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Difficulty: MediumIndifference Curves and Their Properties

Match each fundamental property of a standard indifference curve on the left with its underlying economic principle or theoretical implication on the right.

  • Downward slope from left to rightImplies a negative rate of substitution where gaining one commodity requires surrendering another
  • Convexity to the originReflects the principle of diminishing marginal rate of substitution (MRSxyMRS_{xy})
  • Higher curve placement on indifference mapRepresents larger quantities of commodities and higher total utility
  • Inability of curves to intersectPreserves the logical axioms of consistency and transitivity of preferences

Answer

Downward slope maps to the negative substitution trade-off; Convexity to origin maps to diminishing MRSxyMRS_{xy}; Higher curve placement maps to greater total utility; Inability of curves to intersect maps to preference transitivity.
Each property directly derives from consumer preference axioms. The downward slope stems from commodity trade-offs, convexity stems from diminishing marginal rates of substitution, higher positioning signifies superior satisfaction levels under non-satiation, and non-intersection upholds transitivity in consumer choices.

Step-by-Step Solution

1
Identify the economic rationale for slope
A negative slope indicates that the two commodities are substitutes in consumption.
To remain on the same utility level while gaining more of one commodity, the consumer must sacrifice some of the other commodity.
2
Determine the cause of curvature
Convexity implies that the slope (MRSxyMRS_{xy}) falls continuously as one moves down the curve.
As consumption of Good XX increases, its marginal utility (MUxMU_x) relative to Good YY (MUyMU_y) decreases.
3
Analyze position and intersection rules
Higher curves contain superior bundles, and crossing curves violate logical preference ordering.
Monotonicity ensures higher curves offer more utility, while transitivity requires that if bundle A equals B and B equals C, then A must equal C.

Key Concept

Properties of indifference curves in ordinal utility theory
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Topics

Indifference Curves and Their Properties

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