Question

Why do the indifference curves neither intersect nor are tangent to one another?

Answer 1

If two indifference curves intersect or be tangent to each other, it would mean that an indifference curve indicates two different levels of satisfaction or that two different combinations-one being larger than the other, yield the same level of satisfaction. Such conditions are impossible if consumer’s subjective valuation of a commodity is greater than zero. Also, if two indifference curves intersect, it would mean violation of stability or transitivity assumption in consumer’s preferences.

Suppose when two indifference curves IC₁ and IC₂, intersect at point B. Consider two other points – point F on indifference curve IC₂ and point E on indifference curve IC₁ both falling on vertical line.

Points B, F and E represent three different combinations of commodities X and Y. Note that combination B is common to both the indifference curves, it implies that, in terms of utility,
B = F
B = E
F = E
But, if F equals E, it would mean that in terms of utility,
OD of X + FD of Y = OD of X + ED of Y

Since OD of X is common to both the terms, it means that FD of Y is equal to ED of Y. But, this is not so. Figure shows FD > ED. Therefore, combinations B and C cannot be equal in terms of utility in the objective introspection of the consumer. The intersection, therefore, violates the transitivity rule which is a logical necessity in indifference curve analysis.