Consumption II: Characteristics demand theory and revealed preference theory

 Characteristics demand theory states that consumers derive utility not from the actual contents of the basket but from the characteristics of the goods in it. This theory was developed by Kelvin Lancaster in 1966 in his working paper “A New Approach to Consumer Theory”.

This approach allows us to predict how preferences will change when we change the options or baskets presented to consumers by studying how these vary according to the change in the characteristics that make them up. With conventional theory, the introduction of a new option meant that we could not reliably predict how this would slot into the consumer’s preference map. However, by relying on a study of the characteristics rather than the goods or service involved, we can predict how changes will affect a consumer’s behaviour without needing to start once again empirically.

This allows us to calculate ‘shadow prices’ for different attributes without having a price for the good itself by associating utility to the characteristics that make up the good rather than the good itself. With these ‘shadow prices’, we can solve utility maximisation problems for baskets or options for which we do not have empirical evidence, as Lancaster demand also lends itself to building utility functions (based on the amount of each type of characteristic rather than the amount of each type of good in a particular basket).

Characteristic demand theory also helps justify the existence of brands. Luxury brands are able to charge a surprice for their products by differentiating themselves from competitors that sell similar goods. In the first diagram, if we suppose that both brands have the same characteristics and are perfect competitors, then we will choose the basket that maximises our total consumption. This means will tend to opt for the cheaper brand, which allows us to reach the highest utility curve: for a given amount of money, we are able to buy either a certain amount of brand 1 (point B) or a certain amount of brand 2 (point A). We choose A since it’s on a higher indifference curve. Point C represents a higher utility curve achieved by a drop in the price of brand 1. However, even though brand 1 got cheaper, we’ll still consume A, since it remains on a higher indifference curve.

In the second diagram, if we look at Lancaster demand, our utility functions will be based on the characteristics that each basket contains rather than on the amount of each type of good. Here, it is no longer ‘all or nothing’- we can allow for convex demand curves that represent our preference for variety in consumption: point C. This time, if the price of one brand drops, we will change our outcome: we can opt for point D.

How do we know enough to build an individual’s demand curve? Do we have to watch them endlessly as they affront each new possibility? Revealed preference theory aims to simplify the information necessary to be able to make assumptions about an agent’s choices through two basic tenants.

Revealed preference theory

Revealed preference theory is attributable to Paul Samuelson in his article “Consumption Theory in Terms of Revealed Preference”, 1948. Consumer theory depends on the existence of preferences which materialise into utility functions. These utility functions are maximised by consumers subject to a budget restraint. The issue is that it is difficult to accept that individuals really have a definite mathematical formula in mind when choosing between different options. What revealed preference theory does is work backwards to assume that we can deduce these utility functions from consumer behaviour. Analysing these choices leads us backwards to a set of preferences that influences the choices they make. It therefore allows economists to study consumer behaviour empirically.

There are two main axioms to the theory, both based on completeness and transitivity:

WARP (Weak Axiom of Revealed Preference): If A is revealed preferred to B (A RP B), then it must be so in every case. That is, if a consumer ever chooses B, then we must assume that A was previously chosen and that the budget constraint had enough ‘left over’ to allow a consumer to choose B as well.

SARP (Strong Axiom of Revealed Preference): This adds transitivity. If there are only two goods, then it is clear that WARP already defines a consumer’s choice: A over B. However, the SARP adds the idea of indirectly revealing preferences: if A is chosen over B and B over C, SARP and transitivity dictate that A is also preferred to C, so A is indirectly revealed to be preferable to C (A R* C). This drastically reduces the amount of empirical evidence necessary to define consumer preferences.

 

In the case shown in the figure below, we know that C is indirectly preferred to B (C R* B) because it allows us to reach a higher utility curve. Because C and B define a space (R*), and we know that C, B and A are contained within R*(R*{(C,B)}), then we can say that C RP A RP B, that is, by knowing from observation that C is indirectly preferred to B, we can tell that C is revealed as preferable to A (C RP A) and that A is revealed as preferable to B (A RP B).

If we think of A, B and C as infinitely complex bundles of goods, we can map out all a consumer’s choices. In theory, we can track this backwards to actually build utility functions if we have access to unlimited data. Without actually having to do this, we can aggregate consumer data to reveal general truths about a certain population’s preferences.

As we have seen throughout this Learning Path, consumer theory allows us to understand how consumer needs are met, respecting a certain budget constraint and given possible price changes. Characteristics demand theory and Revealed preference theory expands the way we study consumer theory.

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