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by Valentino Piana (2005)



1. Significance
2. The neoclassical approach
  3. Generalized substitution vs. local substitution  
  4. Why the set of substitute goods is small  
5. A positive alternative
5.1. Substitution with respect to needs
5.2. Substitution with respect to available income
5.1. Substitution with respect to time
6. A comparison between neoclassical and bounded-rational perspective: Actual choice set vs. potential infinite set
7. Substitution in terms of elasticity
  8. Substitution in terms of the cumulative bundle purchased in a point of sale  
9. An example of formal model with bounded rational consumers facing substitutes
  10. A policy aimed at the provision of close substitute to polluting "brown" products  
11. Formal models
12. Data


An excellent paper using our definition of substitute good



Substitute goods are goods that can be used in activities aimed to satisfy the same needs, one in the place of another. The buyer carries out an actual and conscious process of choice about them, which leads the buyer to prefer one to another.

The neoclassical approach

Standard neoclassical textbooks of microeconomics define the substitute goods in a different way from our own. They rather use a catch-all measure of happiness connected with the consumption of any kind of good ("utility") and they define perfect substitute goods in terms of a straight shape of an "indifference curve", which is defined as the set of points perfectly equivalent for the consumer:

Indifference curve of perfect substitutes

Two goods whatsoever X and Y can be consumed in different quantitative proportions but the consumer will obtain exactly the same utility for all the points of the "indifference curve", e.g. in A point or B point of the following diagram:

Perfect substitute goods

In A, the consumer buys (and consume) a lot of Y and a small quantity of X, in B the opposite, still he is exactly at the same level of utility. So his choice will be based on prices only: the consumer will choose the cheapest bundle of that indifference curve [1].

This substitution process be described also in this way:

Substituting Y with X

By renouncing to a QB quantity of X, he will be perfectly compensated by an additional QA quantity of Y.

Substitution is perfect, according to neoclassical approach, since the ration of QA to QB is constant, whichever the B starting point is located (i.e. the indifference curve is a straight line).

No hypothesis or comments are expressed in terms of some objective character of the two goods. The two goods can refer to any set of needs, so substitute goods can be hotdogs and cars, as long as the subjective indifference curve has that shape.

Imperfect substitute goods are characterized by a different shape of the indifference curve:


Cobb-Douglas indifference curve for imperfect substitutes


This shape allows some changing degrees of "equivalence" in utility, with the starting point of the comparison:


Substituting imperfect substitutes (X and Y)


All points (A, B, A1, B1) are on the same indifference curve, thus provide the consumer with exactly the same level of utility. Again, the consumer will choose how much to buy of X and Y by minimizing expenditure [2].

X and Y continue to be substitute, because the consumer is willing to accept to renounce to a certain quantity of one if he is give an additional amount of the other. But now the compensation varies depending on the starting point: the same reduction in X requires a much higher Y quantity if the starting point was B than if it were B1.

Neoclassical consumer faces an "Cartesian space of goods", as we showed with diagrams, unlimited in space and time, where the two substitute goods are completely vague and undefined (X and Y), since an elephant in India could well be, in principle, a substitute of a bottle of cold water in Mexico City, because this approach makes no reference to a common need to be satisfied alternatively by the competiting goods.

The rational consumer is assumed to be able to compare any two goods or services whatsoever (newspapers with fishes, restaurant services with biblical lectures,...), with an extremely high level of precision (e.g. two hours of biblical lectures provides the same level of utility than four press articles, if the starting point was 32 hours but ... if the starting point was...).

It's up to a "given" (by whom? when?) preference subjective scheme to determine the shape of the supposedly existing indifference curve.

Generalized substitution vs. local substitution

In the neoclassical broad culture, everything can be exchanged and substituted with everything. Consumer goods can substitute each other, although usually imperfectly. Everything can be bought, in the sense that whatever you have, it's always possible to find alternative consumption bundles that you would accept as equivalent to your own. Indirectly, money can buy everything. Quantities are the key variables: you accept to change your consumption habits in exchange for enough quantity of substitutes.

More formally, the neoclassical model of general economic equilibrium presented in basic textbooks attributes to all consumer the same (or similar) Cobb-Douglas (or CES) indifference curves. On every market, quantities depends on relative prices of the given good with respect with all others. More sophisticated versions of these relationships are available inside the neoclassical tradition but "well-behaved" indifference curves usually lead to the same broad statements.

By contrast, in our conception of bounded rational consumer, substitution is limited to a small set of goods which are carefully compared, usually not only in terms of prices and quantities, but even more importantly in terms of quality and time.

