Indifference curves and MRS

Ordinal utility analysis does not measure utility in numbers. It only ranks bundles of goods: this one is better than that one, or they are equally good.

An indifference curve joins all the bundles (say, of bananas and mangoes) that give the consumer equal satisfaction. She is indifferent between them. It slopes downward: to get more bananas and stay equally happy, she must give up some mangoes.

The marginal rate of substitution (MRS) is the number of mangoes she is willing to give up for one more banana, keeping her satisfaction the same: MRS = |ΔY ÷ ΔX|.

Example: bundles (1 banana, 20 mangoes), (2, 16), (3, 13), (4, 11) give equal satisfaction. MRS = 4, then 3, then 2. As she has more bananas, she is willing to give up fewer mangoes for each extra one: the MRS diminishes. That makes the indifference curve convex to the origin (bowed in).

For perfect substitutes, such as five-rupee notes and five-rupee coins, the consumer always swaps them one for one: the MRS is constant, and the indifference curve is a straight line.