MRSxy between two combinations is the fall in Y divided by the rise in X, taken as a positive number.

$A\to B$: $\Delta Y=-4,\Delta X=1 \Rightarrow MRS=4$. $B\to C$: $\Delta Y=-3 \Rightarrow MRS=3$. $C\to D$: $\Delta Y=-2 \Rightarrow MRS=2$. $D\to E$: $\Delta Y=-1 \Rightarrow MRS=1$. MRS falls steadily (4, 3, 2, 1), confirmin …

The Marginal Rate of Substitution between two adjacent combinations on the same indifference curve is the amount of Y given up divided by the amount of X gained, taken as a positive value: $MRS_{xy}=-\dfrac{\Delta Y}{\Delta X}$.

The MRS falls steadily — 4, then 3, then 2, then 1 — as the consumer moves down the indifference curve acquiring more X. This is exactly what the Law of Diminishing Marginal Rate of Substitution predicts: as the consumer already holds more units of X, each additional unit of X becomes relatively less valuable to him compared with the Y he still holds, so he is willing to sacrifice progressively SMALLER amounts of Y to obtain one more unit of X. This is …

A common error is inverting the ratio and computing ΔX/ΔY instead of −ΔY/ΔX — MRSxy specifically measures how much Y is sacrificed per additional unit of X gained, not the reverse. Students also sometimes carry through a negative sign into the final answer, whereas MRS is conventionally …