# Substitute good If the price of $x_{i}$ increases, then demand for $x_{j}$ increases

A substitute good is a good that can be used in place of another. In consumer theory, substitute goods or substitutes are goods that a consumer perceives as similar or comparable, so that having more of one good causes the consumer to desire less of the other good. Formally, good $x_{j}$ is a substitute for good $x_{i}$ if, when the price of $x_{i}$ rises, the demand for $x_{j}$ rises. Let $p_{i}$ be the price of good $x_{i}$ . Then, $x_{j}$ is a substitute for $x_{i}$ if

${\frac {\partial x_{j}}{\partial p_{i}}}>0$ .

Potatoes from different farms are an example: if the price of one farm's potatoes goes up, then (other things being equal) fewer people will buy potatoes from that farm; they will buy potatoes from another farm instead. Other examples of substitute goods include margarine and butter, tea and coffee, and beer and wine.

## Introduction

Informally, substitute goods – as contrasted with complementary goods and independent goods – are goods that, as a result of changed conditions, may replace each other in use (or consumption). The fact that one good is substitutable for another has immediate economic consequences: insofar as one good can be substituted for another, the demands for the two goods will be interrelated by the fact that customers can trade off one good for the other if it becomes advantageous to do so. That is, an increase in the price of a good will (ceteris paribus) increase demand for its substitutes. Conversely, a decrease in the price of a good will decrease demand for its substitutes. More formally, the relationship between demand schedules determines whether goods are classified as substitutes or complements. A substitute good is a good with a positive cross elasticity of demand. This means that, if good $x_{j}$ is a substitute for good $x_{i}$ , an increase in the price of $x_{i}$ will result in a leftward movement along the demand curve of $x_{i}$ and cause the demand curve for $x_{j}$ to shift out. A decrease in the price of $x_{i}$ will result in a rightward movement along the demand curve of $x_{i}$ and cause the demand curve for $x_{j}$ to shift in.

## Different types of substitutability

### Perfect and imperfect substitutes

The substitutability of one good for another is a matter of degree. If two goods are highly substitutable, the change in demand due to price changes will be greater than if they are less substitutable. For example, a spike in the cost of a brand of detergent is likely to result in a large increase in demand for other brands of detergents, whereas a change in the price of cars will have a much smaller effect on the demand for bicycles.

One good is a perfect substitute for another if it can be used in exactly the same way. In that case, the utility of a combination of the two goods is an increasing function of the sum of the quantity of each good. Theoretically, if the prices of the goods differed, there would be no demand for the more expensive good. Writable compact disks (CD-Rs) from different manufacturers could be considered perfect substitutes. As the price of one brand of CD-R rises, consumers will be expected to substitute other brands of CD-R one-to-one. The total quantity of CD-Rs purchased would not change. That is to say, perfect substitutes have a linear utility function and a constant marginal rate of substitution.

Imperfect substitutes have a lesser level of substitutability, and therefore exhibit variable marginal rates of substitution along the consumer indifference curve. The consumption points on the curve offer the same level of utility as before, but compensation depends on the starting point of the substitution. Colas are an example. As the price of Coca-Cola rises, consumers could be expected to substitute Pepsi. However, many consumers prefer one brand of cola over the other. Consumers who prefer one brand over the other will not trade between them one-to-one. Rather, a consumer who prefers Coca-Cola (for example) will be willing to exchange more Pepsi for less Coca-Cola.

The degree to which a good has a perfect substitute depends on how specifically the good is defined. For example, different types of cereal generally are substitutes for each other, but Rice Krispies cereal, which is a very narrowly defined good as compared to cereal generally, has few if any perfect substitutes.

### Gross and net substitutes

Economists distinguish gross substitutes from net substitutes. Good $x_{j}$ is a gross substitute for good $x_{i}$ if, when the price of good $x_{i}$ increases, spending on good $x_{j}$ increases, as described above. Gross substitutability is not a symmetric relationship. Even if $x_{j}$ is a gross substitute for $x_{i}$ , it may not be true that $x_{i}$ is a gross substitute for $x_{j}$ .

Goods $x_{i}$ and $x_{j}$ are said to be net substitutes if

$\left.{\frac {\partial x_{j}}{\partial p_{i}}}\right|_{u=const}>0$ That is, goods are net substitutes if they are substitutes for each other under a constant utility function. Net substitutability has the desirable property that, unlike gross substitutability, it is symmetric:

$\left.{\frac {\partial x_{j}}{\partial p_{i}}}\right|_{u=const}=\left.{\frac {\partial x_{i}}{\partial p_{j}}}\right|_{u=const}$ That is, if good $x_{j}$ is a net substitute for good $x_{i}$ , then good $x_{i}$ is also a net substitute for good $x_{j}$ . The symmetry of net substitution is both intuitively appealing and theoretically useful.

### Within-category and cross-category substitutes

Substitutes differ with respect to their category membership. Within-category substitutes are goods that are members of the same taxonomic category, goods sharing common attributes (e.g., chocolate, chairs, station wagons). Cross-category substitutes are goods that are members of different taxonomic categories but can satisfy the same goal. A person who wants chocolate but cannot acquire it, for example, might instead buy ice cream to satisfy the goal of having a dessert.

People exhibit a strong preference for within-category substitutes over cross-category substitutes. Across ten sets of different foods, 79.7% of research participants believed that a within-category substitute would better satisfy their craving for a food they could not have than a cross-category substitute. Unable to acquire a desired Godiva chocolate, for instance, a majority reported that they would prefer to eat a store-brand chocolate (a within-category substitute) than a chocolate-chip granola bar (a cross-category substitute). This preference for within-category substitutes appears, however, to be misguided. Because within-category substitutes are more similar to the missing good, their inferiority to it is more noticeable. This creates a negative contrast effect, and leads within-category substitutes to be less satisfying substitutes than cross-category substitutes.

### Unit-demand goods

Unit-demand goods are categories of goods from which consumer wants only a single item. If the consumer has two unit-demand items, then his utility is the maximum of the utilities he gains from each of these items. For example, consider a consumer that wants a means of transportation, which may be either a car or a bicycle. The consumer prefers a car to a bicycle. If the consumer has both a car and a bicycle, then the consumer uses only the car. Unit-demand goods are always substitutes.

## Substitutability and market structure

One of the requirements for perfect competition is that the goods of competing firms should be perfect substitutes. When this condition is not satisfied, the market is characterized by product differentiation.

Many markets for commonly used goods feature goods that are perfectly substitutable but differently branded and marketed, a condition referred to as monopolistic competition. An example is store brand and name brand versions of medications. The goods may be identical, but the packaging is different. Because the goods are the same, the only differences between them are price and branding. Their vendors rely primarily on price and to effect sales. Consumer choice is usually driven by price. Higher-priced variants rely on a sense of exclusivity created by sticker branding to maintain competitiveness. Other examples of goods subject to monopolistic competition are gasoline (petrol), milk, Internet connectivity (ISP services), electricity, telephony, and airline tickets.

Perfect substitutability is significant in the era of deregulation because there are usually several competing providers (e.g., electricity suppliers) selling the same good. The result is often aggressive price competition between the sellers.