Features of Indifference Curves II

Indifference curves cannot cross because it would violate monotonic preferences. If two curves intersected at a point, baskets on each curve would provide equal satisfaction. However, one basket would contain more of both goods than another, contradicting the principle that consumers prefer more to less. Therefore, indifference curves must remain separate.

An indifference curve is convex or bowed inward toward the origin due to diminishing marginal rate of substitution. As a consumer accumulates more of one good, they become less willing to trade it for another good while maintaining satisfaction. This causes the curve's slope to decrease, creating the characteristic inward-bowing shape.

Monotonic preferences state that consumers always prefer more of both goods to less. This principle prevents indifference curves from crossing, since crossing would imply equal satisfaction between baskets where one clearly contains more of both goods. It ensures indifference curves maintain their distinct, non-intersecting positions on a preference map.

The marginal rate of substitution measures the rate at which a consumer trades one good for another while maintaining equal satisfaction. It diminishes because as consumers accumulate more of one good, they value additional units less and become less willing to give up the other good. This diminishing willingness creates the convex shape of indifference curves.

All points on the same indifference curve provide equal satisfaction to the consumer. For example, if baskets A and C lie on indifference curve IC1, John receives the same level of utility from both baskets despite their different combinations of goods X and Y. This equal satisfaction defines what it means to be on the same indifference curve.

The slope of an indifference curve decreases as the quantity of a good increases because of diminishing marginal rate of substitution. When a consumer has more of one good, they value additional units less and require fewer units of the other good to maintain satisfaction. This changing willingness to trade creates the curve's downward-sloping, convex shape.

If indifference curves could intersect, it would create a logical contradiction with consumer preferences. At the intersection point, both curves would assign equal satisfaction to the same basket. However, one curve would also pass through a basket with more of both goods, violating monotonic preferences. This impossibility proves indifference curves cannot cross.