What happens if ICs are shown to be intersecting, as given in the following diagram:
IC1 and IC2 are intersecting at point a. Points a and b are on IC2, implying a = b in terms of the level of satisfaction. Likewise, points a and c are on IC2, implying that a = c. If a = b, and a = c, then we can infer that b = c. But c is definitely better than b. Because point c offers the same amount OS of Good-2 as to point b, but greater amount of Good-1. At c, consumer is getting sc amount of Good-1 while at b he is getting only sb amount of Good 1 sb < sc, apparently. So that point c must be offering a higher level of satisfaction to the consumer than point b. The intersecting IC1 and IC2 however, reveal that b and c are equal. This must be wrong and hence proved that ICs never touch or intersect each other.
