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Difficulty: Very hardIndifference Curves and Their Properties

Suppose two indifference curves, IC1IC_1 and IC2IC_2, representing a consumer's preferences for Good XX and Good YY, intersect at bundle PP. Bundle QQ lies solely on IC1IC_1, and bundle RR lies solely on IC2IC_2, with bundle RR containing strictly more of both goods than bundle QQ. Which fundamental economic assumption of ordinal utility theory is violated by this intersection, and what is its logical consequence?

  1. The axiom of transitivity and monotonic preferences; it creates a contradiction where a bundle with more goods yields the same satisfaction as a bundle with fewer goods.Answer
  2. B
    The law of diminishing marginal rate of substitution; it causes the marginal rate of substitution to remain constant along both curves regardless of bundle composition.
  3. C
    The principle of total utility maximization; it forces marginal utility to drop to zero at the point of intersection.
  4. D
    The assumption of diminishing returns; it causes the budget line to become concave relative to the origin.

Answer

The axiom of transitivity and monotonic preferences; it creates a contradiction where a bundle with more goods yields the same satisfaction as a bundle with fewer goods.
Indifference curves cannot intersect because such an intersection violates the axiom of transitivity and monotonic preferences. If two curves intersect at a common point, transitive logic forces any two distinct bundles on those separate curves to yield equal satisfaction. However, if one bundle contains more of both commodities, monotonic preference requires it to yield strictly higher utility, producing a direct logical contradiction.

Step-by-Step Solution

1
Analyze the preference relations defined by the intersection point PP
Since PP lies on both IC1IC_1 and IC2IC_2, the consumer is indifferent between PP and QQ (P∼QP \sim Q), and also indifferent between PP and RR (P∼RP \sim R).
By definition, all points on a single indifference curve yield equal total utility.
2
Apply the axiom of transitivity
If Q∼PQ \sim P and P∼RP \sim R, transitivity requires that Q∼RQ \sim R.
Transitivity dictates consistent ordering of consumer preferences across combinations.
3
Compare the bundles QQ and RR using monotonic preferences (non-satiation)
Since bundle RR contains strictly more of both goods than bundle QQ, monotonic preference implies RR must be strictly preferred to QQ (R≻QR \succ Q).
Consumers prefer combinations with larger quantities of goods.
4
Identify the logical contradiction
The deduction Q∼RQ \sim R directly contradicts R≻QR \succ Q, proving that indifference curves can never intersect under standard rational preference axioms.
Intersecting indifference curves destroy the logical consistency of preference ordering.

Key Concept

Non-intersection of Indifference Curves and Transitivity Axiom
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Topics

Indifference Curves and Their Properties

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