Question

Prove that indifference curve slopes from left to right downward.

Answer 1

An Indifference Curve (IC) shows all potential combinations of two commodities that give a consumer the same level of satisfaction or utility. It must slope downward from left to right, and this shape may be shown with the logic below:

Assumptions:

1. Rational Consumer: The consumer always chooses more of a good over less, according to the Non-Satiation or Monotonic Preferences principle.
2. Diminishing Marginal Rate of Substitution (MRS): As a consumer consumes more of one good, they are prepared to sacrifice less of the other in order to retain the same utility level.
3. Divisibility of Goods: Both goods are divisible into smaller parts.

Assume a consumer at Point A on an indifference curve consumes X₁ units of X and Y₁ units of Y.

1. Moving to Point B with more X (X₂ > X₁) while maintaining 100% satisfaction requires sacrificing some Y to maintain the same indifference curve.
2. Y₂ < Y₁ as X and Y increase total utility, which contradicts the indifference curve description (same satisfaction level).
3. To maintain utility when the consumer consumes more X, they must consume less Y, resulting in a downward-sloping curve.