Fundamental Assumptions of Consumer Preference Theory
The fundamental assumptions of consumer preference theory include the properties of completeness, transitivity, reflexivity, non-satiation, continuity, and strict convexity. Let’s analyze each option with respect to these properties:
- Option (A): Either x ⪰ y or y ⪰ x or both: This option follows from the completeness assumption. Completeness states that for any two bundles x and y, a consumer can compare them and determine either x ⪰ y (x is at least as good as y) or y ⪰ x (y is at least as good as x), or both (indifference). Thus, this statement is correct.
- Option (B): y ≻ x if y contains more of at least one good and no less of any other: This option is consistent with the non-satiation assumption. Non-satiation states that “more is better,” meaning a consumer will always prefer a bundle that contains more of at least one good and no less of any other. Thus, this statement is correct.
- Option (C): x is not indifferent to itself: This statement is incorrect. The reflexivity assumption in preference theory states that every bundle is at least as good as itself. In other words, x ∼ x, meaning a bundle x is always indifferent to itself. Therefore, the statement x is not indifferent to itself directly violates the reflexivity assumption. Hence, this is the correct answer to the question, as it is the only statement that is NOT correct.
- Option (D): For x (or y), its better set is strictly convex: This option follows from the strict convexity assumption. Strict convexity implies that if a consumer prefers two bundles x and y, they will also strictly prefer any convex combination (weighted average) of x and y over either bundle. This means the better set (set of bundles preferred to x) will be strictly convex. Thus, this statement is correct.
Explanation of the Correct Answer:
Option (C) violates the fundamental assumption of reflexivity, which states that any bundle x is always at least as good as itself (x ∼ x). Therefore, the statement “x is not indifferent to itself” is incorrect.