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Explain why two indifference curves cannot intersect

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Ch03
sol 03, sol 03, Ch07

4. Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke.

3. Explain why two indifference curves cannot intersect.
The figure below shows two indifference curves intersecting at point A. We know from the definition of an indifference curve that the consumer has the same level of utility for every bundle of goods that lies on the given curve. In this case, the consumer is indifferent between bundles A and B because they both lie on indifference curve U
1
. Similarly, the consumer is indifferent between bundles A and C because they both lie on indifference curve U
2
. By the transitivity of preferences this consumer should also be indifferent between C and B. However, we see from the graph that C lies above B, so C must be preferred to B because C contains more of Good Y and the same amount of Good X as does B, and more is preferred to less. But this violates transitivity, so indifference curves must not intersect.

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Pindyck/Rubinfeld, Microeconomics, Eighth Edition Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.
4. Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one
can of Coke.

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