Mostly summarized from Gregory Mankiw’s Principles of Economics, 5th Ed.
PART 7 Topics for Further Study
Chapter 21 of 36 The Theory of Consumer Choice
Section 7 of 26
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Figure 3 here
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Figure 3 - The Impossibility of Intersecting Indifference Curves
A situation of intersecting indifference curves can never happen.
According to these indifference curves the consumer would be equally satisfied at points A, B, and C, even though point C has more of both goods than point A.
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Four properties of indifference curves:
Property 1 - higher (farther right) indifference curves are preferred to lower ones
Property 2 - indifference curves are downward sloping
Property 3 - indifference curves do not cross
Property 4 - indifference curves are bowed inward
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Property 3 - Indifference curves do not cross
Suppose two indifference curves did cross, as in Figure 3.
Because point A is on the same indifference curve as point B, the two points would make the consumer equally happy.
Because point B is on the same indifference curve as point C, these two points would make the consumer equally happy.
This conclusion, A=B=C, means points A and C would also make the consumer equally happy, even though point C has more of both goods.
At point C the consumer has more of both goods compared with point A.
This shows why indifference curves cannot cross.
Simply, a consumer cannot have two different preferences between products at the same time.

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