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Difficulty: MediumIndifference Curves and Their Properties

Which of the following theoretical reasons explains why standard indifference curves can never intersect each other?

  1. Intersection violates the assumption of transitivity by implying that two distinct levels of total satisfaction yield equal utility.Answer
  2. B
    Intersection causes the marginal rate of substitution between goods to remain constant along both curves.
  3. C
    Intersection forces total utility to reach its maximum point where marginal utility becomes zero.
  4. D
    Intersection implies that the consumer is unwilling to substitute one good for another at any point on the curves.

Answer

Intersection violates the assumption of transitivity by implying that two distinct levels of total satisfaction yield equal utility.
Indifference curves cannot intersect because if they did, the point of intersection would belong to two different utility levels. By transitivity, all points on both curves would yield the exact same utility, which contradicts the concept that higher or distinct curves represent different satisfaction levels.

Step-by-Step Solution

1
Identify the core property being evaluated.
The property is the non-intersection of indifference curves.
Indifference curves represent combinations of two goods that give a consumer equal satisfaction.
2
Analyze the logical consequence if two curves (IC1IC_1 and IC2IC_2) were to cross at a point (AA).
Point AA lies on both IC1IC_1 and IC2IC_2.
If bundle BB is on IC1IC_1, then A∼BA \sim B. If bundle CC is on IC2IC_2, then A∼CA \sim C.
3
Apply the axiom of transitivity.
If A∼BA \sim B and A∼CA \sim C, then B∼CB \sim C.
Transitivity dictates that if bundle AA gives equal satisfaction to BB and CC, then BB and CC must give equal satisfaction. However, BB and CC lie on distinct curves representing different overall utility levels, creating a logical contradiction.

Key Concept

Non-intersection property of indifference curves derived from preference transitivity
Estimated Time:1m 0s
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Topics

Indifference Curves and Their Properties

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