Disclosed preferences

The theory of revealed preferences ( English Revealed Preference Theory ) is used to model consumer decisions on the basis of observable or observed decisions in microeconomics . It is thus differentiated from the assumption of non-directly observable order of preferences or utility functions as the usual starting point for modeling individual decisions in microeconomics. The theory of revealed preferences is closely related to household theory or consumer theory in microeconomics. It was largely founded by Paul A. Samuelson and further developed by Hendrik Houthakker and Hal R. Varian, among others .

approach

The concept of preference orders and utility functions, which is usually used as a basis for the theory of household decisions, is abstract and has been criticized as meaningless: Which consumer is already aware of having a properly defined function that determines all consumer decisions? One can also ask, with some justification, whether consumers really make completely consistent and rational decisions. There are many reasons why this need not be the case. Here is an example:

“If we ask someone what color they would like to paint their apartment with and give them two very similar shades of gray to choose from, they may not be able to tell the two shades apart and say they are indifferent. If we then take the lighter shade of gray and place an even lighter shade of gray next to it, it will also be indifferent if it cannot detect any difference again. If you continue like this and at the end keep the lightest gray tone next to the dark gray tone used at the beginning, it may be that there is now a clear preference in favor of one of the two tones. This would have created a number of preferences that violate the transitivity assumption . "

- Andreu Mas-Colell, Michael D. Whinston, Jerry R. Green : Mas-Colell et al. Microeconomic Theory , Chapter 1B

Usually the order of preferences or utility function of a consumer cannot be observed directly (if it exists at all). At best, one can observe a series of (consumption) decisions (at different prices). This is exactly the starting point of the Revealed Preferences. Assume that in the example above the final decision was in favor of the lighter shade of gray. It can then be said that the consumer prefers the lighter shade of gray over the darker shade in a direct comparison. The lighter tone is therefore directly revealed preferred . Suppose the consumer is supposed to choose between red and blue and he chooses red. Then he is supposed to choose between red and green and he chooses green. We now have two directly revealed preferred relationships. If red is preferred over blue, and green is preferred over red, then green is said to be indirectly revealed preferred over blue .

One often makes further assumptions about the consistency of individual decisions for the further use of the concept of revealed preferences in economic models. The weak axiom of the Revealed Preferences makes the assumption that if he has revealed red to be at least as good over blue, he can no longer clearly prefer blue over red. The strong axiom of the Revealed Preferences assumes that if red is revealed to be better directly compared to blue and green directly compared to red (i.e. green indirectly compared to blue), the consumer can no longer clearly prefer blue directly to green. Only with this additional assumption are the Revealed Preferences equivalent to the alternative theory of preference orders for describing individual decisions.

Formal representation

Note: The type of presentation varies from textbook to textbook, from article to article. In the following, the spelling of Varian is roughly followed, which in turn shows similarities with Houthakker (1950).

Let x ^t , t = 1, ..., T, quantities of a bundle of goods chosen by a consumer in the periods t. Let p ^{t be} the associated prices. The total price of a bundle of goods chosen in t is then p ^t  x ^t .

In a period t, a consumer K has chosen the quantities x ^t at the prices p ^t . In a subsequent period z he selects (possibly different) quantities x ^z at (possibly different) prices p ^z . Assuming that the quantities of the following period would have been available at the prices of the first period at a lower or the same total price than the quantities actually selected in the first period, i.e. p ^t  x  ^z  ≤ p ^t  x ^t . Then this means that the consumer could have chosen x ^z in the first period , but preferred x ^t instead . On the basis of such observable consumer decisions, two relationships are defined:

Directly Revealed Preference

The bundle of goods x ^t is directly preferred compared to an alternative bundle of goods x ^z if both could be chosen, but x ^{t was} actually chosen. That's what we write for  . ${\displaystyle \mathbf {x} ^{t}~R_{D}~\mathbf {x} ^{z}}$

Formal definition: . ${\displaystyle \mathbf {x} ^{t}~R_{D}~\mathbf {x} ^{z}:\Leftrightarrow \exists t,z\in 1,...,T:{\text{K hat }}x^{t}{\text{ gew}}{\ddot {a}}{\text{hlt und }}\mathbf {p} ^{t}\mathbf {x} ^{t}\geq \mathbf {p} ^{t}\mathbf {x} ^{z}}$

Revealed preference

Is a series of Directly preferred-relations for bundle of goods x ^t , x ^u , x ^v ..., x, ^y , x ^z given so that x ^t Directly revealed Preferred compared to x ^u , which revealed again Directly Preferred compared to x ^v is etc. ... until finally x ^{y is} directly preferred to x ^z , we say that x ^{t is} (indirectly) revealed preferred to x ^z and write . ${\displaystyle \mathbf {x} ^{t}~R~\mathbf {x} ^{z}}$

