Indifference curves have a few features. Two of those features are that indifference curves do not cross, and the indifference curve is convex to the origin.

Indifference Curves do not Cross

Indifference curves cannot cross each other. To understand why, consider two indifference curves that cross. Points A and B lie on the same indifference curve. So they provide the same level of satisfaction to the consumer. Similarly, points B and C also provide the same level of satisfaction to the consumer. This means that points A and C should provide equal satisfaction to the consumer. However, point C has more of both goods compared to point A. This contradicts the assumption of monotonic preferences. It states that a consumer always prefers more of both goods to less. This means that indifference curves cannot intersect.

Indifference Curve is Covex to Origin

Indifference curves are convex or bowed inward towards the origin. This is due to the diminishing marginal rate of substitution (MRS). The MRS represents the rate at which a consumer is willing to trade off one good for another while maintaining the same level of satisfaction. This rate decreases as a consumer accumulates more of one good. This means the slope of the indifference curve must decrease as the quantity of a good increases, and vice versa.