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Difficulty: MediumIndifference Curves and Their Properties

Suppose two indifference curves, IC1IC_1 and IC2IC_2, intersect at point AA on a consumer's indifference map. Which fundamental assumption of ordinal utility theory is logically violated by this intersection?

  1. Transitivity and consistency of consumer preferencesAnswer
  2. B
    Diminishing marginal rate of substitution between goods
  3. C
    Maximization of total utility when marginal utility reaches zero
  4. D
    Constant marginal rate of substitution across all utility levels

Answer

Transitivity and consistency of consumer preferences
The correct answer is transitivity and consistency of consumer preferences. Indifference curves cannot intersect because if they did, a shared point of intersection would imply that two different levels of utility are equal, contradicting the axiom of transitivity (If A∼B and A∼C, then B∼CIf\ A \sim B\ and\ A \sim C,\ then\ B \sim C).

Step-by-Step Solution

1
Analyze the definition of an indifference curve
Every point on a single indifference curve yields the exact same level of total utility to the consumer.
An indifference curve represents loci of commodity combinations that offer equal satisfaction.
2
Apply logical deductions to intersecting curves
If point AA lies on both IC1IC_1 and IC2IC_2, then utility at AA equals utility at point BB (on IC1IC_1) and utility at point CC (on IC2IC_2).
Points on the same curve must yield equal utility.
3
Evaluate the outcome against preference transitivity
By transitivity, if B=AB = A and A=CA = C, then BB must equal CC. However, since BB and CC lie on different curves representing different utility levels, this creates a logical contradiction.
Transitivity requires consistent preference ordering (If X∼Y and Y∼Z, then X∼ZIf\ X \sim Y\ and\ Y \sim Z,\ then\ X \sim Z). Therefore, indifference curves can never intersect.

Key Concept

Indifference Curve Properties: Non-intersection and Preference Transitivity
Estimated Time:1m 0s
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Topics

Indifference Curves and Their Properties

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