Preference (economics) - Basic Premises

Basic Premises

In consumer theory, economic actors are thought of as being confronted with a set of possible consumption bundles or commodity space. Of all the available bundles of goods and services, only one is ultimately chosen. The theory of preferences seeks an analytical solution to the problem of getting to this ultimate choice (the optimal choice) using a system of preferences within a budgetary limitation. Choice is an act, whereas preferences are a state of mind.

In reality, people do not necessarily rank or order their preferences in a consistent way. In preference theory, some idealized conditions are regularly imposed on the preferences of economic actors. One of the most important of these idealized conditions is the axiom of transitivity:

If alternative is preferred to alternative, and to, then is preferred to .

The language of binary relations allow one to write down exactly what is meant by "ranked set of preferences", and thus gives an unambiguous definition of order. A preference relation should not be confused with the order relation used to indicate which of two real numbers is larger. Order relations satisfy an extra condition:

, and, implies

which does not always hold in preference relations; hence, an indifference relation is used in its place (the symbol denotes this kind of relation).

A system of preferences or preference structure refers to the set of qualitative relations between different alternatives of consumption. For example, if the alternatives are:

• Apple
• Orange
• Banana

In this example, a preference structure would be:

"The apple is at least as preferred as the orange", and "The orange is as least as preferred as the Banana". One can use to symbolize that some alternative is "at least as preferred as" another one, which is just a binary relation on the set of alternatives. Therefore:

• Apple Orange
• Orange Banana

The former qualitative relation can be preserved when mapped into a numerical structure, if we impose certain desirable properties over the binary relation: these are the axioms of preference order. For instance: Let us take the apple and assign it the arbitrary number 5.Then take the orange and let us assign it a value lower than 5, since the orange is less preferred than the apple. If this procedure is extended to the banana, one may prove by induction that if is defined on {apple, orange} and it represents a well-defined binary relation called "at least as preferred as" on this set, then it can be extended to a function defined on {apple, orange, banana} and it will represent "at least as preferred as" on this larger set.

Example:

• Apple = 5
• Orange = 3
• Banana = 2

5 > 3 > 2 = u(apple) > u(orange) > u(banana)

and this is consistent with Apple Orange, and with Orange Banana.