Preferences Lecture

Introduction to Preferences

• Preferences relate to individual likings (e.g., choosing tea over coffee).
• Basic Assumption: Preferences do not change over the decision period (valid for short periods).
• Goal: Systematically and mathematically formalize decision-making.

Rationality Assumptions

1. Completeness

• Defined over consumption possibility set (or consumption set).
• Preferences are assumed to be defined on the consumption possibility set, not on the budget set.
• For any two bundles from the consumption set (X and Y):
  • X is preferred to Y (X > Y).
  • Y is preferred to X (Y > X).
  • Indifference between X and Y (X ~ Y).
• Assumes no ignorance or indecision among the decision-maker.

2. Transitivity

• Defined over three bundles (X, Y, Z).
• If X is at least as good as Y and Y is at least as good as Z, then X is at least as good as Z.
• Transitivity ensures consistency in choice.
• Violations of transitivity can lead to circular preferences (e.g., mango > guava > banana > mango).

Implications of Rationality Assumptions

• A person satisfying completeness and transitivity is rational in decision-making.
• Rationality allows ranking of bundles in a consistent order.

Continuity Assumption

• Addresses issues with infinite bundles.
• Ensures that bundles closer to each other have closer associated numbers.
• Useful for mathematically ordering multi-dimensional consumption sets into a single dimension.

Utility Functions

• Uses numerical representation to simplify comparison (U(X) > U(Y) if X > Y).
• Continuity ensures that preference relations can be represented by utility functions.
• Utility functions can undergo monotonic transformations without changing the preference order.

Conclusion

• Rationality and continuity assumptions facilitate the mathematical treatment of decision-making.
• Upcoming lectures will discuss additional assumptions and their implications.