1- Choice under uncertainty Flashcards
What does weak preference (≽) mean?
At least as good as
What are axioms?
Self-evident statements which cannot be proven
What is the axiom of transitivity?
If x≽y and y≽z then x≽z
What is the axiom of completeness?
Either x≽y or y≽x or both
When are weak preference relations defined as rational?
The weak preference relation is rational if it satisfies the Axioms of Transitivity and Completeness
What is the indifference preference relation?
x~y if and only if x≽y and y≽x
What are the 3 properties of the indifference preference relation?
- Reflexivity: x~x
- Symmetry: if x~y then y~x
- Transitivity: if x~y and y~z then x~z
What is the strict preference relation definition?
x≻y if and only if x≽y and not y≽x
What are the 3 properties of the strict preference relation?
- Irreflexivity: Not x≻x
- Anti-symmetry: if x≻y then not y≻x
- Transitivity: if x≻y and y≻z then x≻z
What are the 2 requirements of a rational choice?
- rational preference ordering
- choose the most preferred option under the set of alternatives
What is the representation theorem?
For finite domains, there exists a utility function u(·) that represents the weak preference relation ≽ if and only if ≽ is rational
What are explicit costs?
What you have to pay in dollars to get something
What are opportunity (implicit) costs?
The value of the next best option foregone
What is net (utility) surplus?
Utility of your choice minus opportunity cost
What is the opportunity cost proposition?
An alternative is a rational choice if and only if its utility is greater than its opportunity cost