Indifference curves and their properties

Meaning. An indifference curve joins all the bundles of two goods that give a consumer the same level of satisfaction, so that she does not mind which of them she has. It rests on ranking bundles, not on measuring utility in numbers. The set of such curves for one consumer is her indifference map.

Example (our own). Riya is equally happy with any of these monthly bundles of restaurant meals and cinema tickets; plotted and joined, they form one indifference curve.

Assumptions behind the curve. There are two goods; the consumer can rank bundles; her preferences are monotonic, meaning that of two bundles she prefers the one with more of at least one good and no less of the other; and the marginal utility of each good is positive.

Properties.

(i) It slopes downwards from left to right. Bundles on one curve give equal satisfaction. With monotonic preferences, a bundle with more meals gives equal satisfaction only if it has fewer tickets, so the two quantities move in opposite directions.

(ii) It is convex to the origin. The marginal rate of substitution (MRS), the amount of one good she will give up for one more unit of the other, is the absolute value of the curve's slope (the slope itself is negative, equal to minus the MRS). As meals become plentiful and tickets scarce she gives up less and less: 4, then 3, then 2 tickets in the table. This diminishing MRS bends the curve towards the origin.

(iii) Two curves never cross. Suppose two curves met at a point. Each bundle on the first would be as good as the common point, and so would each bundle on the second, making all of them equally good. Yet one curve has a bundle with more of a good than the other at the same quantity of the second good, so it must be better. The two conclusions conflict, so the curves cannot meet.

(iv) A higher curve means more satisfaction. A higher curve has bundles with more of at least one good and no less of the other, so with positive marginal utility, or monotonic preferences, it is preferred.

Exception. For perfect substitutes the MRS stays the same, so the curve is a straight line rather than convex.

Conclusion. An indifference curve shows equal-satisfaction bundles; it slopes down, is convex because the MRS diminishes, never crosses another curve, and stands for more satisfaction the further it lies from the origin.