand curve to shift to the right.

As you can see, the case of perfect substitutes is an extreme example of this kind of behavior: when the price of one good increases beyond a certain threshold, the optimal bundle jumps from buying only one good to buying only the other. But that really is an extreme case: in general, changes in the prices of imperfect substitutes like strawberry jam and grape jelly will affect the demand for the other good, but not necessarily drive it down to zero. After all, sometimes you crave grape jelly, even if it’s pricier!

Independent Goods

Finally, let’s think about goods like t-shirts (good 1) and grape jelly (good 2), which have no obvious connection. For such goods, we would not expect a change in grape jelly to affect the quantity of t-shirts bought at all:

• In Good 1 - Good 2 space, this means that an increase in the price of grape jelly (good 2) leads to a decrease in the quantity demanded of grape jelly, but no change in the quantity demanded of t-shirts: that is, the optimal bundle moves straight down . In other words, the price offer curve for good 2 is a vertical line. (The price offer curve for good 1 will be a horizontal line.)
• If we look at the demand curve for t-shirts (good 1), we can see that the demand curve is unaffected by the price of grape jelly.

The utility function we’ve seen that exhibits this behavior is Cobb-Douglas, in which the consumer will spend a given fraction of their income on each good. For example, with the Cobb-Douglas utility function $u(x_1,x_2) = x_1x_2$, the consumer’s demand for good 1 is $x_1^\star(p_1,p_2,m) = m/2p_1$, which doesn’t depend at all on $p_2$, and is therefore a horizontal line, as we saw previously .

In the next chapter, we’ll go into much more detail about what makes goods complements, substitutes, or independent goods.

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