Question

two indifference curve never intersect or touch each other explain

Answer 1

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Intersection 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.    
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