Revealed Preference

The theory of revealed preference ( in German about: Revealed preference or Expressed preference) is used to model consumer decisions based upon observable and observed decisions in microeconomics. It borders thus the assumption of not directly observable preference orderings or utility functions than usual in microeconomics the usual starting point for the creation of individual decisions. The theory of revealed preference is closely connected with the Financial theory and consumer theory in microeconomics. It was largely founded by Paul A. Samuelson and further developed among others by Hendrik Houthakker and Hal R. Varian.

Approach

The concept of preference orderings and utility functions, which is usually set to the theory of decisions of households is based is abstract and is as meaningless criticized: Which consumer is already aware to exist with a properly defined function that determines all consumer decisions? One can also, with some justification ask whether consumers really decide completely consistent and rational. There are many reasons why this need not be so. Here is an example:

" If we ask someone what color he wants to emphasize his apartment, and give him two very similar shades of gray to choose from, so it may be that he can not distinguish between the two sounds and says he is indifferent. Then we take the lighter shade of gray and set an even lighter shade of gray next to it, he will also be indifferent if he can not tell the difference again. If you keep this up and end up holding the lightest shade of gray next to the dark shade of gray used at the beginning, so it may be that now gives a clear preference for one of the two tones. This would have a number of preferences generated that violates the Transitivitätsannahme. "

Usually leaves the preference ordering or utility function of a consumer not directly observe (if it exists at all ). One can at best observe a number of (consumer) decisions ( at various prices). This is precisely the starting point of Revealed Preferences. Suppose in the example above, the final decision would have been in favor of the lighter shade of gray. Thus it can be said then that the consumer the lighter shade of gray against the darker in direct comparison preferred. The lighter tone is so Directly revealed preferred. Assume that the consumer should now choose between red and blue, and he chooses red is then instructed to choose between red and green, and he chooses green. Now we have two Directly revealed preferred relations. If red to blue is preferred over red and green, then you say that green to blue is indirectly preferred ( Indirectly revealed preferred).

You can meet now widely used for the further use of the concept of Revealed Preferences in economic models further assumptions about the consistency of individual decisions. The weak axiom of Revealed Preferences, the assumption that if he has red to blue at least as good as disclosed, he can no longer clearly prefer blue over red. Strong Axiom of Revealed Preferences assumes that if red ( ie green indirectly to blue ) is compared to blue and green disclosed directly opposite red as better, the consumer can not prefer more blue opposite green unique. Only with this additional assumption, the Revealed Preferences equivalent to the alternative theory of preference orderings for the description of individual decisions.

Formal representation

Note: The nature of the representation varies from textbook to textbook, from item to item. Below is followed roughly the spelling of Varian, which in turn has similarities with Houthakker (1950).

Let xt, t = 1, ..., T, quantities of goods bundle that has elected to the periods t a consumer. Let pt the corresponding prices. The total price of selected goods in t bundle is then xt pt.

A consumer has chosen K pt xt to the prices in period t quantities. In a subsequent period he chooses z (possibly different) amounts to xz (possibly different) prices pz. Assuming that the quantities of the next period would have been to have at the prices of the first period to a lower or same total price as the actually chosen in the first period quantities, ie z ≤ x pt pt xt. Then this means the consumer would have in the first period can choose xz, but has instead preferred to xt. On the basis of such observable consumption decisions defining two relations:

This is therefore a Transitivitätsannahme for preferences expressed. The relation R is the transitive closure of the relation RD.

Axioms of Revealed Preferences

The weak axiom of Revealed Preferences is a basic consistency assumption about the decisions of consumers. It states that, if the consumer had the direct choice between xt and xt xz and he once preferred xz, he no longer reversed xz prefers over xt. For watching decisions that meet the assumptions of a preference ordering, the weak axiom is always fulfilled.

The weak axiom is often, set approach, based on the theory of Revealed Preferences basis. Experiments show, however, that there are situations in which consumers do not act in accordance with the axiom. For example, the decoy effect.

Strong Axiom of Revealed Preferences states that if the consumer has once xt preferred indirectly, to xz, he is xz, and indirectly, no longer prefer xt. So he is also consistent over several periods of time or decisions.

One can prove that it is always to decision-making structures that satisfy the strong axiom of a preference ordering or you can define a utility function. It is essentially equivalent to preference orderings assumption about individual decisions.