3.8Behavior of the MRS

It is sometimes useful to describe the shapes of indifference curves by describing the behavior of the marginal rate of substitution. For example, the “perfect substitutes” indifference curves are characterized by the fact that the MRS is constant at $-1\text{.}$ The “neutrals” case is characterized by the fact that the MRS is everywhere infinite. The preferences for “perfect complements” are characterized by the fact that the MRS is either zero or infinity, and nothing in between.

We’ve already pointed out that the assumption of monotonicity implies that indifference curves must have a negative slope, so the MRS always involves reducing the consumption of one good in order to get more of another for monotonic preferences.

The case of convex indifference curves exhibits yet another kind of behavior for the MRS. For strictly convex indifference curves, the MRS—the slope of the indifference curve—decreases (in absolute value) as we increase $x_1$. Thus the indifference curves exhibit a diminishing marginal rate of substitution. This means that the amount of good 1 the person is willing to give up for an additional amount of good 2 increases as the amount of good 1 increases. Stated in this way, convexity of indifference curves seems very natural: it says that the more you have of one good, the more willing you are to give some of it up in exchange for the other good. (But remember the ice cream and olives example—for some pairs of goods this assumption might not hold!)