Formal definition: . ${\displaystyle \mathbf {x} ^{t}~R~\mathbf {x} ^{z}:\Leftrightarrow \exists t,u,v,...,y,z\in 1,...,T:\mathbf {p} ^{t}\mathbf {x} ^{t}\geq \mathbf {p} ^{t}\mathbf {x} ^{u},\mathbf {p} ^{u}\mathbf {x} ^{u}\geq \mathbf {p} ^{u}\mathbf {x} ^{v},...,\mathbf {p} ^{y}\mathbf {x} ^{y}\geq \mathbf {p} ^{y}\mathbf {x} ^{z}}$

It is therefore a matter of a transitivity assumption for expressed preferences. The ratio R is the transitive closure of the relationship R _D .

Axioms of the theory of revealed preferences

Weak axiom of revealed preferences

If so , then it does not apply . ${\displaystyle \mathbf {x} ^{t}~R_{D}~\mathbf {x} ^{z}}$ ${\displaystyle \mathbf {x} ^{z}~R_{D}~\mathbf {x} ^{t}}$

The weak axiom of revealed preferences is a basic assumption of consistency about consumer choices. It says that if the consumer had the direct choice between x ^t and x ^z and he preferred x ^t to x ^z , he no longer preferred x ^z to x ^t . The weak axiom is always fulfilled for observed decisions that correspond to the assumptions of a preference order .

The weak axiom is often used as a basis for models based on the theory of revealed preferences. However, experiments show that there are situations in which consumers do not act according to the axiom. For example with the decoy effect .

Strong axiom of revealed preferences

If so , then it does not apply . ${\displaystyle \mathbf {x} ^{t}~R~\mathbf {x} ^{z}}$ ${\displaystyle \mathbf {x} ^{z}~R~\mathbf {x} ^{t}}$

The strong axiom of the revealed preferences is that once the consumer has preferred x ^t indirectly to x ^z , he will no longer prefer x ^z , even indirectly, to x ^t . It therefore acts consistently over several periods or decisions.

One can prove that there is always an order of preference for decision structures that fulfill the strong axiom or that a utility function can be defined. So it is essentially an assumption about individual decisions that is equivalent to orders of preference.

criticism

Amartya Sen has repeatedly criticized the theory of revealed preferences. He pointed out, among other things, that the axioms of this theory cannot be based on empirical observations, but are inevitably the result of an implicit behavioral model - something that contradicts the presentation of the theory by its founder, Paul A. Samuelson . Sen also emphasized that the assumption of the consistency of the decisions contradicts the supposed normative neutrality of the theory. He also proposed the idea of ​​“as if behavior”, which could, for example, be used to consciously overcome the prisoner's dilemma if the actors concerned act, for strategic reasons, as if they had a different utility than their actual one, a better one Achieve result. Such anticipatory behavior is also at odds with the theory of revealed preferences.

literature

• Peter Schönfeld: Basic features of the theory of factual preference . In: Journal of Economics . tape 22 , no. 3 , 1962.
• Andreu Mas-Colell, Michael D. Whinston, Jerry R. Green: Microeconomic Theory . Oxford University Press, New York.
• Hal R. Varian: Microeconomic Analysis . Norton, New York 1992.

Individual evidence

1. ^ ^{A b} Paul A. Samuelson: A Note on the Pure Theory of Consumer's Behavior . In: Economica . tape 5 , no. February 17 , 1938, ISSN  0013-0427 , p. 61-71 , JSTOR : 2548836 .
2. ^ Paul A. Samuelson: Consumption Theory in Terms of Revealed Preference . In: Economica . No. 15 , 1948, ISSN  0013-0427 , pp. 243-253 .
3. ^ ^{A b c} S. Hendrick Houthakker: Revealed Preference and the Utility Function . In: Economica . No. 17 , 1950, pp. 159-174 .
4. ^ Hal R. Varian: The Nonparametric Approach to Demand Analysis . In: Econometrica . No. 50 , 1982, pp. 945-972 .
5. ↑ ^{a b c} Hal R. Varian: Revealed Preference . In: Samuelsonian Economics and the 21st Century . September 2006 ( citeseerx.ist.psu.edu [PDF]).
6. ↑ Amartya Sen: Behavior and the Concept of Preference . In: Economica . tape 40 , 1973, pp. 241-259 , JSTOR : 2552796 .