Why the set of substitute goods is small

Consumers do not receive from heaven a given preference structure. They actively analyse, judge, and compare the (material and immaterial) properties of goods so to establish whether they can satisfy their needs, how well this can happen, and with what side-effects (positive and negative). They take into account time limitation and affordability.

This requires a certain effort - lower for routine purchases and higher for high-stake irreversible decisions. The number of features that are compared can well be quite large. When a good is better under certain aspects but worse under others, the choice can involve a really challenging task. The price comparison across goods at different levels of quality, which in turn depends on several factors (both quantitative and qualitative), becomes quite difficult.

According to the bounded rational perspective, which suggests that consumer economizes on attention and time devoted to choice, the consumer structures its decision-making process (e.g. search routines) so to focus on just a few alternatives possessing already some relevant features (e.g. they are immediately available).

Moreover, consumers foresee to use the goods in goal-oriented activities; their skills in performing such activities will constraint the good evaluated (if they do not know how to use a certain product they will simply discard it from the small set of substitutes to be evaluated).

At the same time, the all-too-often-made comparision of just two substitute goods is insufficient, because the choice bundle presented on the shelves is usually larger. When you browse for socks (or stockings) you often make a sequence of requests to the seller about length, size, colour, material, etc. The choice among shoes is even more challenging. To give an example of two substitutes, you may think at a duopoly, where two brands are in tough competition and have eliminated everybody else. A high level of substitutability can be achieved by two products of the same firm having just minor differences (e.g. size).

A commercial catalogue of products can contain several sets of substitute goods, with the consumer induced to make comparison according to the information inside. There are limits of the number of pages or to the time the person is available to spend in such comparison. In physical commercial premises, the choice is restricted to what is on the shelves there, with an additional cost if the consumer want to compare several premises. Conversely, "main streets" and commercial venues reduce the cost of comparison, increasing the variety and the depth of supply, and justifying the visit to the location.

A positive alternative

Substitution with respect to needs

Goods are said to be substitutes if they serve to the same purposes, if they are equivalent in functional terms, if they satisfy the same need(s), if they are considered inputs to different activities, potentially performed by the consuemr, that can meet the same goal.

Imperfect substitution occurs when two goods, while satisfycing the same main need, score differently on quality and features (e.g. a Jaguar and a Mini are substitutes since they both carry people from one place to another, but on several characteristics they are too different - as for comfort, prestige, etc.). Product differentiation is here fundamental.

A subjective irreducible judgement about the degree of effective substitution of one good for another is carried out by a single consumer, possibly depending on very specific circumstances and intentions, as well as longer-term skills, and cumulative experiences. Still, a panel of individuals might show some signs of agreement in some broad correspondence between a set of goods and one or more goals.

Thus, the need-based approach expects to gather valuable inter-personal indications about which goods happens to be "substitute" of each other for a wide spectrum of people and situations, opening the path to several empirical researches.

Most substitution happens among goods produced in the same industry, sold on the same market. However, if the need is broad enough, the choice can be made across very different categories of products (e.g. if you have to make a wedding gift, the goods to be compared can be extremely heterogeous).

To experiment how a flow of goods fulfill a set of needs, try this model, explained here.

Substitution with respect to available income

Two goods can be compared and alternatively selected not because they both satisfy the same need but because the consumer has not the income to afford both [3].

However, this kind of choice is extremely painful for the consumer, because one need will not be satisfied whatever he chooses.

Accordingly, a "normal" middle-class consumer in a developed country will try to avoid this kind of choice, by adopting rules about "need satisfaction" and "price sensibility" that reduces the probability this occurs. For instance, once satisfied the basic needs, many "additional" needs will be satisfied in sequence, with pauses to let income sources provide enough flows for further consumption. This category of consumers also keep "slack resources", intentional or unintentional savings, to cope with unexpected purchase occasions.

By contrast, a poor is often compelled to renounce to satisfy important needs in order to cope with others. In developing countries, the supply of many goods is unsufficient to cover all needs, because the lack of a sufficiently wide demand restricts the actual set of choice, or make them unaffordable, so that even a person of the local middle-class is often captured in difficult and unpleasant choices.

In other words, while neoclassical theory claim generality beyond any circumstances in time and geography, it tends to consider normal what normal is not: a permanent status of unsatisfaction, where people choosing a good are "actually" renouncing to something else they need (and not just losing it as open "opportunity").

To better understand this point, please make this experiment: think at the last time you bought something. Did you really renounce to buy something else you desired and actually compared with the bought thing? Didn't you simply open your wallet and bought, without reflecting on specific goods you were renouncing to buy? Where are you located? And to which social group in terms of income you belong?

