An indifference curve shows a combination of two goods that give a consumer equal satisfaction and utility thereby making the consumer indifferent. ... Typically, indifference curves are shown convex to the origin, and no two indifference curves ever intersect.

Why can't indifference curves never cross?

The indifference curves cannot intersect each other. It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible.

Can indifference curve cross itself?

No, an indifference curve can't cross itself. All the points on an indifference curve represent the same level of utility by consuming two goods....