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Difficulty: Very hardIndifference Curves and Their Properties

Match each geometric property of indifference curves in Column I with its underlying economic foundation or preference axiom in Column II.

  • Downward slope from left to rightNecessary trade-off between goods to maintain constant total utility
  • Convexity towards the originDiminishing marginal rate of substitution (MRSxyMRS_{xy})
  • Non-intersection of indifference curvesAxiom of transitivity and consistency of choice
  • Higher curve lying further from the originMonotonicity of preferences (non-satiation principle)

Answer

Each geometric property maps to its corresponding economic principle: Downward slope relates to the necessary trade-off between goods to keep total utility constant; Convexity towards the origin reflects a diminishing marginal rate of substitution (MRSxyMRS_{xy}); Non-intersection ensures compliance with the axiom of transitivity; Higher curves reflect monotonicity of preferences (non-satiation).
Each geometric property directly corresponds to a fundamental behavioral assumption in ordinal utility theory: downward slope reflects the negative substitution trade-off required for constant utility; convexity reflects diminishing MRSxyMRS_{xy}; non-intersection preserves preference transitivity; and higher curves represent greater satisfaction due to non-satiation.

Step-by-Step Solution

1
Analyze the downward slope property
Downward slope implies a negative marginal rate of substitution (dYdX<0\frac{dY}{dX} < 0), requiring substitution of one good for another to maintain equal utility.
Because total utility along an indifference curve is constant (dU=MUxdX+MUydY=0dU = MU_x dX + MU_y dY = 0), an increase in XX must be balanced by a decrease in YY.
2
Analyze the convexity property
Convexity implies that the slope (MRSxyMRS_{xy}) diminishes in absolute magnitude as consumption of XX increases relative to YY.
As XX becomes more abundant, its marginal utility (MUxMU_x) falls relative to MUyMU_y, reducing the consumer's willingness to sacrifice YY for additional units of XX.
3
Analyze the non-intersection property
Intersecting curves violate preference consistency and transitivity.
If curve IC1IC_1 and IC2IC_2 intersect at point AA, and point BB lies on IC1IC_1 while point CC lies on IC2IC_2, transitivity implies B∼AB \sim A and A∼C  ⟹  B∼CA \sim C \implies B \sim C, contradicting the requirement that distinct curves represent strictly different utility levels.
4
Analyze higher curve position
Curves located further from the origin represent higher utility levels.
Under monotonic preferences (non-satiation), consumption bundles containing more of both goods yield strictly greater satisfaction.

Key Concept

Properties of Indifference Curves and Preference Axioms
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Topics

Indifference Curves and Their Properties

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