Why indifference curves cannot intersect each other?
ntersection of two indifference curves representing different
levels of satisfaction is a logical contradiction. It would mean
that indifference curves representing different levels of
satisfaction are showing the same level of satisfaction at the
point of intersection or contact. We can prove this property of
indifference curves through contradiction. Suppose, two
indifference curves IC1 and 1C2 meet (Fig (a)), intersect (Fig.
(b)) or touch (Fig. (c)) each other at point 'A' in Fig. Point 'C'
is taken just above point 'B', such that it contains same amount of
commodity 'X' and more amount of commodity' Y'. Consider points 'B'
and 'A' on IC1. Consumer is indifferent between these points, as
both lie on the same indifference curve IC. Further, points 'A' and
'C lie on the same indifference curve IC implying same level of
satisfaction to the consumer. Now, by the assumption of
transitivity, points 'B' and 'C' yield same level of satisfaction
to the consumer. But, point 'C' lies on a higher indifference curve
having more amount of commodity' Y'. It must be preferred to point
'B' by the assumption of non-satiety. Further, intersection of two
indifference curves also violates the assumption of positive
marginal utilities of the two commodity. In Fig., intersection of
IC1 and IC2 means additional amount of BC has zero utility.
Therefore, indifference curves can never intersect or touch each
other.