Behavioral eco-lect 1: Introduction part 2 (Reflexivity and symmetry …
Behavioral eco-lect 1: Introduction part 2
Transitivity and Completeness
Transitivity of ≽:
If x ≽ y and y ≽ z, then x ≽ z (for all x, y, z)
Completeness of ≽
: Either x ≽ y or y ≽ x (or both) (for all x, y)
The preference relation ≽ is a
if it satisfies transitivity and completeness.
Note: the book uses the term
“rational preference relation”
. Some economists indeed define rationality in that way, but we will not. In behavioral economics we say that behavior is rational if it is normative.
Assume that his preferences over allocations of money are transitive
Assume that he always tries to choose his most preferred allocation.
Consider a person who is envious.
One could argue that the behavior of this person is irrational.
Reflexivity and symmetry
of ≻ : there exists no x with x ≻ x
: if x ~ y then also y ~ x
of ≽: x ≽ x for all x
: if x ≻ y then it cannot be that y ≻ x (for all x,y)
see slide 23-27/53
: analyze utility u(x), where x depends on the context
Choice under uncertainty
: x is a prospect
e.g. x = (x1, x2), where x1 is consumption if the next president of the US is a
democrat and x2 is consumption if the next president of the US is no democrat
Choice over time
: x is a sequences of outcomes
e.g. x = (x1, x2), where x1 is consumption today and x2 is consumption tomorrow
Choice under certainty
: x is a consumption bundle
e.g. x = (x1, x2), where x1 is nr. of apples and x2 nr. of bananas
Choice in a social context
: x is an allocation
e.g. x = (x1, x2), where x1 is consumption of Ann and x2 is consumption of Bill
Utility presents preferences
This is an important theorem. It is not easy to prove it.
It says that if your preferences are a weak order, then it is possible to construct a utility function that represents your preferences.
If the set of alternatives is finite, then ≽ is a weak order if and
only if there exists a utility function representing ≽.