Indifference Set and Curve:

If we can divide each good into very small pieces we get a very great amount of bundles to compare for the consumer. Assuming that he/she is up to the task of making all these comparisons we can record all the pair wise rankings that the consumer makes. If we have one comparison bundle (A) we may find that the consumer’s preferences can be depicted as in figure shown below. This figure can be divided into three sets;

i) The set of bundles called Qi = (Qⁱ₁,Qⁱ₂) for which the consumer expressed: Qi › ∼ A; (the shaded set),
ii) The set of bundles for which: Qi ∼ A, (the indifference curve); and
iii) The set of bundles for which: A › ∼ Qi. The first two sets are illustrated in the figure, and the last set is the complement to these sets (i.e., all other bundles).

We should note here that there are plenty of indifference curves (possibly an infinite amount of them) and I have only illustrated one of them, the one expressing the rankings of all other bundles relative to one particular bundle (A). If I’ve drawn an indifference curve corresponding to another bundle B, which is worse than A, that indifference curve must lie to the south-west of the indifference curve through A. Similarly, if we had that B › A, the indifference curve would lie to the north-east of the same indifference curve. Note that two indifference curve cannot intersect because of the transitivity axiom.

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