Why do indifference curves not intersect each other?

Indifference curves represent combinations of two goods that provide the same level of utility to a consumer. They do not intersect for the following reasons:

1. Transitivity of Preferences: If a consumer is indifferent between bundles A and B, and between B and C, they must also be indifferent between A and C. If curves intersected, this would violate transitivity.

2. Non-Satiation: Consumers always prefer more of a good to less, given the same amount of the other good. If curves intersected, it would imply that a consumer could be made better off without any additional resources, which contradicts the assumption of non-satiation.

3. Uniqueness of Utility Levels: Each indifference curve represents a unique level of utility. If two curves intersected, it would mean that a single bundle of goods provides two different levels of utility, which is logically inconsistent.

Thus, indifference curves must be downward-sloping, convex to the origin, and non-intersecting.