Indifference curves that are perfect right angles, like in the diagram, violate:

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Question restatement: Indifference curves that are perfect right angles, like in the diagram, violate:

Option 1: transitivity, but not completeness
- If the indifference curves are L-shaped, this typically reflects Leontief (perfect complements) preferences. Such preferences are complete and transitive in standard economic theory, meaning for any two bundles x and y, either x ≽ y or y ≽ x (completeness), and if x ≽ y and y ≽ z, then x ≽ z (transitivity). Therefore, claiming a violation of transitivity but not completeness does not align with the canonical properties of Leontief preferences. This option mischaracterizes the usual behavior of these preferences.

Option 2: completeness, but not transitivity
- Leontief preferences generate a complete and transitive ordering: any two bundles can be ranked (one dominates in both goods or they are not strictly comparable but the standard Leontief setup still yields a complete preorder through the defined dominance relation), and transitivity holds across the ranking. If someone argues about incomparabilities between some bundles, that would contradict the standard completeness of Leontief preferences. Thus this option incorrectly assigns a violation to either completeness or transitivity given the typical interpretation of L-shaped indifference curves.

Option 3: both transitivity and completeness
- Since Leontief (perfect complements) preferences are usually both complete and transitive, claiming that both properties are violated would be inconsistent with the conventional model that the L-shaped indifference curves represent. This option overstates the violation.

Option 4: neither transitivity nor completeness
- If one accepts the standard interpretation that L-shaped indifference curves reflect Leontief preferences, then the preference relation is complete and transitive, meaning no violation occurs for either property. Therefore, this option aligns with the typical theoretical characterization of these preferences: there is no violation of transitivity or completeness in the standard Leontief framework.

Summary of reasoning across options: The right-angled, L-shaped indifference curves are commonly used to depict perfect complements, which, in standard theory, yield a complete and transitive preference relation. The other statements either claim a violation that is not consistent with the usual Leontief model or claim violations in both properties, which is not how these indifference curves are interpreted. Therefore, the claim that none of transitivity or completeness is violated is the most consistent with the standard analysis.

Indifference curves that are perfect right angles, like in the diagram, violate:

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