Substitution in terms of time

Two consumption goods can compete on the limited time the consumer has. A holiday destination competes on another one not only because both are satisfying the same need but also because one cannot be in two places at the same time. Similarly, holiday destinations compete with housework in week-ends, although most of people prefer the former to the latter.

Even if the consumer has sufficient income to buy two goods, he will choose one instead the other if they are to be consumed at the same time.

Neoclassical economics simply ignores this dimension of substitution, since it does not consider the timing of consumption as a positive length.

A comparison between neoclassical and bounded-rational perspective: Actual choice set vs. potential infinite set

The neoclassical approach assumes a perfectly infinitely divisible bundle of goods (e.g. X and Y), with unlimited indifference curves (in the more general case of imperfect substitutes). Consumers have to compare an infinite set of alternatives, each one precisely leading to a certain utility level, always "given" and "known" to the decision-maker.

In real decision-making processes, by contrast, most alternatives are not evaluated, they are simply excluded from a careful analysis and comparison. If you go to a supermarket and you choose a beer, you might take a while for finding the brand you like the most, or the special taste you would like to try, but you will not take into account the entire horizontal differentiation of beers in the world. Having chosen a POS (point of sale), you restrict your attention to its proposals, possibly ending up to no purchases in the expectation of a further POS exploration in a reasonably short span of time.

The neoclassical do not make this crucial difference between what is the full line of supply on the national & international markets from what is the much smaller set which is actually compared in consumer's mind.

By contrast, our approach has the additional advantage - for the marketing man - to introduce room for effective manipulation of consumer choices by careful selection of what to put "on the shelves".

Substitution in terms of elasticity

The abovementioned contraposition between neoclassical and bounded-rational perspectives can be given rise to some common ground, allowing for more specific differences.

An interesting mainstream definition of "substitute goods" relates this property to elasticity, more specifically cross-price elasticity, i.e. the quantity reaction in the sales of one good to changes in the price of the other. If the sign of this elasticity is positive, an increase of price produces an increase of quantity purchased of the former good. This is what happens when two goods are compared and the price change make the other good relatively cheaper. In short, in this perspective, two goods are substitutes if cross-price elasticity is positive.

So defined, substitute goods receive an important empirical property, which indeed is quite relevant. However, in our conception the market effects are due to a few consumers will switch from one good to another, whereas in neoclassical demonstrations all consumers buy somewhat more of the cheaper good [4].

Substitution in terms of the cumulative bundle purchased in a point of sale

In current grocery purchases, people buy many goods at the same point of sale (e.g. a shop or a supermarket). Substitute goods tend not to appear in the same bundle of goods purchased in a certain shopping session. A statistical negative correlation of presence / absence of the two goods in the purchased basket is a sign of (statistical) substitution. One should be, however, aware of possible spurious correlations.

An example of formal model with bounded rational consumers facing substitutes

A simple example of our conception of "substitute goods" is given by this paper. There, two competiting goods, satisfying the same need, are offered to an heterogeneous public of consumers, who choose one of them if it is better then the other in terms of a combination of price and quality (defined along more than one dimension).

Individual cross-price elasticity is zero in most situations (and "infinite" in others), since each consumer, when he decides to buy, buys only one unit (leaving at zero the quantity consumed of the other good), as you can see from this datasheet.

Market cross-price elasticity can be ex-post empirically measured, although consumers having already bought might be different from those who buy after the price change. You can make your own experiments by using this software.

A policy aimed at the provision of close substitute to polluting "brown" products

Within the field of the economics of climate change, urgent substitution of heavy CO2 emitting product, processes and technologies is seen as a key component of mitigation policies. Our book on "Innovative Economic Policies for Climate Change Mitigation" puts forth the proposal of a public-private policy aimed at exploring the product space around of existing products (e.g. fossil-fueled cars), judging the positioning of green alternatives along all relevant axes of choice and co-operatively suggest improvements in their perceived weaknesses. It is, in fact, envisaged that a rise in price of brown products might not lead to a fall in consumption (thus emissions) if there is a lack of close substitutes.


[1] By using this free software on consumer choice, you'll see that this shape of indifference curves provokes an "edge" solution to the utility maximisation under budget constraints of the consumer.

[2] To make experiments about these choices in respect with his budget, use this software.

[3] Or the sum of the prices of the two goods exceeds a threshold in budget that the consumer has set.

[4] For a longer explanation see this paper.

Formal models

Neoclassical model of consumer choice

Consumers rules of bounded rational consumers in agent-based models

Dynamic competition with bounded rational consumers, innovation, advertising, and finance


Consumers microdata


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